Customized Material for Econ 351 –Fall 2015 Chuderewicz

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Chapter 1: Financial Markets: Part 1

To truly understand financial markets and ‘talk the talk,’ you will be required to understand a plethora of jargon. Remember, I am here to answer all your questions, so don’t be shy. The last thing we need is for you to not to understand something because of jargon. Before getting started, it would be helpful to think of financial markets as a giant poker game where it is ‘dealer’s choice’ and you are the dealer. There are many different poker games out there and when you start playing, everybody has an equal chance of winning, that is, it is a fair game. Financial markets are similar in that there are many bets one can make and everyone has the same chance as winning (making a capital gain) and losing (suffer a capital loss). Another way to state this is that there is no free money to be made in financial markets and we will get much deeper into this phenomenon a little later in the course.1

Glass half full or empty (Bulls vs. Bears).

As mentioned above, there are many bets you can make in the financial markets.2 Before deciding on what particular bet to make, you essentially need to decide if you are optimistic (Bullish) or pessimistic (Bearish) as it pertains to the ‘chosen’ asset’s price. Bulls make money when prices rise and lose when prices fall. Conversely, bears make money when prices fall and lose money when prices rise. After you establish whether your are bullish or bearish, you can chose any of the ‘games’ or ‘bets’ that follow, always remembering, a) there is no free money out there and 2) different bets have varying amounts of risked attached to them.

Stocks: Long vs. Short

A US Common stock represents partial equity in the company whose name it bears. Going long, that is, buying and holding shares of stock is probably the simplest (and most familiar) investment one could make. The idea is to buy (relatively) low and sell high, reaping what is referred to as a capital gain. Mutual funds are primarily comprised of long positions in common stock. In taking a long position, the investor is betting (hoping) that the stock price (or stock market index) will rise.

1 For those of you familiar with finance, this concept is known as the efficient market theory.2 When state the word financial markets, we are typically referring to three very large markets:1) the Bond market; 2) the Stock (equity) market, and 3) the Foreign Exchange market.

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Example: Use the space below: Taking a long position (buying 10 shares) in IBM stock:

In contrast to going long, an investor can go “short” on a stock and therefore benefit if the relevant stock price falls (A bearish position). Shorting a stock involves borrowing shares from a creditor (e.g., JP Morgan) and selling them immediately. The key to understanding how shorting stocks works is to recognize that your debt is in stocks and not cash. For example, if I short one hundred shares of IBM stock, I borrow 100 shares of stock from a creditor and it is 100 shares of stock that I owe my creditor (excluding transactions fees)3. The idea is that once the price has fallen, I can buy the (borrowed) shares back for less money than I received when I sold them. Thus, if the stock does fall you pocket the difference. If the stock price rises instead and stays relatively high, then you will (eventually) be forced to buy the stock back at a higher price than you sold it for and will thus suffer a capital loss.

Example: Use the space below: Shorting IBM stock (shorting 10 shares):

In one sense, shorting a stock is more risky than going long because it exposes the investor to the possibility of larger losses. For example, if I short shares of a small biotech company which then announces a drug approval by the FDA tripling its share price, I will lose 200% overnight.4 Conversely, the worst-case scenario with long investments is a loss of 100%, such as occurred when Enron announced accounting scandals and its stock price went to zero.

3 Throughout this course, we will typically ‘assume away’ transactions costs in our numerical calculations and analyses. 4 For example, If I short 100 shares when the price is $10 and the price subsequently rises (triples) to $30, it would cost me $3000 (buying 100 shares at $30 and returning them to my creditor) to close my position. The initial value of my ‘investment’ was $1000 (100 shares times $10) so the loss is 200% (($1000 - $3000)/$1000) x 100. You will be required to calculate rates of return throughout this course.

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Long vs. Short positions on Bonds

Throughout the semester, we will constantly exploit the inverse relationship between the price of bonds and the yield or interest rate on bonds.

Do the “Chud Bond” Example in the space below emphasizing this inverse relationship between the price of bonds and the interest rate on bonds (an Asian financial crisis example).

You would take a long position on bonds if you expect prices to go up, same reasoning as in stocks (above). Saying the same thing a little differently, you would take a long position on bonds if you expect lower interest rates in the future. As we will see throughout the semester, expected Federal Reserve policy (i.e., what the Fed may or may not do in the future) plays a critical role in the determination of bond prices and thus interest rates. Investors are constantly looking for clues that will aid them in this regard and naturally, the continuous stream of incoming economic data is scrutinized for possible clues. For example, if the CPI (consumer price index) report came out and suggested major inflationary pressures that were not expected prior to the report, then investors would immediately expect the Fed to be more hawkish in the future, and thus, interest rates would be expected to be higher in the future.5 Exploiting the inverse relationship between bond prices and interest rates, the previous statement can be stated as “due to the CPI report, investors expect lower bond prices in the future and thus, investors who currently have a short position in bonds will be the winners while those investors who have a long position will be the losers. We will be evaluating the impact of NEWS on the asset markets throughout the semester with NEWS being defined as the “unexpected!” For example, if the consumer price index is expected to rise by .2% and the actual number is .2%, then there is no NEWS since expectations were exactly correct. Naturally, expectations are usually not correct so NEWS is virtually an everyday experience.

Long vs. Short positions on Foreign Exchange

If you go long on the dollar, that means you are hoping the dollar gets stronger relative to the currency that you chose or a basket of currencies as in a dollar index. For example, if I go long on the dollar relative to the Euro, then I will profit if the dollar get stronger relative to

5 Hawkish refers to the Fed aggressively fighting inflation by raising interest rates to slow down aggregate demand. The opposite of hawkish is dovish and refers to the Fed being soft on inflation. An inflation dove typically worries more about employment and economic growth and less about inflation; the opposite can be said about an inflation hawk. These terms will be used throughout the semester, especially when we consider the Fed’s loss function and the Taylor rule.

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the Euro and lose money if the dollar weakens relative to the Euro. If you think the dollar is going to weaken, then you should take a short position on the dollar.

Example: In the space below, do an example of taking a long position on the euro vs. the US dollar.

The currency market is probably the hardest to predict of the three asset markets and we will keep an ‘eye’ on the currency markets throughout the semester.

Exercise

1. a) Suppose you bought (took a long position) 10 shares of IBM stock at a (previous) spot price of $100 and the current IBM spot price is $95. If you closed your position, how much money would you make/lose (assume away all transactions costs)? Show all work.

b) Suppose alternatively that you took a short position by shorting 10 shares of IBM (assume same price change as in 1. a) above. How much money would you make/lose if you closed your position (cover your short)? Explain in detail and show all work.

c) Given either position, what would determine whether or not you would close your position? Again, explain in detail.

Options

Options are contracts giving the owner the right to buy (call option) or the right to sell (put option) shares of stock at a predetermined (strike) price. One call option typically gives the owner the right to buy 100 shares of the underlying security for the strike price stated on the contract. Buying calls is considered bullish because you profit when the underlying stock price rises. A call option is “in the money” when the strike price is below the (current) spot price. In such a case, the price at which you can buy the stock, i.e., the strike price, is less than the price that you can sell the stock, the spot price, so exercising the option would be profitable.

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A put option is the exact opposite (and is thus bearish) and gives the owner the right to sell the underlying security at the strike price. Put options are in the money when the spot price is below the strike price. In this case, the owner could exercise the put by buying the stock at the relatively low spot price and selling the stock at the strike price, since this is exactly what a put option allows you to do.

Option prices are quoted in premium-per-share. The premium is the price you pay for the option contract. Recall that an option contract allows you to buy or sell a specified quantity of an asset during a specified time period (i.e., they expire). To find the actual cost of an option (excluding fees and other possible transactions costs), multiply the quoted premium by 100. We will discuss the specific factors that determine option premiums during class. We will also understand why options are typically not exercised, they are bought and sold much like shares of stock or bonds. The example problem on options that follows will help us understand this entire paragraph.

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Practice option problems

1. Previous HW assignment from Spring 2006

(15 points total) Use the following 3 tables to answer the questions that follow. In this example, you are bearish on Best Buy (BBY). We are going to examine and compare two bearish bets. We assume away all transactions costs and as always, use the ‘last sale’ column, i.e., the premium for your calculations.

TABLE 1BBY 46.20 -4.16

Sep 13, 2005 @ 10:29 ET (Data 20 Minutes Delayed)

Bid N/A Ask N/A Size N/AxN/A Vol 8587300

Calls Last Sale Net Bid Ask Vol Open

Int Puts Last Sale Net Bid Ask Vol Open

Int

05 Sep 43.375 (BXJ IU-E) 4.40 pc 2.80 2.95 0 3119 05 Sep 43.375 (BXJ UU-E) 0.10 pc 0.10 0.15 0 9902

05 Sep 45.00 (BBY II-E) 1.55 -3.65 1.40 1.55 86 826 05 Sep 45.00 (BBY UI-E) 0.35 +0.15 0.30 0.40 761 9084

05 Sep 46.625 (BXJ IV-E) 0.55 -3.65 0.45 0.50 83 5966 05 Sep 46.625 (BXJ UV-E) 0.85 +0.45 0.90 1.00 81 5637

05 Sep 47.50 (BBY IW-E) 0.25 -3.15 0.15 0.25 266 6145 05 Sep 47.50 (BBY UW-E) 1.50 +0.95 1.50 1.60 441 5594

05 Oct 42.50 (BBY JV-E) 6.90 pc 4.30 4.50 0 27 05 Oct 42.50 (BBY VV-E) 0.60 +0.20 0.60 0.70 14 1311

05 Oct 45.00 (BBY JI-E) 2.80 -1.60 2.50 2.60 40 813 05 Oct 45.00 (BBY VI-E) 1.25 +0.45 1.30 1.40 216 1834

05 Oct 47.50 (BBY JW-E) 1.25 -2.95 1.20 1.30 205 1382 05 Oct 47.50 (BBY VW-E) 2.50 +1.20 2.45 2.60 65 4461

05 Oct 50.00 (BBY JJ-E) 0.50 -2.05 0.50 0.55 109 8526 05 Oct 50.00 (BBY VJ-E) 4.10 +1.95 4.20 4.40 42 1127

TABLE 2

BBY 45.29 -5.07Sep 13, 2005 @ 15:11 ET (Data 20 Minutes Delayed)

Bid N/A Ask N/A Size N/AxN/A Vol 24252700

Calls Last Sale Net Bid Ask Vol Open

Int Puts Last Sale Net Bid Ask Vol Open

Int

05 Sep 43.375 (BXJ IU-E) 2.10 -2.30 2.00 2.10 376 3119 05 Sep 43.375 (BXJ UU-E) 0.15 +0.05 0.10 0.20 765 9902

05 Sep 45.00 (BBY II-E) 0.85 -4.35 0.75 0.85 955 826 05 Sep 45.00 (BBY UI-E) 0.50 +0.30 0.45 0.50 1388 9084

05 Sep 46.625 (BXJ IV-E) 0.20 -4.00 0.15 0.20 267 5966 05 Sep 46.625 (BXJ UV-E) 1.35 +0.95 1.45 1.55 247 5637

05 Sep 47.50 (BBY IW-E) 0.10 -3.30 0.05 0.10 275 6145 05 Sep 47.50 (BBY UW-E) 2.10 +1.55 2.20 2.30 678 5594

05 Oct 42.50 (BBY JV-E) 3.50 -3.40 3.60 3.80 5 27 05 Oct 42.50 (BBY VV-E) 0.75 +0.35 0.75 0.85 103 1311

05 Oct 45.00 (BBY JI-E) 2.00 -2.40 1.95 2.05 326 813 05 Oct 45.00 (BBY VI-E) 1.65 +0.85 1.65 1.70 383 1834

05 Oct 47.50 (BBY JW-E) 0.95 -3.25 0.90 0.95 1021 1382 05 Oct 47.50 (BBY VW-E) 2.90 +1.60 3.00 3.10 148 4461

05 Oct 50.00 (BBY JJ-E) 0.35 -2.20 0.35 0.40 458 8526 05 Oct 50.00 (BBY VJ-E) 4.70 +2.55 4.90 5.10 185 1127

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TABLE 3

BBY 43.53 +0.49Oct 01, 2005 @ 07:22 ET (Data 20 Minutes Delayed)

Bid N/A Ask N/A Size N/AxN/A Vol 3075600

Calls Last Sale Net Bid Ask Vol Open

Int Puts Last Sale Net Bid Ask Vol Open

Int

05 Oct 40.00 (BBY JH-E) 4.10 +1.35 3.70 3.90 105 1004 05 Oct 40.00 (BBY VH-E) 0.30 pc 0.15 0.25 0 7023

05 Oct 42.50 (BBY JV-E) 1.65 +0.50 1.75 1.85 8 6866 05 Oct 42.50 (BBY VV-E) 0.60 -0.65 0.60 0.70 128 8718

05 Oct 45.00 (BBY JI-E) 0.70 +0.40 0.50 0.60 313 7907 05 Oct 45.00 (BBY VI-E) 1.85 -0.75 1.85 1.95 22 4167

05 Oct 47.50 (BBY JW-E) 0.15 -- 0.10 0.15 303 5847 05 Oct 47.50 (BBY VW-E) 3.50 -1.00 3.90 4.10 26 4036

05 Nov 40.00 (BBY KH-E) 4.00 pc 4.30 4.50 0 3579 05 Nov 40.00 (BBY WH-E) 0.55 -0.45 0.60 0.70 10 875

05 Nov 42.50 (BBY KV-E) 2.80 +0.80 2.55 2.65 45 4400 05 Nov 42.50 (BBY WV-E) 1.25 -0.40 1.30 1.40 65 685

05 Nov 45.00 (BBY KI-E) 1.45 +0.30 1.25 1.40 25 3203 05 Nov 45.00 (BBY WI-E) 2.30 -0.65 2.50 2.60 64 330

05 Nov 47.50 (BBY KW-E) 0.60 +0.15 0.50 0.60 8 1059 05 Nov 47.50 (BBY WW-E) 4.20 -0.90 4.20 4.40 28 11

It is Sept 13 at 10:29 am (TABLE 1). You are thinking that Best Buy is going down due to hurricane related stuff including high oil prices. You have $2,500 to play the game and you are going to spend it all on BBY put options. You are looking at Oct 45 puts and Oct 47.50 puts.

a) (2 points) Why the difference in the premiums on these two options (use Table 1)? Be specific.

b) (2 points) Suppose you decided to use the entire $2,500 to purchase the Oct 45 puts. How many put options could you buy and what would they collectively, give you the right to do (we are still using Table 1)?

c) (3 points) It is now October 1 (Table 3) and you decided to sell your Oct 45 puts. What is your profit/loss? What is your rate of return? Please show all your calculations.

d) (2 points) Instead of purchasing the Oct 45 puts you decide to use all $2,500 to purchase the October 47.50 puts (again, on Sept 13 at 10:29 am – Table 1). How many Oct 47.50 puts could you buy and what would they, collectively, give you the right to do?

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e) (2 points) It is now October 1 (Table 3) and you decided to sell your October 47.50 puts. What is your profit/loss and your rate of return? Please show all your calculations.

f) (2 points) Given that your profit / loss is different depending on your choice of puts, which selection of put options gave you a higher return (i.e., compare part c) with part e))?

g) (2 points) Now consider Table 2. Since hindsight is 20 / 20, would it have been better in terms of profits and/or returns if you would have sold your options later on September 13 (Table 2) rather than waiting until 10/1 (Table 3)? Why or why not, explain.

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Practice Option Problem number 2.You are to use the tables below to answer all of the following questions. We assume away all transactions costs. 70 points possible. Best of luck!

1. The following 3 tables are successive through time – you are to answer a series of questions. GOOG TABLE 1 296.39 +1.52

Sep 08, 2005 @ 15:17 ET (Data 15 Minutes Delayed)

Bid 296.35 Ask 296.39 Size 1x2 Vol 5837641

Calls Last Sale Net Bid Ask Vol Open

Int Puts Last Sale Net Bid Ask Vol Open

Int

05 Sep 290.0 (GGD IR-E) 8.60 +1.10 8.60 8.90 744 12295 05 Sep 290.0 (GGD UR-E) 2.20 -0.70 2.10 2.20 2004 12374

05 Sep 300.0 (GGD IT-E) 3.30 +0.50 3.20 3.40 2123 24808 05 Sep 300.0 (GGD UT-E) 6.40 -1.60 6.50 6.80 858 6365

05 Sep 310.0 (GGD IB-E) 1.00 +0.15 0.85 1.00 859 15879 05 Sep 310.0 (GGD UB-E) 14.10 -1.80 14.20 14.50 80 2577

05 Oct 280.0 (GGD JP-E) 24.20 +1.40 23.40 23.80 34 1929 05 Oct 280.0 (GGD VP-E) 5.50 -1.00 5.90 6.20 43 2377

05 Oct 290.0 (GGD JR-E) 17.20 +0.70 17.20 17.50 226 2759 05 Oct 290.0 (GGD VR-E) 9.70 -0.90 9.50 9.80 97 1778

05 Oct 300.0 (GGD JT-E) 12.00 +0.40 12.00 12.20 137 4171 05 Oct 300.0 (GGD VT-E) 13.60 -2.20 14.40 14.80 54 547

05 Oct 310.0 (GGD JB-E) 8.90 +0.90 8.20 8.50 249 3881 05 Oct 310.0 (GGD VB-E) 19.60 -5.50 20.60 20.90 5 424

GOOG TABLE 2 309.74 pcSep 13, 2005 @ 06:49 ET (Data 15 Minutes Delayed)

Bid 309.59 Ask 309.70 Size 0x0 Vol 0

Calls Last Sale Net Bid Ask Vol Open

Int Puts Last Sale Net Bid Ask Vol Open

Int

05 Sep 290.0 (GGD IR-E) 20.10 pc 0 0 0 9147 05 Sep 290.0 (GGD UR-E) 0.25 pc 0 0 0 17717

05 Sep 300.0 (GGD IT-E) 10.70 pc 0 0 0 22848 05 Sep 300.0 (GGD UT-E) 0.85 pc 0 0 0 14542

05 Sep 310.0 (GGD IB-E) 3.70 pc 0 0 0 17881 05 Sep 310.0 (GGD UB-E) 4.00 pc 0 0 0 6101

05 Sep 320.0 (GGD ID-E) 0.85 pc 0 0 0 18552 05 Sep 320.0 (GGD UD-E) 10.70 pc 0 0 0 2475

05 Oct 290.0 (GGD JR-E) 26.60 pc 0 0 0 2721 05 Oct 290.0 (GGD VR-E) 5.70 pc 0 0 0 2725

05 Oct 300.0 (GGD JT-E) 20.10 pc 0 0 0 5218 05 Oct 300.0 (GGD VT-E) 9.30 pc 0 0 0 1842

05 Oct 310.0 (GGD JB-E) 14.90 pc 0 0 0 4129 05 Oct 310.0 (GGD VB-E) 13.90 pc 0 0 0 940

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GOOG TABLE 3 303.00 pcSep 15, 2005 @ 06:46 ET (Data 15 Minutes Delayed) Bid 302.41 Ask 299.00 Size 0x6 Vol 0

Calls Last Sale Net Bid Ask Vol Open

Int Puts Last Sale Net Bid Ask Vol Open

Int

05 Sep 290.0 (GGD IR-E) 13.10 pc 0 0 0 7815 05 Sep 290.0 (GGD UR-E) 0.45 pc 0 0 0 19160

05 Sep 300.0 (GGD IT-E) 4.50 pc 0 0 0 21832 05 Sep 300.0 (GGD UT-E) 2.00 pc 0 0 0 20916

05 Sep 310.0 (GGD IB-E) 1.00 pc 0 0 0 23934 05 Sep 310.0 (GGD UB-E) 8.10 pc 0 0 0 8253

05 Sep 320.0 (GGD ID-E) 0.30 pc 0 0 0 18131 05 Sep 320.0 (GGD UD-E) 18.90 pc 0 0 0 3156

05 Oct 290.0 (GGD JR-E) 20.90 pc 0 0 0 2720 05 Oct 290.0 (GGD VR-E) 7.60 pc 0 0 0 2875

05 Oct 300.0 (GGD JT-E) 14.70 pc 0 0 0 6046 05 Oct 300.0 (GGD VT-E) 11.80 pc 0 0 0 2581

05 Oct 310.0 (GGD JB-E) 10.40 pc 0 0 0 7885 05 Oct 310.0 (GGD VB-E) 17.50 pc 0 0 0 1490

05 Oct 320.0 (GGD JD-E) 7.20 pc 0 0 0 5180 05 Oct 320.0 (GGD VD-E) 24.70 pc 0 0 0 380

1. a) You are bullish on Google and therefore you purchase 10 Sept 300 calls on 9/8 (see Table 1). Answer the following questions (refer only to Table 1).

i) (5 points) Is the Sept 300 call in or out of the money? Explain

ii) (5 points) Why is the premium on the Sept 300 put so much higher than the premium on the Sept 300 call? Explain.

iii) (5 points) Why is the premium so different for the Sept 300 call relative to the Oct 300 call? Explain.

iv) (5 points) Provide an argument as to why the Sept 300 call is so “pricy.”

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b) It is now September 13 and you are trying to decide whether or not to close your position. You have two choices: a) simply sell your 10 calls or b) exercise your call options. In the space below, you are to do the math and figure out which is better, selling your calls or exercising them.

b i) (5 points) In the space below, show your calculation of your loss or profit, whichever applies, if you sold your options on 9/13 (Table 2). What is your rate of return? Show all work.

b ii) (5 points) In the space below, show your calculation of your loss or profit, whichever applies, if you exercised your options on 9/13 (Table 2). What is your rate of return? Show all work.

c) Lets say it’s September 13 and you are still bullish on Google and you decide to hold the calls hoping for more price increases. So you wait and close your position on September 15 (see Table 3 ). In the space below, recalculate your profits or losses if you

i) sold your options or ii) exercised your options.

ci) (5 points) Show work – profit/ loss; rate of return, selling options on 9/15

cii) (5 points) Show work – profit/loss: rate of return, exercising options of 9/15

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ciii) Explain why it is always better to sell your options as compared to exercising your options. Include in your answer the special case: What should you do at expiration – sell or exercise?

ciii) (5 points) Was it better to hold onto Google until 9/15 or was it better to close your position on 9/13? Explain.

2) (25 points for completely labeled graph – 5 points off for each blemish!) Graphically illustrate the profit/loss function of the Sept 300 calls that you purchased on 9/8 (Table 1), clearly labeling the out of the money spot, at the money spot, in the money spot, and the break even point (this is all relative to the 9/8 Sept 300 calls (10 of them!)). Label the horizontal line in your graph as spot at expiration. For your diagram, use a price range of 295 – 310 and be sure to label, on the vertical axis, the profit loss associated with the three prices of your 10 Google calls in Tables 1 through 3 respectively. Note importantly that we are assuming three distinct scenarios:

Scenario 1): the spot price of Google stays the same as in Table 1 and your option expires. Locate this point on your diagram as point A, clear labeling the profit or loss associated with this scenario.

Scenario 2): the spot price of Google rises to the price associated with Table 2 and expires that way and you exercise your option. Locate the specific profit or loss on your diagram and label as point B.

Scenario 3): the spot price of Google rises to the price associated with Table 3 and expires that way and you exercise your option. Locate the specific profit or loss on your diagram and label as point C.

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Practice option problem 3

Use the following 3 tables to answer the questions that follow. In this example, you are bearish on Apple Computer (AAPL). We are going to examine and compare two different bets. We assume away all transactions costs and as always, use the ‘last sale’ column for your calculations.

TABLE 1

AAPL 75.51 +0.51Jan 31, 2006 @ 16:38 ET (Data 15 Minutes Delayed)

Bid 74.90 Ask 74.97 Size 34x2 Vol 32327436

Calls Last Sale Net Bid Ask Vol Open

Int Puts Last Sale Net Bid Ask Vol Open

Int

06 Feb 72.50 (QAA BE-E) 4.60 -- 4.30 4.50 895 13485 06 Feb 72.50 (QAA NE-E) 1.45 -0.20 1.35 1.50 466 14288

06 Feb 75.00 (QAA BO-E) 3.00 -- 2.90 3.10 3146 27144 06 Feb 75.00 (QAA NO-E) 2.40 -0.30 2.35 2.50 1275 30241

06 Feb 80.00 (QAA BP-E) 1.20 -0.05 1.10 1.20 4163 49502 06 Feb 80.00 (QAA NP-E) 5.70 -0.10 5.50 5.70 738 18150

06 Feb 85.00 (QAA BQ-E) 0.40 -0.05 0.35 0.45 1091 49601 06 Feb 85.00 (QAA NQ-E) 10.00 -0.20 9.80 10.00 94 14888

06 Mar 72.50 (QAA CE-E) 6.20 +0.10 6.10 6.30 74 1138 06 Mar 72.50 (QAA OE-E) 2.80 -0.40 2.80 3.00 16 700

06 Mar 75.00 (QAA CO-E) 4.80 -0.10 4.80 5.00 716 4479 06 Mar 75.00 (QAA OO-E) 3.80 -0.60 3.90 4.10 280 3128

06 Mar 80.00 (QAA CP-E) 2.75 -0.05 2.70 2.85 1087 16204 06 Mar 80.00 (QAA OP-E) 6.90 -0.20 6.90 7.10 163 1964

06 Mar 85.00 (QAA CQ-E) 1.50 -0.10 1.50 1.60 252 3894 06 Mar 85.00 (QAA OQ-E) 11.30 +0.80 10.60 10.90 10 919

TABLE 2AAPL 71.36 -0.74Feb 03, 2006 @ 15:32 ET (Data 15 Minutes Delayed) Bid 71.35 Ask 71.37 Size 47x5 Vol 19806338

Calls Last Sale Net Bid Ask Vol Open

Int Puts Last Sale Net Bid Ask Vol Open

Int

06 Feb 67.50 (QAA BU-E) 5.10 -0.60 4.80 4.90 206 3456 06 Feb 67.50 (QAA NU-E) 0.85 +0.05 0.80 0.90 742 39675

06 Feb 70.00 (QAA BN-E) 3.30 -0.50 3.10 3.20 1163 11894 06 Feb 70.00 (QAA NN-E) 1.60 +0.10 1.65 1.75 768 23609

06 Feb 72.50 (QAA BE-E) 2.00 -0.45 1.90 2.00 843 15765 06 Feb 72.50 (QAA NE-E) 2.80 +0.15 2.90 3.00 651 16602

06 Feb 75.00 (QAA BO-E) 1.15 -0.35 1.10 1.15 1033 32388 06 Feb 75.00 (QAA NO-E) 4.60 +0.40 4.60 4.70 436 34314

06 Mar 67.50 (QAA CU-E) 7.00 -0.80 6.40 6.60 11 798 06 Mar 67.50 (QAA OU-E) 2.20 +0.25 2.20 2.30 350 1996

06 Mar 70.00 (QAA CN-E) 5.10 -0.50 5.00 5.10 97 2096 06 Mar 70.00 (QAA ON-E) 3.20 +0.30 3.20 3.30 93 8848

06 Mar 72.50 (QAA CE-E) 3.80 -0.40 3.70 3.90 129 1991 06 Mar 72.50 (QAA OE-E) 4.20 +0.10 4.50 4.60 166 2219

06 Mar 75.00 (QAA CO-E) 2.85 -0.35 2.80 2.85 310 8087 06 Mar 75.00 (QAA OO-E) 6.00 +0.30 6.00 6.10 89 5660

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TABLE 3

AAPL 69.22 +1.57Feb 15, 2006 @ 16:17 ET (Data 15 Minutes Delayed) Bid 69.18 Ask 69.22 Size 2x25 Vol 40718818

Calls Last Sale Net Bid Ask Vol Open

Int Puts Last Sale Net Bid Ask Vol Open

Int

06 Feb 65.00 (QAA BM-E) 4.30 +1.20 4.20 4.30 1873 13596 06 Feb 65.00 (QAA NM-E) 0.15 -0.25 0.10 0.15 5011 34562

06 Feb 67.50 (QAA BU-E) 2.05 +0.65 2.10 2.15 5459 25351 06 Feb 67.50 (QAA NU-E) 0.45 -0.65 0.40 0.45 10352 42251

06 Feb 70.00 (QAA BN-E) 0.70 +0.30 0.65 0.70 7838 29640 06 Feb 70.00 (QAA NN-E) 1.50 -1.20 1.40 1.55 2498 17742

06 Feb 72.50 (QAA BE-E) 0.15 +0.05 0.10 0.20 1546 23198 06 Feb 72.50 (QAA NE-E) 3.50 -1.40 3.30 3.50 234 13429

06 Feb 75.00 (QAA BO-E) 0.05 -- 0 0.05 356 35263 06 Feb 75.00 (QAA NO-E) 5.85 -1.45 5.70 5.90 294 23214

06 Mar 67.50 (QAA CU-E) 4.60 +0.80 4.70 4.80 977 5612 06 Mar 67.50 (QAA OU-E) 2.80 -0.40 2.70 2.80 1029 8128

06 Mar 70.00 (QAA CN-E) 3.40 +0.90 3.30 3.40 2821 16025 06 Mar 70.00 (QAA ON-E) 4.00 -0.60 3.80 4.00 1162 10597

06 Mar 72.50 (QAA CE-E) 2.30 +0.60 2.25 2.35 1214 9206 06 Mar 72.50 (QAA OE-E) 5.35 -0.85 5.30 5.50 91 3752

You are in a bearish mood and you are contemplating two different 06 Feb Puts: the 72.50 and the 75.00. Suppose you have $4800 to invest.

a.) (2 points) Why the difference in the premiums on these two options (use Table 1)? Be specific.

b) (3 points) Suppose you decided to use your entire $4,800 to purchase the Feb 72.50 puts. How many put options could you buy (round down to nearest whole number) and what would they collectively, give you the right to do (we are still using Table 1)?

c) (4 points) It is now February 03 (Table 2) and you decided to sell your Feb 72.50 puts. What is your profit/loss? What is your rate of return? Please show all your calculations.

d) (3 points) Instead of purchasing the Feb 72.50 puts you decide to use all $4,800 to purchase the Feb 75.00 puts (again, on January 31– Table 1). How many Feb 75.00 puts could you buy and what would they, collectively, give you the right to do?

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e) (4 points) It is now February 03 (Table 2) and you decided to sell your February 75.00 puts. What is your profit/loss and your rate of return? Please show all your calculations.

f) (2 points) Given that your profit / loss is different depending on your choice of puts, which selection of put options gave you a higher return (i.e., compare part c) with part e))?

g) ( 4 points) For this part of question, assume you that you originally decided to spend the $4800 on the 06 Feb 75.00 puts (Table 1) and it is now Feb 3 (Table 2). You are going on a holiday and you contemplating closing your position (choice = Close) or holding your position until Feb 13 as in Table 3 (choice=Hold). Given perfect foresight, which choice yields the highest return and why?. Show all work!

h) (3 points) Referring to Table 3 which is after the closing bell on 2/15. Would it have been better to sell your puts before the market opened or after the market closed? Explain

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2) (25 points for completely labeled graph – 5 points off for each blemish!)As we did in class, graphically illustrate the profit/loss function of the Feb 75 puts that you purchased on Jan. 31 (Table 1), clearly labeling the out of the money spot, at the money spot, in the money spot, and the break even point (this is all relative to the Feb 75 puts). Label the horizontal line in your graph as spot at expiration. For your diagram, use a price range of 65 - 80 and be sure to label, on the vertical axis, the profit loss associated with the three prices of your Apple puts in Tables 1 through 3 respectively. Note importantly that we are assuming three distinct scenarios:

Scenario 1): the spot price of Apple (AAPL) stays the same as in Table 1 and your option expires. Locate this point on your diagram as point A, clear labeling the profit or loss associated with this scenario.

Scenario 2): the spot price of Apple (AAPL) falls to the price associated with Table 2 and expires that way and you exercise your option. Locate the specific profit or loss on your diagram and label as point B.

Scenario 3): the spot price of Apple (AAPL) falls to the price associated with Table 3 and expires that way and you exercise your option. Locate the specific profit or loss on your diagram and label as point C.

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Practice option problem 4Using the following tables to answer the following questions.TABLE 1

C (CITIGROUP INC) 14.35 -0.89Sep 16, 2008 @ 10:14 ET

Bid 14.35 Ask 14.36 Size 13x40 Vol 33660766

Calls Last Sale Net Bid Ask Vol Open

Int Puts Last Sale Net Bid Ask Vol Open

Int

08 Sep 10.00 (C IB-E) 4.65 -0.80 4.55 4.65 50 1001 08 Sep 10.00 (C UB-E) 0.17 +0.07 0.17 0.18 1557 71497

08 Sep 12.50 (C IZ-E) 2.48 -0.82 2.41 2.49 614 2857 08 Sep 12.50 (C UZ-E) 0.52 +0.26 0.51 0.53 1845 59865

08 Sep 15.00 (C IC-E) 0.80 -0.45 0.76 0.82 962 12146 08 Sep 15.00 (C UC-E) 1.35 +0.61 1.35 1.40 6940 157380

08 Sep 17.50 (C IR-E) 0.14 -0.12 0.14 0.16 1011 57962 08 Sep 17.50 (C UR-E) 3.25 +1.05 3.20 3.25 778 123636

08 Oct 10.00 (C JB-E) 6.35 0.0 5.45 5.60 0 1284 08 Oct 10.00 (C VB-E) 1.11 +0.41 1.06 1.14 4031 26075

08 Oct 12.50 (C JZ-E) 3.70 -0.50 3.60 3.75 2 458 08 Oct 12.50 (C VZ-E) 1.65 +0.49 1.70 1.77 1297 33174

08 Oct 15.00 (C JC-E) 2.12 -0.38 2.17 2.26 234 3398 08 Oct 15.00 (C VC-E) 2.75 +0.75 2.73 2.79 1819 45733

08 Oct 17.50 (C JR-E) 1.17 -0.13 1.16 1.19 599 17400 08 Oct 17.50 (C VR-E) 4.25 +1.00 4.20 4.30 309 49083

TABLE 2

C (CITIGROUP INC) 15.66 +0.42Sep 16, 2008 @ 12:32 ET

Bid 15.63 Ask 15.64 Size 15x114 Vol 130134024

Calls Last Sale Net Bid Ask Vol Open

Int Puts Last Sale Net Bid Ask Vol Open

Int

08 Sep 12.50 (C IZ-E) 2.87 -0.43 3.30 3.40 1077 2857 08 Sep 12.50 (C UZ-E) 0.28 +0.02 0.26 0.29 6678 59865

08 Sep 15.00 (C IC-E) 1.35 +0.10 1.28 1.34 4846 12146 08 Sep 15.00 (C UC-E) 0.74 0.0 0.71 0.76 21944 157380

08 Sep 17.50 (C IR-E) 0.23 -0.03 0.22 0.24 7117 57962 08 Sep 17.50 (C UR-E) 2.40 +0.20 2.15 2.20 4726 123636

08 Sep 20.00 (C ID-E) 0.04 -0.01 0.02 0.05 1090 154008 08 Sep 20.00 (C UD-E) 4.35 -0.20 4.40 4.50 969 100991

08 Oct 12.50 (C JZ-E) 4.60 +0.40 4.25 4.35 36 458 08 Oct 12.50 (C VZ-E) 1.22 +0.06 1.20 1.24 3607 33174

08 Oct 15.00 (C JC-E) 2.59 +0.09 2.60 2.63 967 3398 08 Oct 15.00 (C VC-E) 2.02 +0.02 2.02 2.07 3778 45733

08 Oct 17.50 (C JR-E) 1.40 +0.10 1.38 1.41 5404 17400 08 Oct 17.50 (C VR-E) 3.15 -0.10 3.25 3.35 1251 49083

08 Oct 20.00 (C JD-E) 0.65 +0.06 0.62 0.66 1896 34540 08 Oct 20.00 (C VD-E) 4.90 -0.10 5.00 5.10 127 31671

TABLE 3

C (CITIGROUP INC) 15.75 +0.51Sep 16, 2008 @ 21:01 ET

Bid 16.25 Ask 16.29 Size 77x7 Vol 257367449

Calls Last Sale Net Bid Ask Vol Open

Int Puts Last Sale Net Bid Ask Vol Open

Int

08 Sep 12.50 (C IZ-E) 3.50 +0.20 3.40 3.55 1097 2857 08 Sep 12.50 (C UZ-E) 0.09 -0.17 0.07 0.09 7447 59865

08 Sep 15.00 (C IC-E) 1.30 +0.05 1.21 1.30 8682 12146 08 Sep 15.00 (C UC-E) 0.38 -0.36 0.33 0.39 34248 157380

08 Sep 17.50 (C IR-E) 0.21 -0.05 0.15 0.20 11971 57962 08 Sep 17.50 (C UR-E) 1.76 -0.44 1.73 1.84 7207 123636

08 Sep 20.00 (C ID-E) 0.03 -0.02 0.03 0.05 3398 154008 08 Sep 20.00 (C UD-E) 4.02 -0.53 4.05 4.25 1293 100991

08 Oct 12.50 (C JZ-E) 4.50 +0.30 4.35 4.50 69 458 08 Oct 12.50 (C VZ-E) 1.07 -0.09 1.01 1.07 5341 33174

08 Oct 15.00 (C JC-E) 2.69 +0.19 2.65 2.72 2446 3398 08 Oct 15.00 (C VC-E) 1.76 -0.24 1.74 1.80 5641 45733

08 Oct 17.50 (C JR-E) 1.41 +0.11 1.34 1.41 7346 17400 08 Oct 17.50 (C VR-E) 3.00 -0.25 2.93 3.00 2321 49083

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08 Oct 20.00 (C JD-E) 0.58 -0.01 0.57 0.62 2747 34540 08 Oct 20.00 (C VD-E) 4.80 -0.20 4.60 4.75 208 31671

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TABLE 4

C (CITIGROUP INC) 20.65 +4.00Sep 20, 2008 @ 09:36 ET

Bid 20.00 Ask 20.54 Size 35x3 Vol 265457511

Calls Last Sale Net Bid Ask Vol Open

Int Puts Last Sale Net Bid Ask Vol Open

Int

08 Sep 17.50 (C IR-E) 2.79 +2.49 2.79 3.05 10785 80622 08 Sep 17.50 (C UR-E) 0.01 -1.09 0.0 0.01 3103 98889

08 Sep 20.00 (C ID-E) 0.38 +0.34 0.25 0.38 28289 132763 08 Sep 20.00 (C UD-E) 0.02 -3.48 0.02 0.04 13402 91747

08 Sep 22.50 (C IA-E) 0.02 0.0 0.0 0.01 17882 112043 08 Sep 22.50 (C UA-E) 2.11 -4.39 2.15 2.30 4600 52929

08 Sep 25.00 (C IE-E) 0.01 0.0 0.0 0.03 5938 97936 08 Sep 25.00 (C UE-E) 4.80 -5.50 4.45 5.05 7 15200

08 Oct 17.50 (C JR-E) 3.20 +1.80 3.20 3.90 6826 31867 08 Oct 17.50 (C VR-E) 0.87 -1.30 0.94 0.96 3001 50689

08 Oct 20.00 (C JD-E) 1.83 +1.28 1.82 1.99 9188 35943 08 Oct 20.00 (C VD-E) 1.70 -2.30 1.65 1.75 5214 29323

08 Oct 22.50 (C JA-E) 0.77 +0.57 0.76 0.80 7542 27103 08 Oct 22.50 (C VA-E) 3.10 -4.60 2.94 3.60 727 2466

08 Oct 25.00 (C JE-E) 0.38 +0.35 0.35 0.45 3608 4343 08 Oct 25.00 (C VE-E) 5.00 -5.80 5.05 6.05 201 947

1. ( 5 points) Referring to Table 1, why the difference in the premiums on an Oct 12.50 call vs. the Sept 15 call? State which option is more expensive and why (give 2 specific reasons).

2. ( 5 points) Referring to Table 1, suppose you found a Sept 12.50 call outside of class and picked it up (its free!!). If you exercised it (use Table 1 for all info), how much money would you make / lose? Please show all work.

3. ( 5 points) If instead of exercising as above, you decided to put the call that you found outside of class on Ebay. Do you think you could sell it for more money than you made when you exercised it.? Why or why not. Explain

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4. ( 5 points) Suppose you are bullish on C and purchase 100 Sept 15 calls (see Table 1). How much would they cost and what would they collectively give you the right to do?

5. ( 5 points) If these options expired with the spot price associated with Table 3, what could you sell each one of these 100 options for (assume that markets are functioning well with lots of liquidity)? That is, what would be the premium for each option contract?

2) (25 points for completely labeled graph – 5 points off for each blemish!) As we did in class, graphically illustrate the profit/loss function of the 100 Sept 15.00 calls that you purchased on Sept. 16 (Table 1), clearly labeling the out of the money spot, at the money spot, in the money spot, and the break even point (this is all relative to the 100 Sept 15.00 calls). Label the horizontal line in your graph as spot at expiration. For your diagram, use a price range of 12 - 25 and be sure to label, on the vertical axis, the profit loss associated with the three distinct scenarios below.

Scenario 1): the spot price of C stays the same as in Table 1 and your option expires. Locate this point on your diagram as point A, clear labeling the profit or loss associated with this scenario.

Scenario 2): the spot price of C rises to the price associated with Table 2 and expires that way and you exercise your option. Locate the specific profit or loss on your diagram and label as point B.

Scenario 3): the spot price of C rises to the price associated with Table 4 and expires that way and you exercise your option. Locate the specific profit or loss on your diagram and label as point C.

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Futures

A futures contract is an obligation to deliver or receive a financial asset or commodity on a predetermined date for a stated price.6 Futures contracts exist for everything from pork bellies to interest rates. Futures contracts are generally preferred to forward contracts because they are standardized and for the most part, more liquid. Interest rate futures are always denominated by a face value of $100,000; other commodities have standardized qualities as well. Futures are often used as a hedge (insurance) against unwanted price movements. For example, a farmer who produces wheat would want to insure against a low price at harvest time by selling wheat futures to lock in a price for his/her wheat. By selling a wheat futures contract, the farmer is obligated to deliver a specified quantity of wheat at a specified future time.7 When the wheat is harvested, he/she must deliver it at the price as described by the futures contract. In much the same way, a baker who uses wheat can ensure against a high price at harvest time by purchasing wheat futures, thus locking in a price for this vital input. In this sense, the baker is hedging (insuring) against a high price of wheat at harvest time. As you can see, there is a ‘natural market’ that develops here; The farmer insuring against low prices at harvest time, and a baker insuring against high prices at harvest time.

Speculators operate in the futures market as well tending to improve the liquidity to the futures market. We will discuss speculators in the futures market when we do the problem that follows.

To trade futures, an investor must keep approximately 10% of the value of the contract in his account as margin. Futures accounts are marked to market daily meaning that if your account falls below margin, you must add funds to the account immediately. Conversely, if you make money, cash is added to your account at the close of trading each day. This property of the futures market give accountants headaches and as a result, the relatively new futures options markets has blossomed.

Futures contacts are very risky, since you can place a very large bet for a relatively small amount of money. If there are significant changes in the value of your futures contract, the the gains/losses can easily exceed 100% in a short period of time.

Futures Options

A futures option is simply the option to buy (a call) or sell (a put) a specified quantity of commodity at a predetermined price by the expiration date. These options trade on exchanges just like regular stocks or options and their prices, therefore, are market-determined. Advantages of futures options over futures are:

a) Futures options preserve the possibility of profits while limiting potential losses to the price of the option. That is, the most you can lose is what you paid for the option (referred to as the premium).

b) Futures options do not require daily settlement via a margin account and thus are much easier to handle from an accounting standpoint.

6 One major difference between options and futures is that futures contract require you to close your position where as options do not (i.e., options can expire without any action between the buyer and seller).7 As in at harvest time. In the real world, the standardized quantity for a futures wheat contract is 5,000 bushels!

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While futures expose investors to virtually infinite risk, the most one can lose with the purchase of a futures option is the cost of that option (i.e., the premium). As with stock options, if the contract is not “in the money,” the contract will not be exercised and no additional losses will be incurred.

Practice futures / futures options problems

Problem #1

(15 points total) Suppose you are a weaver and you need 10,000 pounds of cotton to make handkerchiefs. Harvest time is six months from now and you want to lock in a price per lb now via a futures contract. Suppose you can make an agreement, that is, enter into a futures contract for 10,000 lbs with a cotton farmer with an agreed upon price of $1.00 lb (which happens to be the current spot price).

a) (2 points) Explain the terminology of the transaction – that is, what exactly are you doing and why: what is the farmer doing and why?

b) (2 points) Now suppose, due to a trade war and a great growing season, cotton prices plunge to 50 cents ($0.50) per pound at harvest time. Who looks smart for acquiring the futures contract, the cotton farmer or the weaver? Explain.

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c) (3 points) Now, let’s assume that they are both speculators. Plot the profit function (futures profit functions) for the speculator cotton farmer (in one graph) and the speculator weaver (in another graph). Locate the profit or loss for each with a label of point A (where the price equals $0.50). Please use the space below for your diagram.

d) (3 points) Now assume that instead that the speculators play the futures options market. In particular, the speculator cotton farmer buys a futures options put for 10,000 lbs of cotton for $1000 (strike price = $1.00 lb) and the speculator weaver buys a futures options call for 10,000 lbs of cotton for $1000 (strike price = $1.00 lb). Assume that the price per pound plunges to 50 cents ($0.50) as before and that the futures options expire at harvest time. Add the futures option profit function for each speculator to your diagram above. Locate the profit or loss for both players in the futures options game as point B. Be sure to label your diagram with all the specific numbers that apply. Which option is “in the money?”

e) (4 points) Are these results consistent with a zero sum game (hint, there are four players here)? Explain.

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Problem 2

1.(56 points total) Suppose you are in charge of an oil refinery which means you, as in your firm, are a user of crude oil and a producer of gasoline. As we know, both crude oil and gasoline are part of a well developed financial market so that futures and futures options markets exist that are extremely liquid for these two commodities. Suppose that you know next to nothing about markets and so you need to hire someone to help you make decisions as to how to the ‘play the game’ and maximize profits. Naturally, you maximize profits by minimizing the cost of the input…oil … and maximizing your revenue…..selling gas. We assume away all costs except for the input oil and we have the following production figures – each oil contract consists of 1000 barrels of crude and with 1000 barrels we can produce 100,000 gallons of gas. Each gas contract is for 50,000 gallons so for every oil contract that we buy we produce the equivalent of two gasoline contracts. We have a contract with BP for 500,000 gallons of gasoline for delivery at the end of February 2011 (10 gasoline contracts worth) and we need to buy the oil (5 contracts), the input, at the end of November to give us time to refine it in time for delivery. The charts below represent the two futures contracts we consider – the Dec 2010 oil contract that expires on 11/19/10 and the March 2011 gasoline contract that expires on 2/28/2011.

Four different job applicants come in and you interview them….they all advise you a little differently.

1) Future guy – this person simply plays the futures market – so they would advise you buy oil futures and to sell gas futures.

2) Going naked – this person doesn’t hedge and would advise you to take your chances in the spot market – think of this person as having a high risk appetite.

3) The option buyer – this person would advise you to buy futures options calls on oil and futures options puts on gas.

4) The option writer – this person would advise you to write futures options puts on oil and to write futures options calls on gas.

We consider the oil market first (see graph below). Suppose that the futures price of oil is $80 per barrel and that futures options, both puts and calls, are available at a price of $2,000 each (STRIKE PRICE = $80, EACH CALL AND PUT REPRESENTS ONE FUTURE CONTRACT).. We consider two different scenarios with regard to this oil market and you need to figure out which of the job applicants have the best strategy given each scenario.

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Scenario #1: The spot price of oil is $80 per barrel at expiration. Recall, you need to buy 5 contracts or 5000 barrels of oil to make the gas.

a) (9 points) Given Scenario #1, which of the four strategies is the best in terms of minimizing the cost of obtaining the 5000 barrels of oil and which strategy is the worst in terms of the costs of obtaining the oil? Be specific and provide the costs associated with each strategy for full credit. , Please use real numbers and show all work!

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Scenario #2: The spot price of oil is $75 per barrel at expiration. Recall, you need to buy 5 contracts or 5000 barrels of oil to make the gas.

b) (9 points) Given Scenario #2, which of the four strategies is the best in terms of minimizing the costs of obtaining the 5000 barrels of oil and which strategy is the worst in terms of the costs of obtaining the oil? Be specific and provide the costs associated with each strategy for full credit. , Please use real numbers and show all work!

We now consider the market for gasoline (see graph below). Suppose that the futures price of gasoline is $2.00 per gallon and that futures options, both puts and calls are available at a price of $4,000 each (STRIKE PRICE = $2.00, EACH CALL AND PUT REPRESENTS ONE FUTURE CONTRACT). . We consider two different scenarios with regard to this gasoline market and you need to figure out which of the job applicants have the best strategy in terms of maximizing revenue, given each scenario.

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Scenario #1: The spot price of gasoline is $2.00 per gallon at expiration. Recall, you need to sell 10 contracts or 500,000 gallons (10 X 50,000) of gas to sell to BP.

c) (9 points) Given Scenario #1, which of the four strategies is the best in terms of maximizing your revenue and which strategy is the worst in terms of revenue. Be specific and provide the revenue associated with each strategy for full credit. , Please use real numbers and show all work!

Scenario #2: The spot price of gasoline is $2.20 per gallon at expiration. Recall, you need to sell 10 contracts or 500,000 gallons (10 X 50,000) of gas to sell to BP.

d) (9 points) Given Scenario #2, which of the four strategies is the best in terms of maximizing your revenue and which strategy is the worst in terms of revenue. Be specific and provide the revenue associated with each strategy for full credit. , Please use real numbers and show all work!

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Graphing – In the space below, please graph the futures and futures option profit function for the oil market given each Scenario (two diagrams – the bear on the left and the bull on the right). Recall, Scenario 1(LABEL AS POINTS A) is when the spot oil price is $80 per barrel at expiration and Scenario 2 (LABEL AS POINTS B) is when oil expires at $75 per barrel. Be sure to label diagram completely including the break even points! 10 points for completely labeled graph.

Graphing – In the space below, please graph the futures and futures option profit functions for the gasoline market given each Scenario (two diagrams – the bear on the left and the bull on the right) Recall, Scenario 1(LABEL AS POINTS A) is when the spot price of gasoline is $2.00 per gallon at expiration and Scenario 2 (LABEL AS POINTS B) is when the spot price of gasoline is $2.20 at expiration.. Be sure to label diagrams completely including the break even points! 10 points for completely labeled graph.

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Problem 3

1. Let’s pretend you are the owner of a car dealership (and it is summer 2009 – we are going back in time!) and along with being the owner you are also in charge of the finances of the dealership. This summer (2009) your dealership participated in the ‘cash for clunkers’ program and it worked well, with sales picking up significantly. The bad news is that the Federal Government, with their seemingly never ending red tape, has not paid you the cash for clunkers. You just received a note in the mail from Uncle Sam and ‘he’ promised that the check will be in the mail by early December of this year (2009) and you will receive the money by mid December, 2009.

Now you know that tax time is in mid April, 2010 and therefore, you want to park these ‘cash for clunker’ funds in 10 year Treasuries for 3 months and then get hold of the cash at the end of March to pay the tax bill by mid April (of next year (2010)). Let’s suppose that you sold 500 cars during the cash for clunkers program and Uncle Sam will pay you $3,000 per clunker meaning that the check from Uncle Sam (arriving in Dec.) will be for 500 x $3,000 = $1.5 million.

a) It is the second week of August 2009 and you are thinking of three different hedges to protect against bad things happening. What do we mean by bad things happening and what in particular, could cause bad things happening? Give me two real world examples.

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The three hedges are as follows. Note, to simplify matters, we consider only one contract (makes the math easier!)

Scenario #1: You buy a Dec. future contract for 114 and the price at expiration is 116.

Scenario #2: You buy a Dec. futures option call with a strike price at 114 for $1,500 and the price at expiration is 116.

Scenario #3: You write a Dec. futures option put with a strike price of 114 for a price of $1,500 and the price at expiration is 116.

1.b) (10 points) Suppose the price at expiration of these futures is 116. Compare the costs of acquiring the Treasury contract in Dec. for each scenario and rank them accordingly from lowest cost to highest cost.

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Given that these Dec. 09 futures contracts expire at 116, please draw your profit functions for each of the three scenarios above. In particular, draw the futures profit function, the futures option call profit function and the profit function for writing the put all on the same diagram. Be sure to label each profit function and label as points 1, 2, and 3 to coincide with each scenario. Be sure to label all the break even points. (20 points for completely labeled graph).

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Let’s move on to the next hedge. As noted above, you need to pay the tax bill in April and thus, you decide to sell March futures contracts (i.e., to get the cash in March to pay the tax bill).

Consider the following 3 scenarios:

Scenario #1 - You sold a March futures at 116 and the contract expires at 120.

Scenario # 2 - You bought a futures option put at a price of $1,500 with a strike price of 116 and the contract expires at 120.

Scenario #3 - You wrote a future option call at a price of $1,500 with a strike price of 116 and the contract expires at 120.

1.f) (10 points) Now compare the revenue that you receive to pay the taxes under each scenario and rank them 1st, 2nd and 3rd. Please show all work.

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Given that these March 10 futures contracts expire at 120, please draw the profit function for each of the three scenarios above. In particular, draw the futures profit function, the futures option put profit function and the profit function for writing the call all on the same diagram. Be sure to label each profit function and label as points 1, 2, and 3 to coincide with each scenario. Be sure to label all the break even points. (20 points for completely labeled graph).

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Problem 4

1. Suppose you are a chocolate maker and you need 5000 lbs of cocoa beans in December so that you can make chocolate in time for Valentine’s Day. As a risk averse person, you want to lock in a price per lb now via a futures contract. Suppose you can make an agreement, that is, enter into a futures contract for 5000 lbs with a cocoa bean farmer with an agreed upon price of $3.00 lb (which happens to be the current spot price).

a) (4 points) Explain the terminology of the transaction – that is, what exactly are you doing and why: what is the farmer doing and why?

b) (4 points) Now suppose, for whatever reason, the spot price of cocoa beans rises to $4.50 per lb at expiration (December). Who looks smart for acquiring the futures contract, the cocoa farmer or the chocolate maker? Explain.

c) (8 points) Now, let’s assume that they are both speculators. Plot the futures profit function for the speculator cocoa bean farmer, the bear, (in one graph) and the speculator chocolate maker, the bull, (in another graph). Locate the profit or loss for each with a label of point A (where price equals $4.50).

Now assume that instead that the speculators play the futures options market. In particular, the speculator cocoa bean farmer buys a (Dec.) futures options put for 5000 lbs of cocoa beans for $3000 (strike price = $3.00 lb) and the speculator chocolate maker buys a (Dec.) futures options call for 5000 lbs of cocoa beans for $3000 (strike price = $3.00 lb).

d) (4 points) Assuming that the price rises to $4.50 lb as before, and that the futures options expire in December, which option is “in the money?” Explain.

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e) (8 points) Add the profit function for each speculator to your diagram above (the futures options profit function).

f) (4 points) Finally, what is the profit / loss for each speculator in the futures options market (locate this as point B on your diagram above (show work).

g) (8 points) Find the break- even spot price (at expiration) for the farmer AND the chocolate maker and locate on these points on your diagram (label as “break even spot”) Show work as to why this is the break even point.

h) (10 points) Are these results consistent with a zero sum game (hint, there are four players here)? Explain and show all work.

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Terms to be familiar with (not in any particular order):

1. Options – calls, puts.2. Derivatives – what does this term mean and why?3. Shorting stocks and short covering.4. Long vs. Short positions.5. NEWS.6. Futures.7. Closing your position.8. Hedging vs Speculating9. Bulls vs. Bears.10. Exercise.11. In the money.12. Rally (apply to all three of the asset markets).13. Spot price.14. Zero Sum game.15. Strike price.16. Expiration date.17. Futures options.18. Determination of option premium.19. Covered vs. Naked calls/puts.20. Writing options.21. Risk.22. Expected return.23. Liquidity.

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Chapter 2: Financial Markets: Part 2

Portfolio Allocation and the demand for assets

There are three main determinants of asset pricing:

1) Expected return: The higher the expected return of the asset, all else constant, the higher the price of the asset. Naturally, we will discuss at length the factors that influence the expected return of the asset(s) throughout the course. I do want to mention at this point how important expectations and changes in expectations are in terms of determining not only asset prices, but also, aggregate economic activity.

Asset price = f (Rete) : +

stated as “the asset price is a positive (+) function (f) of it’s expected return (Rete), all else constant

2) Liquidity: Liquidity is an attractive quality in any asset and a highly liquid asset has three qualities: 1) it is easy (low cost) to convert the asset into money where money is defined as transactions money; 2) it can be converted to money quickly and 3) the amount that it is converted to is representative of its fundamental value (i.e., I can sell my house very quickly and easily for $5, but that doesn’t mean it is liquid!). Typically, the more liquid the asset, the lower the return. Take money, typically considered to be the most liquid asset of all. Money earns a nominal return of zero and a real return equal to the ‘negative’ of the inflation rate.8

Liquidity is especially attractive in a highly uncertain environment. When we discuss financial crises and shocks like 9/11, we will see the impact on financial markets when investors demand more liquid assets. US Treasuries are often considered very liquid and thus the term: “rush to the safe haven of US Treasuries.” The safe haven refers naturally to the perceived zero default risk quality of US Treasuries.

Asset price = f (Liq) : +stated as “the asset price is a positive (+) function (f) of it’s liquidity (Liq), all else constant

3) Risk: The more risky the asset, the more uncertain as to the assets’ return. Risk arises for a variety of reasons and we assume that all else equal, investors prefer assets with less

8 Suppose inflation over a year is 10% and I keep $100 in my pocket. That $100 next year would be able to purchase 10% less in real goods and services given the 10% rise in the general price level that has occurred over the year.

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risk (i.e., on average, investors are risk averse). We also note that risk and expected return are related – typically, the higher the risk, the higher the expected return (investors require a higher expected return to take on the higher risk).

Asset price = f (Risk) : -stated as “the asset price is a negative (-) function (f) of it’s Risk, all else constant

Stock Price Determination

As most of us could gather, the obvious driving force underlying any the price of any stock is the expected future stream of profits or earnings (earnings and profits are used interchangeably). We need to be more specific, it is the present value (PV) of current and future earnings that matter. We all should recall that the present value of say $1,000 today is larger than the present value of $1,000 ten years from now. But how much larger? The answer depends on the expected nominal interest rate to prevail over the next ten years. Let’s make life simple, let us suppose that the interest rate over the next ten years will be 10% year in and year out. In this case, given these assumptions, the PV of $1,000 ten years from now would be:

PV1000 = $1,000/(1 + 0.10)10 = $ 385.54

What does $385.54 represent? The answer is that if we take $385.54 and invest it today at a 10% annual return and take the principal and interest and continue rolling it over for 10 years, at the end of the 10th year, we would have $1,000. An equivalent way of thinking about this is, and the way most relevant for understanding how stock prices are determined is the following: Given the above conditions, I would be willing to pay $385.54 today, to receive $1,000 ten years from now. In what follows, the $1,000 in this example would be the “expected profits” of the firm ten years from now. These expected profits are continuously changing given the continuous NEWS that investors digest and process on a day to day basis.

In terms of stock price determination, investors form expectations as to the future profits of any particular firm as well as the expected path of interest rates, since together, they determine the present value of the firm. Similar to the above, the present value of a firm can be thought of as the most investors would be willing to pay for the firm today, to have the ownership rights to all the current and future profits expected in the future. When we divide the present value of the firm by the number of shares of stock outstanding, we arrive at the price of the stock. Before getting into more specifics, please read the following summation.

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Three major factors to keep in mind when considering stock price determination

1) Stock prices are driven by expectations and changes in expectations. Just about everything influences expectations and these changes in expectations are reflected immediately in the relevant stock price.9

2) Stock prices are positively related to expected earnings and expected earnings nearer to the present have a stronger influence on stock prices than do the same expected earnings further out into the future. For example, the present value of $10,000 in expected earnings 2 years from now is larger than the present value of $10,000 in expected earnings 10 years from now (assuming away zero interest rates)10

3) Stock Prices are typically negatively related to the expected path of interest rates. The expected path of interest rates is so important in financial markets, not to mention, aggregate economic activity. Many investors spend much of their time trying to figure out what the Federal Reserve may or may not do. Interest rates also change for reasons not directly related to Fed policy, and a big portion of this class revolves around interest rate determination. For the present, we need to understand why lower interest rates are ‘typically’ good for stocks. First, the present value of future profits rises the lower the expected path of interest rates. Let’s return to our example above. It was shown that the PV of $1,000 ten years from now, assuming 10% interest rates year in and year out, was:

PV1000 = $1,000/(1 + 0.10)10 = $ 385.54

Now let’s let the expected path of interest rates be 5% year in and year out. What is the PV of $1,000 ten years from now given this lower expected path of interest rates?

PV1000 = $1,000/(1 + 0.05)10 = $ 613.91

So if the expected path of interest rates fall, all else constant, that should be good for stocks as the PV of the firm will rise.

Second, we can not ignore the influence of the change in the expected path of interest rates on expected profits. This influence is very real but also very hard to analyze and therefore, the context must be taken into account. For example, on one hand, lower interest rates in the future should stimulate economic activity and according to this version of the story, should result in higher expected profits. On the other hand, if people expect lower interest rates due to a poorly performing economy, then perhaps expected profits will fall instead of rise. So the influence of lower expected interest rates on the expectations of future profits is ambiguous, and thus, needs to be examined on a case by case basis.9 This notion applies to bond and foreign exchange markets as well.10 In addition to the PV, near term expected profits have less uncertainty than expected profits well into the future, so when the expected profits change, it is the nearer term(s) of expected profits that have the most influence on the stock price.

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Numerical Example and some Terminology

The stock price of any firm is equal to the (expected) present value of the firm (market cap) divided by the number of shares outstanding. Any factor, and there are many, that changes the expected present value of the firm, will change that stock price.11

The assumption (in the numerical example that follows) is that this firm falls off the face of the earth after three years, a more realistic example would include many more terms (an infinite amount!).

Example:

Company ABC (10,000 shares outstanding)Year 1 2 3Exp. Earnings $15,000 $50,000 $100,000Exp. 1 yr Interest Rate

0.03 0.04 0.05

Price to earnings ratio (PE ratio): The price to earnings ratio is often used by investors as a guidepost as to whether a stock is “overvalued” or “undervalued.” Given that stock prices are determined by expectations of the future, we NEVER know whether a stock price is overvalued, undervalued, or valued ‘just right.’12

11 Psychology also plays a role here. How people feel, waves of optimism and pessimism certainly move stocks, and a strand of finance referred to as behavioral finance will be addressed at a later time. Needless to say, when we add psychology to the ‘equation,’ analysis becomes that much more difficult as well as less concrete in nature.12 In December of 1996, Alan Greenspan stated that investors were “irrationally exuberant,” implying that investors were erroneously optimistic about future profits. Another way to state the same thing is that a bubble had formed in the stock market! Alan Greenspan was heavily criticized for this comment and truly regrets saying it. The moral of the story is that we don’t know when stocks are overvalued or undervalued and thus, major figureheads should refrain from giving their personal opinion. The following statement is believed by just about everyone in finance and economics: “We never know if there is an asset market

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The price to earning ratio can be calculated in two equivalent ways:

1) Take the market cap, which is equal to the number of shares outstanding times the current price of the stock and divide it by current year earnings. From the example above:

PE ratio = $147,175 / $15,000 = 9.81

2) Take the price per share and divide it by current year earnings per share:PE ratio = $14.72 / $1.50 = 9.81

We can now do some exercises:

1) Suppose the Federal Reserve makes a dovish announcement and as a result, investors expect the path of short term interest rates to be steady at 3% (as opposed to previous expectations over the three year life of the firm of 3, 4, and 5% respectively).

Exercise: What will happen to the Stock Price?13

Exercise: What will happen to the PE ratio?

2) Suppose the CEO of Company ABC makes a statement that the company’s expected earnings are now lower than previously expected (i.e., a pessimistic outlook) so that investors now expect profits to be ‘flat’ at $15,000 for the next three years (assume the initial expected path of interest rates of 3, 4, and 5% in year 1, 2, and 3 respectively).

Exercise: What will happen to the Stock Price?

Exercise: What will happen to the PE ratio?

3) Give two specific reasons why the PE ratio would be high for a firm and comment on the type of firm that may have a high PE ratio. Finally, does a high PE ratio imply that the firm is over valued? Why or why not?

bubble until the bubble breaks.”13 We are holding expected earnings constant in this example.

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The Optimal Forecast and Rational Expectations.

Example 1: Rational Expectations and a Question Before You Hand in Your Exam!

When I was at Grad School here at PSU, a professor told a story that I believe really clarifies exactly what we mean by rational expectations. Suppose I would say to the class before anyone handed in their exam (assume it is a multiple choice exam):

“Put an asterisk next to the three questions that you think you missed”

So let’s think about this for a moment……. which questions would you pick? The answer is that if you have rational expectations formation, you should not pick any! Why?? If you pick a question that you think you missed, then change the answer! Of course I know a lot of you are thinking that well…. some questions are harder than others and I will simply choose the three hardest questions! That is fine and consistent with rational expectations, but that is not admitting that you think you missed them because if you think you missed it, again, you would change the answer. So again, if I asked you how many questions you think you missed, your answer should be zero!

Another interesting and useful feature of this example is the concept of a probability distribution – some questions probably fall into the ‘no brainer’ category and thus, you are quite certain that you got them correct; some are in the easy but not that easy, etc. As we shall see, probability distributions and the associated uncertainty plays a critical role in financial markets and the economy.

Example 2: Using Rational Expectations on Your Drive to Work Each Day

Suppose you live in Port Matilda and work in State College. Suppose also that you do not want to arrive at work “too” early and you don’t want to arrive at work “too” late. Suppose through experience, you estimate the commute to be 15 minutes and thus leave 15 minutes before you are scheduled to work.14 Suppose you begin work at 8 am and thus you leave at 7:45 am.

Questions:

1) Would you expect to get to work at starting time each and everyday?

14 Let’s assume that your employer is okay with you being a little late or a little early and thus, as long as you are to work on time, on average, all is well.

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2) Would you actually get to work at exactly the same time?

3) Is your forecast of the time it takes to get to work optimal? Why or why not?

Consider the following two scenarios:

a) One the way to work you get stuck in traffic due to an accident, somebody hit a deer and you end up getting to work 15 minutes late!

Question: Would you change your forecast on how long it takes to get to work and would this forecast be optimal?

b) The state begins construction (on the road you travel) and you are 15 minutes late for work. You learn that the construction is going to last for 6 months. Would you change your forecast on how long it takes to get to work and would this forecast be optimal?

Let’s define the forecast error (FE) as the starting time (8 am) minus (-) the actual arrival time. If the actual arrival time is 8am, then the forecast error equals zero; if the arrival time is not 8 am, then the FE is non-zero. What are the properties of this forecast error (there are three of them)?

a.

b.

c.

Predicting Tomorrow’s Stock Price and the Efficient Market Theory In the driving to work example above, we had the incentive to obtain an optimal forecast for the commute and thus, we used all the relevant information available to formulate that optimal forecast. For example, if it snowed all night and you believed the roads are likely to be slippery, you would use that relevant and available information immediately and

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incorporate (process the information) it into your forecast of the time it will take to get to work. In terms of jargon, we would say you were irrational if you did not account for the snowfall.

Naturally, any investor would love to be able to predict the future, because if you can predict future movements in asset prices, you could place the appropriate bet(s) and make lots of money! The example that follows applies to stocks, but the same line of reasoning can be applied to the bond and foreign exchange markets. Suppose you were to try to predict tomorrow’s stock price today. Let us define the information set available to you today as Ωt. Naturally, Ωt contains ALL information that is available at time t, where the subscript t stands for today, the subscript t+1 stands for tomorrow (next period in general).

We can write the following:

St+1 = f (Ωt): stated as: “Tomorrow’s stock price is a function of the (entire) information set available today.”

Naturally, we would want to use all the relevant information that is currently available in predicting an asset price. Another way to say this is that it would be irrational if we did not use all the relevant and available information that was available today (recall the drive to work and ignoring the snowfall example). In fact, rational expectations formation simply means that agents use all the information that is available today in making their forecasts and thus, the forecast is optimal.

Predicting stock prices is very similar in that you rationally use all the relevant information that is available to you when formulating your optimal forecast.

Predicting Stock Prices: A forecasting model

In the equation below, we could add a plethora of information that is available today.15 Naturally, we would want to use only the relevant information but how do we know what information is relevant and what information is not? In the equation below, ie stands for expected interest rates, UR for unemployment rates, CC for consumer confidence, GDP for gross domestic product, HS for housing starts, etc. Naturally, we could just keep on adding variables to the model and thus, the forecasting model will become very complex (Ωt is extremely large). Thankfully, we have the efficient market theory to make ‘life’ much easier.

15 In the conduct of monetary policy, the Fed monitors over 850,000 data series.

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THE EFFICIENT MARKET THEORY

Definition: If markets are efficient, then the current asset price has already incorporated all the relevant and available information related to that asset. Furthermore, if markets are efficient, then NEWS, as defined as the ‘unexpected,’ is immediately reflected in the asset price. That is, asset prices process new information very quickly and accurately (as in the snowfall and commute to work example).

Implications of the efficient market theory – since efficient markets imply that the current asset price has already incorporated all the relevant and currently available information, then it would be a waste of our time (fruitless) building fancy and complex models to predict future asset prices, since today’s price has already processed all the current, relevant and available information. The good news is that it makes our forecasting equation very simple. The bad news is that in order to predict changes the stock price, we would need to predict the unexpected; e.g., we would need a crystal ball.16 Good luck with that!

Best forecasting equation assuming efficient markets:

St+1 = f (St)

In other words, the best predictor of tomorrow’s stock price is today’s stock price. This fact supports the Efficient Market Theory which states that today’s stock price contains all current and relevant information associated with the fundamental value of the firm that is available today (it efficiently processes what is in Ωt). According to efficient markets, the only reason that tomorrow’s stock price will differ from today’s would be due to NEWS that occurs between today and tomorrow. So, in effect, the NEWS is exactly equal to FE, which is defined as the forecast error. If there is no news then FE=zero, and St = St+1.17

Properties of the forecast error, assuming efficient markets (recall commute to work ex.).

1. The FE must have a mean of zero (we assume that good news is as likely as bad news).

2. The FE must be independent of Ωt, where Ωt is the entire information set that is available at time t. If FE is not independent, that implies that St is not

16 We would actually need two crystal balls, one to predict the NEWS and another to predict the (asset price) reaction to the NEWS.17 This statement ignores what is often referred to as the ‘equilibrium return’ in the ‘market.’ We know that the bond market and the stock market are often substitutes for investors’ funds and thus, investing in the stock market embodies a positive expected return.

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processing all the relevant and available information contained in Ωt, and thus, violates the assumption of the efficient market theory.

3. The FE must be uncorrelated with past FE’s (serially uncorrelated). Another way to state this is that NEWs is completely absorbed immediately so that today’s forecast error does not help us predict tomorrows forecast error. Recall specifically the commute to work example when there was a 1) accident that resulted in being late for work and 2) the road construction. Even though these was a large forecast error (we were really late for work), does that forecast error help us predict the forecast error tomorrow. The answer is no, the expected forecast error would again be zero, since rational expectations formation ensures that we use all relevant information available.

TESTING THE EFFICIENT MARKET THEORY (EMT)

My goal in what follows is to give you a clue as to what many economists do for a living, and that is, crunch numbers! A good amount of economic research is theoretical, and a good amount of economic research is empirical. I much prefer empirical analysis, and empirical analysis is often utilized to test (prove or disprove) economic theories.18

A Primer on Regression Analysis: A Consumption Function Example

The example below should be a little familiar to you from econ 004. Consumption accounts for about 70% of GDP and is thus, very much studied by economists and other economic actors interested in understanding and predicting economic activity. In econ 004 you should, at the very least, recall that disposable income and the level of consumption are tightly related, that is, if we have data on disposable income, then we can make pretty good guesses as to the level of consumption. You should also recall that consumption is also influenced by other factors as well. In what follows, we develop a fairly realistic model of consumption, and then we simplify it when interpreting the empirical results.

18 The proper jargon is thateconomists use econometrics to conduct empirical analysis. Keep in mind that the results from empirical analyses are often contentious since the results are often sensitive to the econometric techniques employed and/or the sample selection.

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Consumption Function

where: Yd is personal disposable incomeWSM is wealth in the stock marketWRE is wealth in real estater is the real interest rateEX is the exchange rate where an increase implies the dollar is

appreciatingCC is consumer confidence

If we used all the variables (above) to predict consumption, the regression equation will take the following form:

The ai’s are sensitivity parameters. They tell us which direction and by how much consumption is affected by changes in each of the variables. For instance, a1 is the marginal propensity to consume (MPC), and tells us how sensitive consumption is to changes in disposable income.19

Empirical Results – The Consumption Function

The set up: I estimate a consumption function that includes all the arguments: above except for the exchange rate. The purpose of this example is to get you familiar with the usefulness and interpretation of these empirical results.

Important features of regression output:

R2 represents the fit of the model; the higher the R2, the better the fit. The maximum value for R2 is 1.00 and the minimum value is zero.

t-stats; if the absolute value of the t-stat exceeds 2.00, then we say that the associated variable ‘belongs’ in the regression. t-stats basically test whether or not a coefficient is significantly different than zero. If the t-stat exceeds two, then the coefficient is said to be ‘statistically different than zero.’

Coefficient interpretation: We are typically interested in the sign of the coefficient (i.e., is it consistent with economic theory) as well as the size (this has to do with economic significance). Example: the MPC (a1) in the equation above should be positive, close to one, and significant.20

19 You should recall the marginal propensity to consume from your principles classes and also that the value of the MPC plays a critical role in determining the “multiplier” and thus, determining, in part, the ‘power’ of monetary and fiscal policy.20 Most believe that the MPC in the US is quite high relative to the rest of the world with the empirical estimates somewhere around 0.9, which implies that for each $1.00 increase in disposable income,

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Empirical Results on the consumption function

Equation estimated

C = a0 + a1 Yd + a2 r + a3 WSM + a4 WRE + a5 CC

Priors:

a1 is the marginal propensity to consume and should be somewhere around 0.9 in value and very significant (high t-statistic) since we know there does exist a tight relationship between consumption and disposable income.

a2 should be negative since the lower the real rate of interest, the less in pays to save (i.e., consume!).

a3 should be positive and significant – i.e., the wealth effect in terms of stock market wealth.

a4 should be positive and significant – i.e., the wealth effect in terms of real estate wealth. Note also that the claim is that a4 should be greater than a3, that is, dollar for dollar, the wealth effect in real estate is great than the wealth effect in stocks since changes in the former (real estate wealth) are perceived by economic agents to be more permanent and stable than the latter (changes in stock market wealth ,’here today, gone tomorrow.’

a5 should be positive, the more confident you are, the more you consume!

Also, the overall fit should be quite good, since we know that there is tight relationship between C and Yd

consumption will rise by 90 cents with the remaining 10 cents being saved.

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Regression Output: 1977Q3 – 2006Q2

C = -115 + .788(Yd) – 10.486(r) + .032(WSM) + .078(WRE) + .516(CC)

Dependent Variable: ConsumptionMethod: Least SquaresDate: 04/23/07 Time: 19:04Sample: 1977:3 2006:2Included observations: 116

Variable Coefficient Std. Error t-Statistic Prob.

C -115.9823 31.78627 -3.648819 0.0004Yd(-1) 0.787909 0.015640 50.37847 0.0000r (-1) -10.48553 2.276948 -4.605081 0.0000

WSM(-1) 0.032054 0.005459 5.871944 0.0000WRE(-1) 0.078031 0.005771 13.52198 0.0000CC(-1) 0.515951 0.279377 1.846792 0.0675

R-squared 0.999554 Mean dependent var 4512.648Adjusted R-squared 0.999534 S.D. dependent var 2243.232S.E. of regression 48.44171 Akaike info criterion 10.64894Sum squared resid 258125.9 Schwarz criterion 10.79136Log likelihood -611.6384 F-statistic 49299.63Durbin-Watson stat 0.802282 Prob(F-statistic) 0.000000

We will interpret all of this in class!

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Testing of the efficient market hypothesis

S = closing price of Google Stock. Daily Data from Yahoo!!

The data: Daily Data from August 20, 2004 – August 30, 2007 (790 observations)

0

100

200

300

400

500

600

700

8/19/04 5/26/05 3/02/06 12/07/06 9/13/07

Spot price of "goog"

Equation estimated

(1) St+1 = α + β St + FEt+1

which is, if you back date (go back one day ), the same as

(2) St = α + β St-1 + FEt

Equation (2) is the equation that is estimated: What are our priors?

α should be positive, yet small, and should represent the “equilibrium” market return

β should be one, implying that the difference between today’s and tomorrows spot price is (ignoring α for a second)

equal to FEt+1.

We are going to test here shortly the properties of FEt+1. Recall what they are?

1)

2)

3)

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But first, let’s look at some results predicting tomorrow’s stock price with todays!

Check out the fit!

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-20

0

20

40

0

200

400

600

800

8/20/04 5/27/05 3/03/06 12/08/06

FE t+1 Actual Spot Fitted Spot

Equation Estimated: St = α + β St-1 + FEt

Dependent Variable: GOOGMethod: Least SquaresDate: 10/09/07 Time: 23:01Sample(adjusted): 8/20/2004 8/30/2007Included observations: 790 after adjusting endpoints

Variable Coefficient Std. Error t-Statistic Prob. C 1.222339 0.748589 1.632858 0.1029

GOOG(-1) 0.998410 0.001970 506.8233 0.0000R-squared 0.996942 Mean dependent var 359.5207Adjusted R-squared 0.996938 S.D. dependent var 125.0430S.E. of regression 6.919524 Akaike info criterion 6.709099Sum squared resid 37729.29 Schwarz criterion 6.720927Log likelihood -2648.094 F-statistic 256869.8Durbin-Watson stat 1.911456 Prob(F-statistic) 0.000000

Note that β is very close to one and the fit is very good!

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Lets try to improve the fit by adding more “Cats and Dogs” to the right hand side of the equation.

Dependent Variable: GOOGMethod: Least SquaresDate: 10/09/07 Time: 22:55Sample(adjusted): 8/27/2004 8/29/2007Included observations: 784 after adjusting endpoints

Variable Coefficient Std. Error t-Statistic Prob. C 2.977423 4.155744 0.716460 0.4739

GOOG(-1) 1.039484 0.036204 28.71193 0.0000GOOG(-2) -0.017874 0.052057 -0.343355 0.7314GOOG(-3) -0.045028 0.052110 -0.864088 0.3878GOOG(-4) 0.079843 0.052103 1.532399 0.1258GOOG(-5) -0.071880 0.052165 -1.377945 0.1686GOOG(-6) 0.014510 0.036306 0.399663 0.6895

YIELD10YR(-1) 1.818302 5.814346 0.312727 0.7546YIELD10YR(-2) 2.780892 8.115906 0.342647 0.7320YIELD10YR(-3) -1.921781 8.096711 -0.237353 0.8124YIELD10YR(-4) -3.839147 8.113601 -0.473174 0.6362YIELD10YR(-5) 1.075725 8.157192 0.131874 0.8951YIELD10YR(-6) -0.365652 5.839052 -0.062622 0.9501

R-squared 0.996877 Mean dependent var 360.8032Adjusted R-squared 0.996828 S.D. dependent var 123.5483S.E. of regression 6.958013 Akaike info criterion 6.734107Sum squared resid 37327.15 Schwarz criterion 6.811451Log likelihood -2626.770 F-statistic 20508.10Durbin-Watson stat 1.994819 Prob(F-statistic) 0.000000

Note – nothing helps! The only significant predictor is today’s stock price! Is this consistent with the efficient market theory????

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We now exam the properties of FE!

Let try to predict it with Ωt

Dependent Variable: FEMethod: Least SquaresDate: 10/10/07 Time: 07:15Sample(adjusted): 8/27/2004 8/29/2007Included observations: 784 after adjusting endpoints

Variable Coefficient Std. Error t-Statistic Prob. C 2.977423 4.155744 0.716460 0.4739

GOOG(-1) 0.039484 0.036204 1.090603 0.2758GOOG(-2) -0.017874 0.052057 -0.343355 0.7314GOOG(-3) -0.045028 0.052110 -0.864088 0.3878GOOG(-4) 0.079843 0.052103 1.532399 0.1258GOOG(-5) -0.071880 0.052165 -1.377945 0.1686GOOG(-6) 0.014510 0.036306 0.399663 0.6895

YIELD10YR(-1) 1.818302 5.814346 0.312727 0.7546YIELD10YR(-2) 2.780892 8.115906 0.342647 0.7320YIELD10YR(-3) -1.921781 8.096711 -0.237353 0.8124YIELD10YR(-4) -3.839147 8.113601 -0.473174 0.6362YIELD10YR(-5) 1.075725 8.157192 0.131874 0.8951YIELD10YR(-6) -0.365652 5.839052 -0.062622 0.9501

R-squared 0.008677 Mean dependent var 0.639936Adjusted R-squared -0.006752 S.D. dependent var 6.934641S.E. of regression 6.958013 Akaike info criterion 6.734107Sum squared resid 37327.15 Schwarz criterion 6.811451Log likelihood -2626.770 F-statistic 0.562386Durbin-Watson stat 1.994819 Prob(F-statistic) 0.872886

THE FIT IS TERRIBLE – R2 = 0.008677, We can’t predict the change in price of Google between today and tomorrow with today’s information set.

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NOW LETS TRY TO PREDICT FE WITH ITS PAST

Dependent Variable: FEMethod: Least SquaresDate: 10/10/07 Time: 07:14Sample(adjusted): 8/30/2004 8/30/2007Included observations: 784 after adjusting endpoints

Variable Coefficient Std. Error t-Statistic Prob. C 0.606648 0.253054 2.397310 0.0168

FE(-1) 0.043617 0.035867 1.216089 0.2243FE(-2) 0.028162 0.035995 0.782389 0.4342FE(-3) -0.022462 0.036045 -0.623170 0.5334FE(-4) 0.057552 0.036051 1.596412 0.1108FE(-5) -0.013378 0.036096 -0.370624 0.7110FE(-6) -0.025935 0.036047 -0.719473 0.4721

R-squared 0.006995 Mean dependent var 0.649273Adjusted R-squared -0.000673 S.D. dependent var 6.936333S.E. of regression 6.938667 Akaike info criterion 6.720985Sum squared resid 37408.74 Schwarz criterion 6.762631Log likelihood -2627.626 F-statistic 0.912226Durbin-Watson stat 2.004756 Prob(F-statistic) 0.485310

SAME KIND OF STORY, PAST FORECAST ERRORS DO NOT HELP PREDICT FUTURE FORECAST ERRORS

ALL TOLD – IT IS IMPOSSIBLE TO PREDICT CHANGES IN THE SPOT PRICE OF GOOGLE

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Does FE have mean of zero???

0

50

100

150

200

-40 -30 -20 -10 0 10 20 30

Series: FESample 8/20/2004 8/30/2007Observations 790

Mean 3.12E-14Median -0.325965Maximum 35.95978Minimum -37.51833Std. Dev. 6.915138Skewness 0.055580Kurtosis 7.276715

Jarque-Bera 602.4621Probability 0.000000

Summary: Our empirical results are consistent with the efficient market theory implying that it is impossible to predict changes in stock prices, suggesting that the closing price of coke follows a random walk.21

Another way to state this is that it is impossible to “beat the market.”

21 A very well known book regarding this topic is titled “A Random Walk Down Wall Street,” and is authored by Burton G. Malkiel.

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Updated results

SAMPLE - DAILY DATA - 1/2/2007

VARIABLES

DAAA: Moody's Seasoned Aaa Corporate Bond Yield

DBAA: Moody's Seasoned Baa Corporate Bond Yield

DGS10: 10-Year Treasury Constant Maturity Rate

DGS3MO: 3-Month Treasury Constant Maturity Rate

DJIA: Dow Jones Industrial Average

SP500: S&P 500 Stock Price Index

VIXCLS: CBOE Volatility Index: VIX

CPN3M: 3-Month AA Nonfinancial Commercial Paper Rate

VIX measures market expectation of near term volatility conveyed bystock index option prices. Copyright, 2011, Chicago Board OptionsExchange, Inc. Reprinted with permission.

VXDCLS: CBOE DJIA Volatility Index

WILL5000IND: Wilshire 5000 Total Market Index

INTEREST RATE SPREADS - 'HAND" CALCULATED

"risk structure spreads"

paperbillspread = rate on 3 month paper minus rate on 3 month Tbill

corpspread = rate on baa minus aaa

yield spread

slopeyc = rate on 10 year Treasury minus 3 month Tbill

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LET'S LOOK AT THE DATA!

OUR DEPENDENT VARIABLE - WHAT WE ARE TRYING TO PREDICT!

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2007 2008 2009 2010 2011 2012 2013

DJIA

SPREADS

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0.5

1.0

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3.0

3.5

4.0

2007 2008 2009 2010 2011 2012 2013

CORPSPREAD

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CORPSREAD AND DJIA AVERAGE TOGETHER

6,000

8,000

10,000

12,000

14,000

16,000 0.51.01.52.02.53.03.54.0

2007 2008 2009 2010 2011 2012 2013

CORPSPREAD DJIA

RUN A REGRESSION - PRIORS????

Dependent Variable: DJIAMethod: Least SquaresDate: 10/11/13 Time: 07:10Sample (adjusted): 1/03/2007 10/04/2013Included observations: 1633 after adjustmentsWhite Heteroskedasticity-Consistent Standard Errors & Covariance

Variable Coefficient Std. Error t-Statistic Prob.

C 14837.08 75.28027 197.0912 0.0000CORPSPREAD(-1) -2298.243 47.85215 -48.02801 0.0000

R-squared 0.501559 Mean dependent var 11855.05Adjusted R-squared 0.501253 S.D. dependent var 1909.018S.E. of regression 1348.186 Akaike info criterion 17.25213Sum squared resid 2.96E+09 Schwarz criterion 17.25874Log likelihood -14084.37 Hannan-Quinn criter. 17.25458F-statistic 1641.203 Durbin-Watson stat 0.013821Prob(F-statistic) 0.000000

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A LOOK AT THE FITTED VALUES, ACTUAL VALUES AND THE RESIDUALS

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2007 2008 2009 2010 2011 2012 2013

Residual Actual Fitted

VIX

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90

2007 2008 2009 2010 2011 2012 2013

VIXCLS

62

Dependent Variable: DJIAMethod: Least SquaresDate: 10/11/13 Time: 07:15Sample (adjusted): 1/04/2007 10/04/2013Included observations: 1640 after adjustmentsWhite Heteroskedasticity-Consistent Standard Errors & Covariance

Variable Coefficient Std. Error t-Statistic Prob.

C 14839.96 99.19846 149.5987 0.0000VIXCLS(-1) -128.3368 4.361714 -29.42348 0.0000

R-squared 0.514798 Mean dependent var 11851.36Adjusted R-squared 0.514501 S.D. dependent var 1910.515S.E. of regression 1331.203 Akaike info criterion 17.22677Sum squared resid 2.90E+09 Schwarz criterion 17.23336Log likelihood -14123.95 Hannan-Quinn criter. 17.22922F-statistic 1737.911 Durbin-Watson stat 0.062123Prob(F-statistic) 0.000000

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0

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6,0004,000

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2007 2008 2009 2010 2011 2012 2013

Residual Actual Fitted

Both together

Dependent Variable: DJIAMethod: Least Squares

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Date: 10/11/13 Time: 07:17Sample (adjusted): 1/04/2007 10/04/2013Included observations: 1629 after adjustmentsWhite Heteroskedasticity-Consistent Standard Errors & Covariance

Variable Coefficient Std. Error t-Statistic Prob.

C 15174.71 92.57123 163.9247 0.0000CORPSPREAD(-1) -1205.753 72.93067 -16.53287 0.0000

VIXCLS(-1) -75.51517 5.220112 -14.46620 0.0000

R-squared 0.565048 Mean dependent var 11854.11Adjusted R-squared 0.564513 S.D. dependent var 1910.907S.E. of regression 1261.035 Akaike info criterion 17.11909Sum squared resid 2.59E+09 Schwarz criterion 17.12903Log likelihood -13940.50 Hannan-Quinn criter. 17.12278F-statistic 1056.172 Durbin-Watson stat 0.034814Prob(F-statistic) 0.000000

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0

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4,0004,000

6,000

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2007 2008 2009 2010 2011 2012 2013

Residual Actual Fitted

LET'S ADD SOME MORE 'CATS AND DOGS'

Dependent Variable: DJIAMethod: Least SquaresDate: 10/11/13 Time: 07:20Sample (adjusted): 1/04/2007 10/04/2013Included observations: 1583 after adjustments

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White Heteroskedasticity-Consistent Standard Errors & Covariance

Variable Coefficient Std. Error t-Statistic Prob.

C 16168.56 103.1214 156.7915 0.0000CORPSPREAD(-1) -1247.905 57.17984 -21.82422 0.0000

VIXCLS(-1) -86.68247 5.108776 -16.96737 0.0000PAPERBILLSPREAD(-1) 674.9472 40.23692 16.77433 0.0000

SLOPEYC(-1) -449.4423 28.91532 -15.54340 0.0000

R-squared 0.666942 Mean dependent var 11933.80Adjusted R-squared 0.666098 S.D. dependent var 1867.028S.E. of regression 1078.849 Akaike info criterion 16.80833Sum squared resid 1.84E+09 Schwarz criterion 16.82528Log likelihood -13298.79 Hannan-Quinn criter. 16.81463F-statistic 789.9790 Durbin-Watson stat 0.053805Prob(F-statistic) 0.000000

SO THESE RHS VARIABLES ARE ALL PART OF THE INFORMATION SET

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0

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4,000 4,000

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2007 2008 2009 2010 2011 2012 2013

Residual Actual Fitted

LET'S ADD THE OBVIOUS - a lagged DJIA term

Dependent Variable: DJIAMethod: Least SquaresDate: 10/11/13 Time: 07:23Sample (adjusted): 1/04/2007 10/04/2013Included observations: 1582 after adjustments

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White Heteroskedasticity-Consistent Standard Errors & Covariance

Variable Coefficient Std. Error t-Statistic Prob.

C 26.39219 59.36265 0.444593 0.6567CORPSPREAD(-1) -17.51524 13.44292 -1.302935 0.1928

VIXCLS(-1) 1.845633 1.176906 1.568207 0.1170PAPERBILLSPREAD(-1) -28.88434 14.17016 -2.038392 0.0417

SLOPEYC(-1) -6.238820 3.475534 -1.795068 0.0728DJIA(-1) 0.998321 0.003233 308.8019 0.0000

R-squared 0.994691 Mean dependent var 11933.10Adjusted R-squared 0.994674 S.D. dependent var 1867.416S.E. of regression 136.2845 Akaike info criterion 12.67115Sum squared resid 29271790 Schwarz criterion 12.69151Log likelihood -10016.88 Hannan-Quinn criter. 12.67871F-statistic 59052.57 Durbin-Watson stat 2.144099Prob(F-statistic) 0.000000

CHECK OUT THE POWER OF YESTERDAY'S DJIA IN THE MODEL!

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2007 2008 2009 2010 2011 2012 2013

Residual Actual Fitted

LET'S

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67

TESTING THE EFFICIENT MARKET THEORY

Dependent Variable: DJIAMethod: Least SquaresDate: 10/10/13 Time: 12:55Sample (adjusted): 1/04/2007 10/04/2013Included observations: 1639 after adjustmentsWhite Heteroskedasticity-Consistent Standard Errors & Covariance

Variable Coefficient Std. Error t-Statistic Prob.

C 27.80542 26.44765 1.051338 0.2933DJIA(-1) 0.997742 0.002098 475.6008 0.0000

R-squared 0.994459 Mean dependent var 11850.64Adjusted R-squared 0.994456 S.D. dependent var 1910.876S.E. of regression 142.2824 Akaike info criterion 12.75472Sum squared resid 33139872 Schwarz criterion 12.76132Log likelihood -10450.50 Hannan-Quinn criter. 12.75717F-statistic 293808.2 Durbin-Watson stat 2.218066Prob(F-statistic) 0.000000

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2007 2008 2009 2010 2011 2012 2013

Residual Actual Fitted

ADD LAGS

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Dependent Variable: DJIAMethod: Least SquaresDate: 10/10/13 Time: 12:56Sample (adjusted): 1/30/2007 10/04/2013Included observations: 1114 after adjustmentsWhite Heteroskedasticity-Consistent Standard Errors & Covariance

Variable Coefficient Std. Error t-Statistic Prob.

C 41.65038 30.70866 1.356308 0.1753DJIA(-1) 0.874143 0.043242 20.21502 0.0000DJIA(-2) 0.081718 0.067250 1.215134 0.2246DJIA(-3) 0.047933 0.065094 0.736358 0.4617DJIA(-4) -0.013973 0.061607 -0.226812 0.8206DJIA(-5) -0.020373 0.063273 -0.321994 0.7475DJIA(-6) 0.023064 0.072414 0.318501 0.7502DJIA(-7) -0.036536 0.067062 -0.544818 0.5860DJIA(-8) 0.102430 0.070459 1.453754 0.1463DJIA(-9) -0.074870 0.069470 -1.077729 0.2814

DJIA(-10) 0.012848 0.049960 0.257175 0.7971

R-squared 0.994211 Mean dependent var 11839.00Adjusted R-squared 0.994158 S.D. dependent var 1929.595S.E. of regression 147.4832 Akaike info criterion 12.83513Sum squared resid 23991675 Schwarz criterion 12.88466Log likelihood -7138.168 Hannan-Quinn criter. 12.85386F-statistic 18941.78 Durbin-Watson stat 2.026282Prob(F-statistic) 0.000000

NOTE - NONE OF THE ADDED LAGS ARE SIGNIFICANT - THE FIT HAS NOT CHANGED

LET'S CHECK OUT THE RESIDUALS - THE FORECAST ERRORS - SAME AS PREDICTING THE CHANGE IN THE DJIA FROM ONE DAY TO THE NEXT"

Dependent Variable: FEMethod: Least SquaresDate: 10/11/13 Time: 07:46Sample (adjusted): 1/04/2007 10/04/2013Included observations: 1582 after adjustmentsWhite Heteroskedasticity-Consistent Standard Errors & Covariance

Variable Coefficient Std. Error t-Statistic Prob.

C 60.86573 44.64669 1.363275 0.1730DJIA(-1) -0.003049 0.002490 -1.224893 0.2208

CORPSPREAD(-1) -3.948232 12.29165 -0.321213 0.7481PAPERBILLSPREAD(-1) -18.76430 13.35854 -1.404667 0.1603

SLOPEYC(-1) -5.431679 3.444850 -1.576753 0.1151

R-squared 0.005825 Mean dependent var 0.688103Adjusted R-squared 0.003303 S.D. dependent var 136.7859S.E. of regression 136.5597 Akaike info criterion 12.67456Sum squared resid 29408787 Schwarz criterion 12.69152

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Log likelihood -10020.57 Hannan-Quinn criter. 12.68086F-statistic 2.309998 Durbin-Watson stat 2.176839Prob(F-statistic) 0.055856

AS YOU CAN SEE, YOU CANNOT PREDICT THE FORECAST ERROR TODAY, WITH INFORMATION YESTERDAY! HERE WE SAY TODAY'S FORECAST ERROR IS ORTHOGONAL TO YESTERDAY'S INFORMATION SET - WE DID THE BEST WE COULD - THIS NEWS IS UNPREDICTABLE!

LET'S CHECK TO SEE IF THE FORECAST ERRORS ARE AUTO-CORRELATED - THAT IS, DO THEY HAVE A PATTERN

Dependent Variable: FEMethod: Least SquaresDate: 10/11/13 Time: 07:52Sample (adjusted): 1/05/2007 10/04/2013Included observations: 1577 after adjustmentsNewey-West HAC Standard Errors & Covariance (lag truncation=7)

Variable Coefficient Std. Error t-Statistic Prob.

C 0.310619 3.417839 0.090882 0.9276FE(-1) -0.104658 0.032695 -3.200989 0.0014

R-squared 0.011214 Mean dependent var 0.366532Adjusted R-squared 0.010586 S.D. dependent var 141.6477S.E. of regression 140.8960 Akaike info criterion 12.73519Sum squared resid 31266408 Schwarz criterion 12.74199Log likelihood -10039.70 Hannan-Quinn criter. 12.73772F-statistic 17.86160 Durbin-Watson stat 2.031995Prob(F-statistic) 0.000025

HERE WE HAVE A SLIGHT VIOLATION OF THE EMT - INTERPRET??

ADD MORE LAGS - NOT MUCH HELP

Dependent Variable: FEMethod: Least SquaresDate: 10/11/13 Time: 07:54Sample (adjusted): 1/11/2007 10/04/2013Included observations: 1339 after adjustmentsNewey-West HAC Standard Errors & Covariance (lag truncation=7)

Variable Coefficient Std. Error t-Statistic Prob.

C -0.334619 3.864469 -0.086589 0.9310FE(-1) -0.111541 0.038642 -2.886483 0.0040FE(-2) -0.042194 0.052573 -0.802573 0.4224FE(-3) 0.011283 0.041409 0.272488 0.7853FE(-4) -0.016290 0.040956 -0.397734 0.6909FE(-5) -0.026073 0.046839 -0.556660 0.5779

R-squared 0.014599 Mean dependent var -0.302586Adjusted R-squared 0.010903 S.D. dependent var 144.2587S.E. of regression 143.4701 Akaike info criterion 12.77460

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Sum squared resid 27438023 Schwarz criterion 12.79790Log likelihood -8546.595 Hannan-Quinn criter. 12.78333F-statistic 3.949889 Durbin-Watson stat 2.049769Prob(F-statistic) 0.001468

LET'S CHECK OUT THE ERRORS FROM THE MODEL WITHOUT DJIA - I COPY AND PASTE FROM ABOVE

Dependent Variable: DJIAMethod: Least SquaresDate: 10/11/13 Time: 07:20Sample (adjusted): 1/04/2007 10/04/2013Included observations: 1583 after adjustmentsWhite Heteroskedasticity-Consistent Standard Errors & Covariance

Variable Coefficient Std. Error t-Statistic Prob.

C 16168.56 103.1214 156.7915 0.0000CORPSPREAD(-1) -1247.905 57.17984 -21.82422 0.0000

VIXCLS(-1) -86.68247 5.108776 -16.96737 0.0000PAPERBILLSPREAD(-1) 674.9472 40.23692 16.77433 0.0000

SLOPEYC(-1) -449.4423 28.91532 -15.54340 0.0000

R-squared 0.666942 Mean dependent var 11933.80Adjusted R-squared 0.666098 S.D. dependent var 1867.028S.E. of regression 1078.849 Akaike info criterion 16.80833Sum squared resid 1.84E+09 Schwarz criterion 16.82528Log likelihood -13298.79 Hannan-Quinn criter. 16.81463F-statistic 789.9790 Durbin-Watson stat 0.053805Prob(F-statistic) 0.000000

SO THESE RHS VARIABLES ARE ALL PART OF THE INFORMATION SET

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-4,000

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2007 2008 2009 2010 2011 2012 2013

Residual Actual Fitted

I LABELED THESE ERRORS AS WITHOUTDJIARESIDS

Dependent Variable: WITHOUTDJIARESIDSMethod: Least SquaresDate: 10/11/13 Time: 08:01Sample (adjusted): 1/04/2007 10/04/2013Included observations: 1582 after adjustmentsNewey-West HAC Standard Errors & Covariance (lag truncation=7)

Variable Coefficient Std. Error t-Statistic Prob.

C -3919.148 494.1908 -7.930436 0.0000DJIA(-1) 0.328474 0.040920 8.027284 0.0000

R-squared 0.323801 Mean dependent var 0.057241Adjusted R-squared 0.323373 S.D. dependent var 1077.822S.E. of regression 886.5876 Akaike info criterion 16.41390Sum squared resid 1.24E+09 Schwarz criterion 16.42068Log likelihood -12981.40 Hannan-Quinn criter. 16.41642F-statistic 756.5915 Durbin-Watson stat 0.099424Prob(F-statistic) 0.000000

SO THERE IS INFORMATION AVAILABLE IN YESTERDAY'S INFORMATION SET THAT IS NOT BEING USED - VIOLATION OF THE EMT

DO THESE ERRORS HAVE A PATTERN?

72

Dependent Variable: WITHOUTDJIARESIDSMethod: Least SquaresDate: 10/11/13 Time: 08:04Sample (adjusted): 1/05/2007 10/04/2013Included observations: 1494 after adjustmentsNewey-West HAC Standard Errors & Covariance (lag truncation=7)

Variable Coefficient Std. Error t-Statistic Prob.

C 1.787490 3.933498 0.454428 0.6496WITHOUTDJIARESIDS(-1) 0.976777 0.005286 184.7729 0.0000

R-squared 0.946850 Mean dependent var -8.203185Adjusted R-squared 0.946815 S.D. dependent var 1079.034S.E. of regression 248.8461 Akaike info criterion 13.87288Sum squared resid 92391176 Schwarz criterion 13.87999Log likelihood -10361.04 Hannan-Quinn criter. 13.87553F-statistic 26579.66 Durbin-Watson stat 2.849583Prob(F-statistic) 0.000000

YES!!! THE ERRORS FROM THE INCOMPLETE MODEL ARE HIGHLY AUTOCORRELATED - IF POSITIVE TODAY, POSITIVE TOMORROW AND VICA VERSA

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The Wall Street Journal tested this random walk proposition by comparing the return of professional investors against a portfolio that was chosen by throwing darts. For more information, see:

Journal's Dartboard RetiresAfter 14 Years of Stock Picks

By GEORGETTE JASEN Staff Reporter of THE WALL STREET JOURNAL

Below is a graphic summarizing the results:

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Most economists believe that all three of the asset markets; stocks, bonds, and foreign exchange are quite efficient.

This article contains a discussion among two very prominent economists from the University of Chicago about how efficient the ‘market’ may or may not be..

October 18, 2004

PAGE ONE

Stock CharactersAs Two Economists

Debate Markets,The Tide Shifts

Belief in Efficient ValuationYields Ground to RoleOf Irrational InvestorsMr. Thaler Takes On Mr. Fama

By JON E. HILSENRATH Staff Reporter of THE WALL STREET JOURNALOctober 18, 2004; Page A1

For forty years, economist Eugene Fama argued that financial markets were highly efficient in reflecting the underlying value of stocks. His long-time intellectual nemesis, Richard Thaler, a member of the "behaviorist" school of economic thought, contended that markets can veer off course when individuals make stupid decisions.

In May, 116 eminent economists and business executives gathered at the University of Chicago Graduate School of Business for a

conference in Mr. Fama's honor. There, Mr. Fama surprised some in the audience. A paper he presented, co-authored with

a colleague, made the case that poorly informed investors could

75

theoretically lead the market astray. Stock prices, the paper said, could become "somewhat irrational."

Coming from the 65-year-old Mr. Fama, the intellectual father of the theory known as the "efficient-market hypothesis," it struck some as an unexpected concession. For years, efficient market theories were dominant, but here was a suggestion that the behaviorists' ideas had become mainstream.

"I guess we're all behaviorists now," Mr. Thaler, 59, recalls saying after he heard Mr. Fama's presentation.

Roger Ibbotson, a Yale University professor and founder of Ibbotson Associates Inc., an investment advisory firm, says his reaction was that Mr. Fama had "changed his thinking on the subject" and adds: "There is a shift that is taking place. People are recognizing that markets are less efficient than we thought." Mr. Fama says he has been consistent.

The shift in this long-running argument has big implications for real-life problems, ranging from the privatization of Social Security to the regulation of financial markets to

the way corporate boards are run. Mr. Fama's ideas helped foster the free-market theories of the 1980s and spawned the $1 trillion index-fund industry. Mr. Thaler's theory suggests policy makers have an important role to play in guiding markets and individuals where they're prone to fail.

Take, for example, the debate about Social Security. Amid a tight election battle, President Bush has set a goal of partially privatizing Social Security by allowing younger workers to put some of their payroll taxes into private savings accounts for their retirements.

In a study of Sweden's efforts to privatize its retirement system, Mr. Thaler found that Swedish investors tended to pile into risky

technology stocks and invested too heavily in domestic stocks. Investors had too many options, which limited their ability to make good decisions, Mr. Thaler concluded. He thinks U.S. reform, if it happens, should be less flexible. "If you give people 456 mutual funds to choose from, they're not going to make great choices," he says.

If markets are sometimes inefficient, and stock prices a flawed measure of value, corporate boards and management teams would have to rethink the way they compensate executives and judge their performance. Michael Jensen, a retired Harvard economist who worked on efficient-market theory earlier in his career, notes a big lesson from the 1990s was that overpriced stocks could lead executives into bad decisions, such as massive overinvestment in telecommunications during the technology boom.

Even in an efficient market, bad investments occur. But in an inefficient market where prices can be driven way out of whack, the problem is acute. The solution, Mr. Jensen

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says, is "a major shift in the belief systems" of corporate boards and changes in compensation that would make executives less focused on stock price movements.

Few think the swing toward the behaviorist camp will reverse the global emphasis on open economies and free markets, despite the increasing academic focus on market breakdowns. Moreover, while Mr. Fama seems to have softened his thinking over time, he says his essential views haven't changed.

A product of Milton Friedman's Chicago School of thought, which stresses the virtues of unfettered markets, Mr. Fama rose to prominence at the University of Chicago's Graduate School of Business. He's an avid tennis player, known for his disciplined style of play. Mr. Thaler, a Chicago professor whose office is on the same floor as Mr. Fama's, also plays tennis but takes riskier shots that sometimes land him in trouble. The two men have stakes in investment funds that run according to their rival economic theories.

Highbrow Insults

Neither shies from tossing about highbrow insults. Mr. Fama says behavioral economists like Mr. Thaler "haven't really established anything" in more than 20 years of research. Mr. Thaler says Mr. Fama "is the only guy on earth who doesn't think there was a bubble in Nasdaq in 2000."

In its purest form, efficient-market theory holds that markets distill new information with lightning speed and provide the best possible estimate of the underlying value of listed companies (IT’S THE FUNDAMENTALS – RECALL THE EQUATION). As a result, trying to beat the market, even in the long term, is an exercise in futility because it adjusts so quickly to new information.

Behavioral economists argue that markets are imperfect because people often stray from rational decisions. They believe this behavior creates market breakdowns and also buying opportunities for savvy investors(THIS IN A SENSE IS ARGUING THAT YOU CAN BEAT THE MARKET AT CERTAIN TIMES!) Mr. Thaler, for example, says stocks can under-react to good news because investors are wedded to old views about struggling companies.

For Messrs. Thaler and Fama, this is more than just an academic debate (WHAT DOES MORE THAN ACADEMIC MEAN??). Mr. Fama's research helped to spawn the idea of passive money management and index funds. He's a director at Dimensional Fund Advisers, a private investment management company with $56 billion in assets under management. Assuming the market can't be beaten, it invests in broad areas rather than picking individual stocks. Average annual returns over the past decade for its biggest fund -- one that invests in small, undervalued stocks -- have been about 16%, four percentage points better than the S&P 500, according to Morningstar Inc., a mutual-fund research company.

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Mr. Thaler, meanwhile, is a principal at Fuller & Thaler, a fund management company with $2.4 billion under management. Its asset managers spend their time trying to pick stocks and outfox the market (TRYING TO PICK WINNERS!) The company's main growth fund, which invests in stocks that are expected to produce strong earnings growth, has delivered average annual returns of 6% since its inception in 1997, three percentage points better than the S&P 500.

Mr. Fama came to his views as an undergraduate student in the late 1950s at Tufts University when a professor hired him to work on a market-forecasting newsletter. There, he discovered that strategies designed to beat the market didn't work well in practice. By the time he enrolled at Chicago in 1960, economists were viewing individuals as rational, calculating machines whose behavior could be predicted with mathematical models. Markets distilled these differing views with unique precision, they argued.

"In an efficient market at any point in time the actual price of a security will be a good estimate of its intrinsic value," Mr. Fama wrote in a 1965 paper titled "Random Walks in Stock Market Prices." Stock movements were like "random walks" because investors could never predict what new information might arise to change a stock's price. In 1973, Princeton economist Burton Malkiel published a popularized discussion of the hypothesis, "A Random Walk Down Wall Street," which sold more than one million copies.

Mr. Fama's writings underpinned the Chicago School's faith in the functioning of markets. Its approach, which opposed government intervention in markets, helped reshape the 1980s and 1990s by encouraging policy makers to open their economies to market forces. Ronald Reagan and Margaret Thatcher ushered in an era of deregulation and later Bill Clinton declared an end to big government. After the collapse of Communist central planning in Russia and Eastern Europe, many countries embraced these ideas.

As a young assistant professor in Rochester in the mid-1970s, Mr. Thaler had his doubts about market efficiency. People, he suspected, were not nearly as rational as economists assumed.

Mr. Thaler started collecting evidence to demonstrate his point, which he published in a series of papers. One associate kept playing tennis even though he had a bad elbow because he didn't want to waste $300 on tennis club fees. Another wouldn't part with an expensive bottle of wine even though he wasn't an avid drinker. Mr. Thaler says he caught economists bingeing on cashews in his office and asking for the nuts to be taken away because they couldn't control their own appetites (THESE ARE SUPPOSEDLY EXAMPLES OF IRRATIONAL BEHAVIOR)

Mr. Thaler decided that people had systematic biases that weren't rational, such as a lack of self-control (LACK OF SELF CONTROL – THALER WANTS TO EXPLOIT THIS!!). Most economists dismissed his writings as a collection of quirky anecdotes,

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so Mr. Thaler decided the best approach was to debunk the most efficient market of them all -- the stock market.

Small Anomalies

Even before the late 1990s, Mr. Thaler and a growing legion of behavioral finance experts were finding small anomalies that seemed to fly in the face of efficient-market theory. For example, researchers found that value stocks, companies that appear undervalued relative to their profits or assets, tended to outperform growth stocks, ones that are perceived as likely to increase profits rapidly. If the market was efficient and impossible to beat, why would one asset class outperform another? (Mr. Fama says there's a rational explanation: Value stocks come with hidden risks and investors are rewarded for those risks with higher returns.)

Moreover, in a rational world, share prices should move only when new information hit the market. But with more than one billion shares a day changing hands on the New York Stock Exchange, the market appears overrun with traders making bets all the time.

Robert Shiller, a Yale University economist, has long argued that efficient-market theorists made one huge mistake: Just because markets are unpredictable doesn't mean they are efficient. The leap in logic, he wrote in the 1980s, was one of "the most remarkable errors in the history of economic thought." Mr. Fama says behavioral economists made the same mistake in reverse: The fact that some individuals might be irrational doesn't mean the market is inefficient (IN OTHER WORDS, AS LONG AS THE MAJORITY OF INVESTORS ARE RATIONAL THEN MARKETS WILL BE EFFICIENT – ADD IN THE FOOTBALL BETTING THESIS)

Shortly after the stock market swooned, Mr. Thaler presented a new paper at the University of Chicago's business school. Shares of handheld-device maker Palm Inc. -- which later split into two separate companies -- soared after some of its shares were sold in an initial public offering by its parent, 3Com Corp., in 2000, he noted. The market gave Palm a value nearly twice that of its parent even though 3Com still owned 94% of Palm. That in effect assigned a negative value to 3Com's other assets. Mr. Thaler titled the paper, "Can the Market Add and Subtract?" It was an unsubtle shot across Mr. Fama's bow. Mr. Fama dismissed Mr. Thaler's paper, suggesting it was just an isolated anomaly. "Is this the tip of an iceberg, or the whole iceberg?" he asked Mr. Thaler in an open discussion after the presentation, both men recall (HIGH BROW INSULT FOR SURE!!)

Mr. Thaler's views have seeped into the mainstream through the support of a number of prominent economists who have devised similar theories about how markets operate. In 2001, the American Economics Association awarded its highest honor for young economists -- the John Bates Clark Medal -- to an economist named Matthew Rabin who devised mathematical models for behavioral theories (I WONDER IF THESE MATHEMATICAL MODELS FAILED RECENTLY??) . In 2002, Daniel Kahneman won a Nobel Prize for pioneering research in the field of behavioral economics. Even Federal Reserve Chairman Alan Greenspan, a firm believer in the benefits of free

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markets, famously adopted the term "irrational exuberance" in 1996 (PARSE THIS TERM! RECALL THALER ARGUES THAT AT TIMES, PEOPLE EXPERIENCE LACK OF CONTROL!)

Andrew Lo, an economist at the Massachusetts Institute of Technology's Sloan School of Management, says efficient-market theory was the norm when he was a doctoral student at Harvard and MIT in the 1980s (OF COURSE IT WAS THE NORM!!! )"It was drilled into us that markets are efficient. It took me five to 10 years to change my views." In 1999, he wrote a book titled, "A Non-Random Walk Down Wall Street."

In 1991, Mr. Fama's theories seemed to soften. In a paper called "Efficient Capital Markets: II," he said that market efficiency in its most extreme form -- the idea that markets reflect all available information so that not even corporate insiders can beat it -- was "surely false." Mr. Fama's more recent paper also tips its hand to what behavioral economists have been arguing for years -- that poorly informed investors could distort stock prices.

But Mr. Fama says his views haven't changed. He says he's never believed in the pure form of the efficient-market theory. As for the recent paper, co-authored with longtime collaborator Kenneth French, it "just provides a framework" for thinking about some of the issues raised by behaviorists, he says in an e-mail. "It takes no stance on the empirical importance of these issues."

The 1990s Internet investment craze, Mr. Fama argues, wouldn't have looked so crazy if it had produced just one or two blockbuster companies, which he says was a reasonable expectation at the time. Moreover, he says, market crashes confirm a central tenet of efficient market theory -- that stock-price movements are unpredictable. Findings of other less significant anomalies, he says, have grown out of "shoddy" research.

Defending efficient markets has gotten harder, but it's probably too soon for Mr. Thaler to declare victory. He concedes that most of his retirement assets are held in index funds, the very industry that Mr. Fama's research helped to launch. And despite his research on market inefficiencies, he also concedes that "it is not easy to beat the market, and most people don't." (PUT YOUR MONEY WHERE YOUR MOUTH IS AND NO KIDDING, IT IS TOUGH TO BEAT THE MARKET!)

Write to Jon E. Hilsenrath at jon.hilsenrath@wsj.com1

URL for this article:http://online.wsj.com/article/0,,SB109804865418747444,00.html

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Using technical analysis

Although there are many, these Bollinger Bands examples will give us a good feel for the notion of technical analysis. Note that technical analysis is completely removed from the fundamentals, which are based on expected profits and interest rates. As such, “technical analysts” are often referred to as “chart watchers,” as the following, as the following analysis demonstrates.

Bollinger bands are a very useful and popular technique in predicting stock movements. They provide many useful signals, such as whether a price is relatively high or low, whether a current trend is likely to continue or reverse, and market volatility. What separates Bollinger bands from most other price channeling techniques is in the way the bands are derived. Rather than setting the channels at a fixed percentage above and below the moving average, Bollinger bands are plotted two standard deviations above and below the moving average. This is done to ensure that 95% of price data will fall between the bands. It also ensures that the bands are sensitive to volatility.

When speaking of market trends, Bollinger bands can provide a signal based on both penetrations of the bands, as well as width of the bands. A penetration of either band, high or low, implies a continuation of the current trend. When the bands move far apart relative to the norm, the current trend may be ending. If the bands are unusually tight, it may be a sign of a new trend beginning.

Price targets can also be achieved through the use of Bollinger bands. For example, if a price is moving along the lower band and proceeds to cross above the moving average, the upper band will become a price target. Of course, the opposite also applies.

Finally, momentum can also be checked through the use of Bollinger bands. If a price is seen to move above or below a band, and on a subsequent move, fails to reach the band for a second time, there is a good chance that momentum is being lost and a reversal may be in the works. It is important to note that even if the subsequent move reaches a higher or lower price, it must still penetrate the respective band in order to indicate lasting momentum.

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Bollinger Bands – Test One

Above we see a current six-month chart of Dell Inc. (DELL) The standard set up for use of Bollinger bands includes a six-month chart, along with a 20-day moving average. Starting from the left portion of the graph, you can see the sell signals, indicated by red arrows. As you can see, as the price bars pass through the bottom band during mid-March, a trend may be starting. In addition, the bands are fairly tight during this time period. As we progress into the early and middle of April, the lower band continues to be penetrated by the price, confirming the downtrend. As the bands widen into May, the price begins to stabilize and then rise. Dell’s price then crosses through the moving average and continues up through the upper band. However, it does not continue to hug the band, so no uptrend can be confirmed. As the bands become very wide through late May and early June, the price evens out. Two more potential buy signals are seen in June and July, but once again, only for a couple of days at a time. During this time, attention should also be focused on the bands, which are once again becoming tighter.

Looking back on what was just covered; it is safe to say that the rules regarding Bollinger bands seem to work just as described. For each change in price, the bands properly adjusted and did not provide any erratic signals. That being said, the buy and sell signals shown on the graph should not be immediately followed as soon as a band is penetrated. While each instance would provide a profit if followed, most would be minimal.

Using the rules provided by Bollinger bands, it would seem quite easy to predict the short-term future for Dell’s stock price. However, there are no definitive movements currently in progress. We can still take a look at what the chart is showing us and try to make an educated guess. The bands are beginning to widen once again, implying less volatility. The price has recently dropped below the moving average and seems to be staying somewhat near the lower band. The price drop does not appear to look dramatically sharp, and looking at similar trends and price levels throughout the past six months, it seems as though there will be no drastic price changes in the near future. But,

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if the price continues to descend throughout the following week and eventually hugs the bottom band, there is a good chance we may be seeing the start of a downtrend worth moving in on with a short-position.

Bollinger Bands – Test TwoTo get a better view of the accuracy and potential gains associated with Bollinger

bands, let’s take a look at some more examples and see how they fare. The chart below depicts the current state of Ford Motor Company’s (F) stock. It provides a good look at a consistent downtrend beginning in late February through mid-April. Taking a short position at first sign of a downtrend on February 25 at a price of 13.00 and riding it out through April 22 at 9.89 would provide a change of 23.92%. Comparing this change to the S&P 500 rate of 4.89%, we can undoubtedly say that we would have beaten the market. Also interesting to point out is the single buy signal, which if followed would provide a false signal, and thus a loss.

Bollinger Bands – Test ThreeThe next chart shows the previous six months of International Business Machines

(IBM) stock and a good opportunity to profit from both the drop and rise in price during this time. If a short position was taken at the first sell signal on March 22 at a price of 89.50 and held onto until it was clear that the trend was over on, say, April 26 at 74.65, then it would clearly show a market beating opportunity (-16.59% change). During the same time period, the S&P 500 was growing at a rate of -1.70%, so it is clear that following the bands would have paid off.

In the second part, taking a long position at the sign of an uptrend starting July 11 at a price of 78.96 and selling off on July 22 (84.44) once it appears the trend is over, another profitable opportunity is seen. A change of 6.94% is seen, as compared to the S&P 500 of 1.17%.

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Bollinger bands can provide information about the market that many other technical strategies cannot. When seeking information regarding volatility, the bands are second to none. Furthermore, once locked into a trend, Bollinger bands can give us a very good idea of what to expect in the near future. One needs to use caution when studying Bollinger bands however, as prices movements which penetrate the outer bands do not always send the correct signal. Instead, it is the movement that occurs near the outer bands that is most important, especially when the movements are consistent. That is where the real strength of Bollinger bands shines through.

Key Terms

1. Stock price determination formula.2. The efficient market theory.3. Autoregressive properties.4. Technical analysis.5. Jawboning.6. Price to earnings ratio.7. Earnings per share.8. Inside information.9. Random walk.10. Two Crystal Balls11. Bollinger bands

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Exam #1Econ 351

Spring 2015Good Luck!

Name ______________________________________ Last 4 PSU ID __________

Please put the first two letters of your last name on the top right hand corner of this cover sheet. Also, ONLY NON-PROGRAMMABLE CALCULATORS ARE ALLOWED - THERE ARE NO SUBSTITUTES. THANKS FOR YOUR COOPERATION!

GOOD LUCK!!!

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1. (30 points total)

a) (10 points) The Table below is from January 31, 2015 so that these Jan 30 options have already expired. The ‘last’ column for all the 8 options is wrong. Please enter the correct last sale price to the left of the existing and wrong last sale price for all 8 options.

b) (20 points total) We are going to evaluate two of the futures bets I made on Stock Trak using the boardofdart account.... I went short on Platinum and short on Feeder Cattle by selling March 2015 futures contracts. The pertinent information is below, please answer the following questions: (for full credit, please show all work).

Prices in table were those that prevailed on Feb 3, when I made the bets.

Contract Margin Requirement (each contract)

# of Contracts Contract Size (each contract)

Price

Platinum $3,465 15 50 troy ounces $1,200 per troy ounce

Feeder cattle $2,025 10 50,000 lbs. $ 2.00 per pound

As of Friday, February 13, 2015, the (March) futures price of Platinum was $1,212 per troy ounce and the (March) futures price of feeder cattle was $2.04 per pound. I am closing both positions since my ‘fur is burning.’

(5 points) Considering the bet on Platinum, what is the $ value of each Platinum futures contract when I initially made the bet and what is the leverage ratio (please take the leverage ratio to three decimal spaces)?

b) (5 points) Calculate the rate of return when I close using the leverage ratio and the percent change in the price of platinum. What is my profit or loss?

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c) (5 points) Now consider the bet on feeder cattle. What is the $ value of each feeder cattle futures contract when I initially made the bet and what is the leverage ratio (please take the leverage ratio to three decimal spaces)?

d) (5 points) Calculate the rate of return when I close using the leverage ratio and the percent change in the price of feeder cattle. What is my profit or loss?

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3. (35 poits total)

Use the three tables below to answer the following questionsTable 1

Table 2

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Table 3

a) (5 points) Suppose we play a long straddle by purchasing one 535 call option and one 535 put option at Table 1 and close both positions on Table 2. Calculate the profit or loss AND rate of return.

b) (5 points) Suppose instead that we waited and closed on Table 3, calculate the profit or loss and rate of return. How much money did we make (+) or lose (-) by waiting until Table 3 to close as compared to closing on Table 2.

c) (5 points) Suppose we play a strangle by buying a 545 call and a 525 put on Table 1 and close at Table 2. How much money did we make (+) or lose (-) by waiting until Table 3 to close as compared to closing on Table 2.

d) (5 points) Name two reasons why each of the options (2 reasons for call and put) in the strangle above are so cheap on Table 3! Be very specific

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e) (5 points) Suppose your friend plays a short straddle by writing one 535 call and writing one 535 put on Table 1 and closes on Table 3. How much does your friend make (+) or lose (-)? Does your answer relate to one of your answers above – why or why not? Explain.

.

f) (5 points) Suppose we gave your friend who played the short straddle a choice to close as above at Table 3 (choice 1) or to close at expiration assuming the spot price of Google remains as it is at Table 3 until expiration (choice 2). Compare the difference in losses or profits if they close at Table 3 vs. waiting until expiration (again, assume price is frozen until expiration as in Table 3).

g) (5 points) Considering your answer in part f), explain what would determine the magnitude of the difference between closing at Table 3 or waiting until expiration with the spot price frozen at Table 3.

3) (40 points total)

a) (20 points) We are now going to graph the profit functions for the long and short straddle as above where we opened up the positions at Table 1. We are only going to plot the profit / loss for both players for one point, let's call it point B, with the spot at expiration as it is in Table 2: spot = $510.66 (there are two points B's, one for player of short straddle and one for player of long straddle). Be sure to include the math as to how you calculated the payoffs for each player and prove that this is indeed a zero sum game! Be sure to label the break even points (there are two of them!).

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b) (20 points) We are now going to graph the profit functions for the strangle for both the buyer and writer of the strangle above where both players opened up the positions at Table 1. We are only going to plot the profit / loss for both players for one point, let's call them points B, with the spot at expiration as it is in Table 2: spot = $510.66 (there are two points B's, one for buyer of the strangle and one for the writer of the strangle). Be sure to include the math as to how you calculated the payoffs for each player and prove that this is indeed a zero sum game! Be sure to label the break even points (there are two of them!).

4. (25 points total)

a) (5 points) Suppose you purchased the 540 put at Table 1 and close the position on Table 2. Calculate the profit/loss and rate of return (please show work).

b) (5 points) Plot the evolution of the premium of the 540 put that you purchased on Table 1 assuming that the spot price of Google is frozen as it is in Table 1.

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c) (15 points) In the space below, graph the profit function of the 540 put that you purchased on Table 1 given the following three scenarios:

Scenario 1): the option expires with the spot price of GOOG as it is on Table 1 and your position is closed. Locate this point on your diagram as point A, clear labeling the profit or loss associated with this scenario.

Scenario 2): the option expires with the spot price of GOOG as it is on Table 2 and your position is closed. Locate the specific profit or loss on your diagram and label as point B.

Scenario 3): the option expires with the spot price of GOOG as it is on Table 3 and your position is closed. Locate the specific profit or loss on your diagram and label as point C.

5. (30 points) Let’s pretend that you graduated in December of 2014 and you scored a job as chief financial officer for a golf resort in New York. Your ‘season’ ended in the fall and the person that you replaced 'parked' all the cash made during the 2014 golf season in ten year Government securities. In particular, they purchased 10 ten year Treasury contracts during the fall of 2014. The CEO, let's call her Betty, tells you that you need to use those 10 ten year Treasury contracts to pay taxes in April of this year (2014).

a) (5 points) So Betty comes to you and tells you that she can't sleep because of this stress and asks you to buy insurance (make a hedge) against bad things happening (in terms of paying the tax bill). What are the bad things happening and how can you make the hedge? I am looking for 3 different hedges.

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So here we are in the January of 2015 and you are considering three different hedges:

Scenario #1: You sell 10 March futures contracts for 132 and the price at expiration is 135.

Scenario #2: You buy 10 March futures option puts with a strike price at 132 for a price of $3,000 per put and the price at expiration is 135.

Scenario #3: You write 10 March futures option calls with a strike price of 132 for a price of $3,000 per call and the price at expiration is 135.

b) (10 points) Compare the revenue obtained to pay the tax bill under each scenario and rank them accordingly from highest to lowest. Please show all work.

c) (15 points) Given that these March futures contracts expire at 135, please draw your profit functions for each of the three scenarios above. In particular, draw the futures profit function, the futures option puts profit function and the profit function for writing the calls all on the same diagram. Be sure to label each profit function and label as points 1, 2, and 3 to coincide with each scenario. Be sure to label all the break even points.

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6. (30 points) So the next day, Betty comes to you and tells you that she plans to do some renovations to the resort next winter (in December 2015) and wants to do some more hedging since she really trusts you and your excellent education at Penn State University. The resort makes some serious cash beginning in May and ending in early September. She wants you to 'park' half of the seasons money in Treasuries by buying 10 June Treasury contracts and then wants you to sell these Treasuries in December to pay for the renovations. So it is Jan 2015 and you need to do some more hedging by playing the futures market.

a) (5 points) What is your natural position in June and how could you hedge against bad things happening? Name the three hedges and make sure you explain what we mean by 'bad things happening.'

The June hedge - consider the following 3 scenarios

So it is still in January of 2015 and there are futures options, both calls and puts available with a strike price of 123 for $3,000 each. Consider the following 3 scenarios.

Scenario #1: You buy 10 June futures contracts for 123 and the price at expiration is 127.

Scenario #2: You buy 10 June futures option calls with a strike price at 123 for a price of $3,000 per call and the price at expiration is 127.

Scenario #3: You write 10 June futures option puts with a strike price of 123 for a price of $3,000 per put and the price at expiration is 127.

b) (10 points) Compare the costs of acquiring the 10 Treasury contracts in June for each scenario and rank them accordingly from lowest cost to highest cost. Please show all work.

c) (15 points) Given that these June futures contracts expire at 127, please draw your profit functions for each of the three scenarios above. In particular, draw the futures profit function, the futures option calls profit function and the profit function for writing the puts all on the same diagram. Be sure to label each profit function and label as points 1, 2, and 3 to coincide with each scenario. Be sure to label all the break even points.

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7. (50 points total) Now on to the December Hedges:

a) (5 points) What is your natural position in December and how could you hedge against bad things happening? Name the three hedges and make sure you explain what we mean by 'bad things happening.'

Scenario #1: You sell 10 December futures contracts for 125 and the price at expiration is 128.

Scenario #2: You buy 10 December futures option puts with a strike price at 125 for a price of $3,000 per put and the price at expiration is 128.

Scenario #3: You write 10 December futures option calls with a strike price of 125 for a price of $3,000 per call and the price at expiration is 128.

b) (10 points) Compare the revenue obtained to pay for the new equipment under each scenario and rank them accordingly from highest to lowest. Please show all work.

c) (15 points) Given that these December futures contracts expire at 128, please draw your profit functions for each of the three scenarios above. In particular, draw the futures profit function, the futures option puts profit function and the profit function for writing the calls all on the same diagram. Be sure to label each profit function and label as points 1, 2, and 3 to coincide with each scenario. Be sure to label all the break even points.

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d) (10 points) So let us pretend your are at the paving company's Holiday party in December of 2015 and the CEO, Lee, wants to give you a Holiday bonus. Lee gives you an envelope and tells you that he decided to give you 20% of the money you saved the paving company given all the hedging. We assume, importantly, that you had a crystal ball the whole time and played the best hedge for each of the three hedges (March, June and December). Compare the total revenue left for buying the equipment assuming you played the best hedge to the total revenue that you would have left for the new equipment if you went naked and didn't hedge at all. How much is the check for or is the envelope empty? Please show all work.

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Exam #1Econ 351Fall 2014

Good Luck!

Name ______________________________________ Last 4 PSU ID __________

Please put the first two letters of your last name on the top right hand corner of this cover sheet. Also, ONLY NON-PROGRAMMABLE CALCULATORS ARE ALLOWED - THERE ARE NO SUBSTITUTES. THANKS FOR YOUR COOPERATION!

GOOD LUCK!!!

97

1. (30 points total) We are going to evaluate two of the bets I made on Stock Trak.... I went long on gold by buying 10 Dec 2014 futures contracts and I went short on heating oil by selling 10 Dec 2014 contracts. The pertinent information is below, please answer the following questions: (for full credit, please show all work).

Prices in table were those that prevailed when I made the bets.

Contract Margin Requirement (each contract)

# of Contracts Contract Size (each contract)

Price

Gold $8,800 10 100 oz $1,290 per ozHeating Oil $4,290 10 42,000 gallons $ 2.70 per gallon

As of Friday, September 26, the Dec 2014 futures price of gold was $1,250 per oz and the Dec 2014 price of heating oil was $2.50 per gallon. I close both of my positions on this day at these prices.

a) (5 points) Considering the bet on gold, what is the $ value of each gold futures contract when I initially made the bet and what is the leverage ratio?

b) (5 points) When I close my position on gold, what is my profit/loss rate of return?.

c) (5 points)What was the percent change in the futures price of gold and how does my rate of return on the gold bet relate to the percent change in the futures price of gold? Be very specific.

d) (5 points) Considering the bet on heating oil, what is the $ value of each heating oil futures contract when I initially made the bet and what is the leverage ratio?

e) (5 points) When I close my position on heating oil, what is my profit/loss rate of return.

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f) (5 points)What was the percent change in the futures price of heating oil and how does my rate of return on the heating oil bet relate to the percent change in the futures price of heating oil? Be very specific.

2. (112 points total) Let’s pretend that you graduated in Spring of 2014 and you scored a job as chief financial officer for a large paving company in the Pittsburgh area. Your ‘season’ ended in the fall and the person you replaced 'parked' all the cash in ten year Government securities. In particular, they purchased 10 ten year Treasury contracts during the fall of 2014. The CEO, let's call him Lee, tells you that you need to use those 10 ten year Treasury contracts to pay taxes in April of next year (2015). The CEO is worried about bad things happening and thus wants you to hedge against bad things happening.

a) (5 points) What is the CEO worried about and how can you hedge against these bad things happening?

So here we are in the fall of 2014 and you are considering three different hedges:

Scenario #1: You sell ten March 2015 futures contracts for 135 and the price at expiration is 133.

Scenario #2: You buy ten March 2015 futures option puts with a strike price at 135 for a price of $2,000 per put and the price at expiration is 133.

Scenario #3: You write ten March 2015 futures option calls with a strike price of 135 for a price of $2,000 per call and the price at expiration is 133.

b) (9 points) Compare the revenue obtained to pay the tax bill under each scenario and rank them accordingly from highest to lowest. Please show all work.

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c) (20 points) Given that these 10 March futures contracts expire at 133, please draw your profit functions for each of the three scenarios above. In particular, draw the futures profit function, the futures option puts profit function and the profit function for writing the calls all on the same diagram. Be sure to label each profit function and label as points 1, 2, and 3 to coincide with each scenario. Be sure to label all the break even points. (20 points for completely labeled graph).

So the next day, Lee comes to you and tells you that he plans to buy some new equipment next winter (in December 2015) and wants to do some more hedging since he really trusts you and your excellent education at Penn State University. The paving company makes some serious cash beginning in May and ending in early September. He wants you to 'park' half of the season's money in Treasuries by buying 10 June 2015 Treasury contracts and then wants you to sell these Treasuries in December to pay for the new equipment. So it the fall of 2014 and you need to do some more hedging by playing the futures market.

d) (5 points) What is your natural position in June 2015 and how could you hedge against bad things happening? Name the three hedges and make sure you explain what we mean by 'bad things happening.'

e) (5 points) What is your natural position in December 2015 and how could you hedge against bad things happening? Name the three hedges and make sure you explain what we mean by 'bad things happening.'

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The June hedge - consider the following 3 scenarios:

Scenario #1: You buy 10 June futures contracts for 133 and the price at expiration is 130.

Scenario #2: You buy 10 June futures option calls with a strike price at 133 for a price of $2,000 per call and the price at expiration is 130.

Scenario #3: You write 10 June futures option puts with a strike price of 133 for a price of $2,000 per put and the price at expiration is 130.

f) (9 points) Compare the costs of acquiring the 10 Treasury contracts under each scenario and rank them accordingly from lowest to highest.

g) (20 points) Given that these June futures contracts expire at 130, please draw your profit functions for each of the three scenarios above. In particular, draw the futures profit function, the futures option calls profit function and the profit function for writing the puts all on the same diagram. Be sure to label each profit function and label as points 1, 2, and 3 to coincide with each scenario. Be sure to label all the break even points. (20 points for completely labeled graph).

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Now on to the December Hedges:

Scenario #1: You sell 10 December futures contracts for 134 and the price at expiration is 130.

Scenario #2: You buy 10 December futures option puts with a strike price at 134 for a price of $2,000 per put and the price at expiration is 130.

Scenario #3: You write 10 December futures option calls with a strike price of 134 for a price of $2,000 per call and the price at expiration is 130.

h) (9 points) Compare the revenue obtained to pay for the new equipment under each scenario and rank them accordingly from highest to lowest. Please show all work.

i) (20 points) Given that these December futures contracts expire at 130, please draw your profit functions for each of the three scenarios above. In particular, draw the futures profit function, the futures option puts profit function and the profit function for writing the calls all on the same diagram. Be sure to label each profit function and label as points 1, 2, and 3 to coincide with each scenario. Be sure to label all the break even points. (20 points for completely labeled graph).

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j) (10 points) So let us pretend your are at the paving company's Holiday party in December of 2015 and the CEO, Lee, wants to give you a Holiday bonus. Lee gives you an envelope and tells you that he decided to give you 50% of the money you saved the paving company given all the hedging. We assume, importantly, that you had a crystal ball the whole time and played the best hedge for each of the three hedges (March, June and December). Compare the total revenue left for buying the equipment assuming you played the best hedge to the total revenue that you would have left for the new equipment if you went naked and didn't hedge at all. How much is the check for or is the envelope empty? Please show all work.

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3. (70 points total) Use the following 3 Tables to answer the questions that follow:TABLE 1

C (CITIGROUP INC) 14.35 -0.89Sep 16, 2008 @ 10:14 ET

Bid 14.35 Ask 14.36 Size 13x40 Vol 33660766

Calls Last Sale Net Bid Ask Vol Open

Int Puts Last Sale Net Bid Ask Vol Open

Int

08 Sep 10.00 (C IB-E) 4.65 -0.80 4.55 4.65 50 1001 08 Sep 10.00 (C UB-E) 0.17 +0.07 0.17 0.18 1557 71497

08 Sep 12.50 (C IZ-E) 2.48 -0.82 2.41 2.49 614 2857 08 Sep 12.50 (C UZ-E) 0.52 +0.26 0.51 0.53 1845 59865

08 Sep 15.00 (C IC-E) 0.80 -0.45 0.76 0.82 962 12146 08 Sep 15.00 (C UC-E) 1.35 +0.61 1.35 1.40 6940 157380

08 Sep 17.50 (C IR-E) 0.14 -0.12 0.14 0.16 1011 57962 08 Sep 17.50 (C UR-E) 3.25 +1.05 3.20 3.25 778 123636

08 Oct 10.00 (C JB-E) 6.35 0.0 5.45 5.60 0 1284 08 Oct 10.00 (C VB-E) 1.11 +0.41 1.06 1.14 4031 26075

08 Oct 12.50 (C JZ-E) 3.70 -0.50 3.60 3.75 2 458 08 Oct 12.50 (C VZ-E) 1.65 +0.49 1.70 1.77 1297 33174

08 Oct 15.00 (C JC-E) 2.12 -0.38 2.17 2.26 234 3398 08 Oct 15.00 (C VC-E) 2.75 +0.75 2.73 2.79 1819 45733

08 Oct 17.50 (C JR-E) 1.17 -0.13 1.16 1.19 599 17400 08 Oct 17.50 (C VR-E) 4.25 +1.00 4.20 4.30 309 49083

TABLE 2C (CITIGROUP INC) 15.66 +0.42Sep 16, 2008 @ 12:32 ET

Bid 15.63 Ask 15.64 Size 15x114 Vol 130134024

Calls Last Sale Net Bid Ask Vol Open

Int Puts Last Sale Net Bid Ask Vol Open

Int

08 Sep 12.50 (C IZ-E) 2.87 -0.43 3.30 3.40 1077 2857 08 Sep 12.50 (C UZ-E) 0.28 +0.02 0.26 0.29 6678 59865

08 Sep 15.00 (C IC-E) 1.35 +0.10 1.28 1.34 4846 12146 08 Sep 15.00 (C UC-E) 0.74 0.0 0.71 0.76 21944 157380

08 Sep 17.50 (C IR-E) 0.23 -0.03 0.22 0.24 7117 57962 08 Sep 17.50 (C UR-E) 2.40 +0.20 2.15 2.20 4726 123636

08 Sep 20.00 (C ID-E) 0.04 -0.01 0.02 0.05 1090 154008 08 Sep 20.00 (C UD-E) 4.35 -0.20 4.40 4.50 969 100991

08 Oct 12.50 (C JZ-E) 4.60 +0.40 4.25 4.35 36 458 08 Oct 12.50 (C VZ-E) 1.22 +0.06 1.20 1.24 3607 33174

08 Oct 15.00 (C JC-E) 2.59 +0.09 2.60 2.63 967 3398 08 Oct 15.00 (C VC-E) 2.02 +0.02 2.02 2.07 3778 45733

08 Oct 17.50 (C JR-E) 1.40 +0.10 1.38 1.41 5404 17400 08 Oct 17.50 (C VR-E) 3.15 -0.10 3.25 3.35 1251 49083

08 Oct 20.00 (C JD-E) 0.65 +0.06 0.62 0.66 1896 34540 08 Oct 20.00 (C VD-E) 4.90 -0.10 5.00 5.10 127 31671

TABLE 3

C (CITIGROUP INC) 13.20 -2.55Sep 17, 2008 @ 12:41 ET Bid 13.21 Ask 13.22 Size 41x99 Vol 152391812

Calls Last Sale Net Bid Ask Vol Open

Int Puts Last Sale Net Bid Ask Vol Open

Int

08 Sep 10.00 (C IB-E) 4.10 -1.50 3.45 3.55 20 1311 08 Sep 10.00 (C UB-E) 0.23 +0.19 0.22 0.25 9833 69074

08 Sep 12.50 (C IZ-E) 1.50 -2.00 1.42 1.48 2336 3621 08 Sep 12.50 (C UZ-E) 0.70 +0.61 0.70 0.71 5172 62467

08 Sep 15.00 (C IC-E) 0.35 -0.95 0.30 0.38 4316 14178 08 Sep 15.00 (C UC-E) 2.00 +1.62 1.98 2.11 7942 159794

08 Sep 17.50 (C IR-E) 0.08 -0.13 0.07 0.09 1880 66836 08 Sep 17.50 (C UR-E) 4.25 +2.49 4.25 4.40 1650 109581

08 Oct 10.00 (C JB-E) 4.36 -1.77 4.30 4.45 34 1346 08 Oct 10.00 (C VB-E) 1.11 +0.52 1.07 1.13 7645 38018

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08 Oct 12.50 (C JZ-E) 2.60 -1.90 2.57 2.67 182 624 08 Oct 12.50 (C VZ-E) 1.85 +0.78 1.83 1.88 2442 33215

08 Oct 15.00 (C JC-E) 1.41 -1.28 1.35 1.43 3997 5269 08 Oct 15.00 (C VC-E) 3.05 +1.29 3.05 3.15 10526 49708

08 Oct 17.50 (C JR-E) 0.69 -0.72 0.65 0.70 2655 27398 08 Oct 17.50 (C VR-E) 5.00 +2.00 4.75 4.95 736 49221

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a) (5 points) Use Table 1 to answer this question. Assume that we freeze the spot of Citigroup as it is in Table 1, On the same diagram, plot the evolution of the term premium for the Oct 12.50 and Oct 15 put. Please label your diagram completely making sure you clearly indicate which option each line represents.

You and a friend are not sure of the direction Citigroup is going to go so you both decide to play what is known in option talk as straddle(s). You decide to play a short straddle by writing a Sept 15 call and Sept 15 put at Table 1: Your friend plays a long straddle by buying a Sept 15 call and Sept 15 put at Table 1.

b) (10 points - 5 for correct calculations and 5 for intuition) Given your short straddle bet as above, would it be better to close your position in Table 2 or Table 3? Show all work. Explain the intuition.

c) (10 points - 5 for correct calculations and 5 for intuition) Given the long straddle played by your friend, would it be better to close his/her position in Table 2 or Table 3? Show all work. Explain the intuition.

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d) (5 points) How your answers in b) and c) are related. What characteristic of options markets applies here? Explain.

(30 points total) In the space below, we are going to plot two profit functions on the same graph: one for the buyer of one Sept 15 put and one for the writer of one Sept 15 put. We open these positions on Table 1.

Scenario 1): the spot price of Citigroup stays the same as in Table 1 and the option expires. Locate these two points (one for buyer of put and one for writer of put) and label as points A, clearly labeling the profit or loss for each. Show all work.

Scenario 2): the spot price of Citigroup stays the same as in Table 2 and the option expires. Locate these two points (one for buyer of put and one for writer of put) and label as points B, clearly labeling the profit or loss for each. Show all work.

Scenario 3): the spot price of Citigroup stays the same as in Table 3 and the option expires. Locate these two points (one for buyer of put and one for writer of put) and label as points C, clearly labeling the profit or loss for each. Show all work.

Be sure to label the break even point.

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e) (10 points) Prove that we have a zero sum game with Scenario 3). That is, go through the math with you, the buyer of the Sept 15 put and someone else, the writer of the Sept 15 put. Recall that you bought the puts in Table 1 and the spot at expiration is that on Table 3.

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Exam #2Econ 351

Spring 2015Good Luck!

Name ______________________________________ Last 4 PSU ID __________

Please put the first two letters of your last name on the top right hand corner of this cover sheet. Also, ONLY NON-PROGRAMMABLE CALCULATORS ARE ALLOWED - THERE ARE NO SUBSTITUTES. THANKS FOR YOUR COOPERATION!

GOOD LUCK!!!

Total Points for exam = 240

Test time = 120 minutes

One minute for every two points - if you keep this pace you will have 10 minutes left over

To help with time management if spreading time evenly

Question #1 = 40 points..... 20 minutes

Question #2 = 45 points ......22 minutes

Question #3 = 30 points.... 15 minutes

Question #4 = 40 points ....20 minutes

Question #5 = 35 points..... 17 minutes

Question #6 = 25 points.... 12 minutes

Question #7 = 25 points.... 12 minutes

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1. a) (40 points total) In the space below, draw a reserve market diagram depicting points A, B, and C. Assume that the Fed held reserve supply constant and that the volatility in the effective (actual) federal funds originated entirely from the volatility in reserve demand. Note, this period is well before the Fed obtained the authority to pay interest on reserves. The period we are considering is where the target for the federal funds rate is 7%. During this time, the discount rate was set below the target as was not used by banks since there was such a stigma associated with borrowing from the Fed - so the discount rate is irrelevant for this part of problem.

(10 points for correct and completely labeled diagram)

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b) (10 points) In hindsight the Fed could have done a better job in terms of hitting their federal funds target = 7%. Explain in words what they should have done to avoid point A and what they should have done differently to avoid point C. Be sure to be clear on two things in your explanation: 1) when we say 'what THEY should have done differently,' who exactly is 'THEY?' and 2) what is the operational aspect of avoiding points A and C - ie., what do 'THEY' have to do and how do they do it and who do they do it with? Please refer to each of the two cases (i.e., avoiding both points A and C). Recall, this is before the Fed had the authority to pay interest on reserves.

c) (20 points total: 10 points for diagram and 10 points for explanation) Now let's pretend that we were in a new regime (as they are now) where the Fed sets the interest rate they pay on reserves at 25 basis points below the federal funds target and the discount rate set 25 basis points above the federal funds target = 7% In the space below, redraw the reserve market diagram accounting for this new regime. Make sure you label the new points A, B, and C under this new and current regime. Explain why the old points A and C do not exist anymore - the word arbitrage should be in your answer numerous times - be sure you convey to us you know exactly what is going on here. Note, the shocks to reserve demand occur just as before and the Fed does not respond (i.e., they do not conduct any open market operations). Note also that we are assuming zero transactions costs, that is, there is no cost of arbitrage.

(10 points for correct and completely labeled diagram)

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Write your essay for part 1.c) in the space below.

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2. (45 points) As we know, the Fed recently finished up a two day FOMC meeting on Wednesday March 18. The Table below provides data on selected interest rates. What we want to do in this problem is to explain why the rates changed as a result of the meeting. In particluar, we are comparing interest rates on Tuesday, 3/17 (the day before the FOMC statement and press conference) to Wednesday, 3/18 which is after the announcement and press conference. Please answer the questions below.

a) (5 points) In general, what happened to all the interest rates above and why between Tuesday, 3/17 and Wednesday, 3/18? Be sure to use an equation in your answer.

b) (10 points) Now calculate what has happened to the one year interest rate expected one year from now between Tuesday, 3/17 and Wednesday, 3/18. Please show all work. Are your results consistent with your answer from part a)?

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c) (10 points) Now calculate what has happened to the one year interest rate expected two years from now between Tuesday, 3/17 and Wednesday, 3/18. Please show all work. Are your results consistent with your answer from part a)?

d) (10 points) The two graphics below show the reaction of the federal funds futures contract for Dec. of 2015 from two events - one event is the reaction of this federal funds futures contract as a result of the FOMC meeting as above and the other is the reaction of this federal funds futures contract from the employment report Friday, March 6, 2015. Identify which graph applies to the FOMC meeting (graphic A or B) and which graph applies to the employment report (graphic A or B). Make sure you explain exactly why this federal funds futures contract reacted the way it did and whether, with perfect hindsight, you should have been a bear or a bull on this futures contract for each event. Please identify on each graphic when the news came out , what the news was exactly, and whether the reaction of the fed futures contract is consistent with the efficient market theory.

Graphic A

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Graphic B

Write your answer to part d) here:

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e) (10 points) Now explain what happened in the stock market after most recent FOMC meeting and why. Please use the stock price determination expression we used in class to support your explanation. Finish your essay commenting on the following: A Fed watcher, commenting on the results of the FOMC meeting was quoted as saying: "on one hand, there was no news, on the other hand, there was plenty of news." What was this Fed watcher talking about? Please refer to each of the Fed watcher's hands.

3) (30 points, 10 points for each explanation) Explain the three reasons why the Fed wanted to pay interest on reserves. Please be as specific as possible and feel free to refer to question #1 on this exam for one of the reasons (you already did this work!). For reason #3, use the balance sheet below and identify, by CLEARLY marking on the graph below when the Fed got the authority to pay interest on reserves. Also locate on the graph the period of sterlization and be sure to explain what exactly sterilized intervention means.

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write your answer to question #3 here:

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4) (40 points) The table below contain some money supply data - we are going to compare and contrast the information in the last row of each table (2008-01-01 and 2014-08-01). The target for the federal funds rate at the end of January of 2008 was 3% (this is the rate we use) and was a range or 0 - .25% in August of 2014. All numbers are in billions of dollars except for the ratios and money multiplier (MM).

a) Let's return to January 2008 (2008-01-01), the beginning of the year that will go down in history as one of the worst years ever for the global economy. Recall that this was before the Fed obtained the authority to pay interest on reserves that happened in October of 2008. In the space below, draw a reserve market diagram depicting these conditions and label as point A (assume that the Fed does perfect in terms of predicting reserve demand so that the actual funds rate is equal to its target rate = 3%). The discount rate was 3.5% at the end of January 2008.

(10 points for correct and completely labeled diagram)

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b) Let us update to August of 2014. As you know, since the Fed has hit the 'zero bound' in December of 2008, where the official target for the federal funds rate is now and has been a range: 0% - .25% or in words, zero to 25 basis points. In the space below, redraw the diagram as above with point A (from January 2008) and add a point B, that corresponds to the conditions in August of 2014. Assume importantly and for simplicity, that the position of reserve demand remains constant from January 2008 to August 2014. Assume also that the actual funds rate is at its upper bound of the target range. The discount rate was set at .75% (75 basis points) in August of 2014.

(10 points for correct and completely labeled diagram)

c. (10 points) If the Fed wants to raise the federal funds rate to 3.00% like it was at the end of January, 2008, what type and how many open market operations would they need to conduct? What are the implications on the economy if the Fed pursued such a strategy?

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d) (10 points) Given that the Fed preferred not to conduct the open market operations as above in part c), what else could they do to raise the federal funds rate to 3%. Be very specific and explain exactly how this 'alternative' policy would work in terms of influencing the federal funds rate and why. The word arbitrage needs to be in your answer.

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5. (35 points) We discussed the important results from a research paper on forward guidance.

a) (10 points) Fill in the blank below.

The authors of this paper argue that the FED could have done better in their forward guidance. Write an essay explaining how forward guidance is supposed to work in terms of influencing the economy and what the Fed should have done differently and why (according to the authors). Use the two graphics (below) to support your answer. That is, mark the period where the Fed achieved maximum 'bite' on their forward guidance as 'maximum bite' on both diagrams identifying the date and what the Fed did exactly to achieve this 'maximum bite.'

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b) (10 points) Now explain how we can use the diagrams to identify the period of maximum bite. That is, on the first graph, how exactly can we tell, by viewing the graph, the period of maximum bite. Be sure to comment on the similarities or differences in the movement of the various interest rates before the period of maximum bite as well as during the period of maximum bite.

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c) (10 points) Similarly, using the second graphic, how can we identify the period of maximum bite in the Fed's forward guidance? Be sure to comment on what exactly the vertical axis represents in the second graph and how we should interpret it before the period of maximum bite as well as during the period of maximum bite. How does all of this relate to the pure expectations theory of the term structure (PET)?

d) (5 points) Let’s go back to question #2 on this exam - How would the graphics A and B in question #2 of this exam be different , if at all, if we were still in a period of maximum bite in the Fed’s forward guidance? – explain.

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6. Merck Problem. (50 points total) Pretend that you are hired by Merck to do some research on the behavior of their stock price. The CEO wants you to develop a report investigating two rumors that she has been hearing about Merck stock: 1) The behavior of Merck stock is consistent with the efficient market theory and 2) Changes in Merck stock, just like any other stock, are impossible to predict. That is, Merck stock follows a random walk.

In this problem, you are going to prepare the report. I will help!

To begin, I went to Yahoo finance and copied a picture depicting the behavior of Merck’s stock for the week of (10/31/05 – 11/04/05). I also went to the WSJ online and copied and pasted an excerpt from “Merck and Qualcomm Gain, But ImClone, Guidant Decline”By KAREN TALLEY, DOW JONES NEWSWIRES November 4, 2005.

Excerpt“Merck was the best percentage gainer among the Dow industrials, rising $1.07, or 3.8%, to $29.48. The drug maker scored a court victory in its second Vioxx liability case; thousands of cases lie ahead.”

Answer the following questions:

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a) (5 POINTS) To begin this “make believe” report (the CEO treasures completeness), explain exactly what determines stock prices. Write out our general formula of stock price determination, explaining exactly what each term means, and the intuition underlying the formula itself.

Now discuss some of the factors that could influence the terms of your expression above.

b) (5 POINTS) Now use your expression above to explain the movement in Merck stock on Thursday, November 3. Be specific as to the cause of the movement as well as well the movement itself, i.e., the duration.

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c) (5 POINTS) Use the expression in a) above to explain the behavior of Merck stock on Tuesday, November 1, the day the FOMC raised their target for the federal funds rate. Again, be very specific as to the cause of this behavior, using your expression in a). Below is an excerpt fromthe official statement from the 11/1 meeting.

Release Date: November 1, 2005

For immediate release

The Federal Open Market Committee decided today to raise its target for the federal funds rate by 25 basis points to 4 percent.

Write your answer for part c) here.

d) (10 POINTS) Are your results consistent with the efficient market theory? Begin your answer with explaining exactly what the efficient market theory is making sure you refer to the best investment advice assuming that markets are efficient. Apply your definition of the efficient market theory to your answers on both b) and c) above. Be very specific and be sure to use the term NEWS numerous times in your explanations.

128

NEW GRADER) We now move on to addressing whether or not changes in Merck stock are predictable. Begin with a little notation. Let MRKt be the current spot price of Merck at time t (right now; today) and let MRKe

t+1 be the spot price of Merck expected tomorrow.

Of course the information set available to you is Ωt and includes all information, relevant or not, that is available up until time t (right now!).

e) (10 POINTS) According to the efficient market theory (along with our class discussion), what is the best forecasting model that you can come up with to predict MRKt+1 (the price of Merck stock tomorrow)? Be very specific and justify the choice of your forecasting model (i.e., justify why your model is the best of all the possible choices, being sure to identify some of the other possible forecasting models! (hint – redundant variables everywhere!!)).

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f) (15 POINTS TOTAL, 5 FOR EACH EQUATION WITH SOLID ACCOMPANYING DISCUSSION) We are now ready to test whether or not Merck (stock) follows a random walk. Using the forecasting model above, explain exactly how we would test whether or not Merck follows a random walk. Be sure to identify the expected empirical results using all the equations that we set up in class. There are a minimum of three equations to set up and discuss. Be sure to continuously refer to the efficient market theory and the random walk properties of Merck throughout your discussion.

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Exam #2Econ 351Fall 2014

Good Luck!

Name ______________________________________ Last 4 PSU ID __________

Please put the first two letters of your last name on the top right hand corner of this cover sheet. Also, ONLY NON-PROGRAMMABLE CALCULATORS ARE ALLOWED - THERE ARE NO SUBSTITUTES. THANKS FOR YOUR COOPERATION!

GOOD LUCK!!!

Total Points for exam = 240

Test time = 120 minutes

Approximately one minute for every two points - if you keep this pace you will have 10 minutes left over

To help with time management if spreading time evenly

Question #1 = 50 points..... 25 minutes

Question #2 = 40 points ......20 minutes

Question #3 = 30 points.... 15 minutes

Question #4 = 40 points ....20 minutes

Question #5 = 30 points..... 15 minutes

Question #6 = 50 points..... 25 minutes1. (50 points) Leading up to and during the Lehman Brothers collapse, overnight lending markets became quite volatile, as shown by the figure below.

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1. a) In the space below, draw a reserve market diagram depicting points A, B, and C. Assume that the Fed held reserve supply constant and that the volatility in the effective federal funds came originated from the volatility in reserve demand. Note, this is the period before the Fed obtained the authority to pay interest on reserves.

(10 points for correct and completely labeled diagram)

b) (10 points) In hindsight the Fed could have done a better job in terms of hitting their federal funds target = 2%. Explain in words what they should have done to avoid point B and what they should have done differently to avoid point C. Note that we are still in the period before the Fed obtained the authority to pay interest on reserves.

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c) (10 points) Draw a reserve market diagram depicting your answer for part b) above. Be sure to label points A, B and C. Note that we are still in the period before the Fed obtained the authority to pay interest on reserves.

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d) (20 points total: 10 points for diagram and 10 points for explanation) Now let's pretend that we were in a new regime (as they are now) where the Fed sets the interest rate they pay on reserves at 25 basis points below the federal funds target and the discount rate set 25 basis points above the federal funds target. In the space below, redraw the reserve market diagram accounting for this new regime. Make sure you label points A, B, and C under this new and current regime. Explain in detail as to why the implied (actual) funds rate is different in this new regime relative to the old regime as in 1.a).

(10 points for correct and completely labeled diagram)

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2. (40 points total) Use the Sept 17, 2014 FOMC Statement at the back of exam to answer the question below.

2.a) (10 points) List the three policy alternatives and prove, by using excerpts from the FOMC statement provided at the end of exam, that the Fed has been pursuing these 3 policy alternatives. Simply circle the excerpts that refer to each of the three policy alternatives at the zero bound (label the excerpts with the policy alternative that applies).

b) (30 points, 10 points for each explanation) Explain how these three policy alternatives (aka unconventional policy) are supposed to work in terms on influencing the economy. Be very specific in explaining how each of these are supposed to influence the economy. In your answer you should use the equation that we used in class, as well as any diagrams that you deem appropriate.

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continue your answer for 2)b. here

3. (30 points, 10 points for each explanation) Explain the three reasons why the Fed wanted to pay interest on reserves. Please be as specific as possible. The terms sterilization, balance sheet capacity, tax, and control should be part of your answer(s).

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continue your answer to 3. here

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4. (40 points total)) We discussed how federal funds market operated during more normal times (before the Fed obtained the authority to pay interest on reserves) with a picture just like the one below. To review, there are two phones on the desk.

a) (10 points) Discuss how this federal funds market worked in more normal times - feel free to use one of the examples we used in class as in finding cash outside the classroom / me getting mad at PNC bank and moving my money (deposit) to M & T bank. Be sure to refer to how the federal funds rate is determined.

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b) (10 points) Let us fast forward to the present. Using the graph below, explain how things have changed in the federal funds market. Are the phones still ringing? Why or why not? Explain.

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Now consider the graph below. Note that the federal funds is hypothetical and remains between the upper bound (the discount rate) and the lower bound (the interest paid on reserves).

c) (10 points). Explain why this federal funds rate would not prevail given the current conditions in reserve markets. Be sure to explain what would happen to the federal funds rate and why. Be sure to refer to the desk with the phones on it.

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d) (10 points) Under what conditions would the federal funds rate lie between its upper bound (the discount rate) and its lower bound (the interest paid on reserves) as it does in the graph. How could the Fed make this hypothetical federal funds rate a reality in the sense of the actual federal funds rate remaining between its lower bound and upper bound?

5. (30 points total) Us the table below to answer the following questions.

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a) Let's return to January 2008 (2008-01-01), the beginning of the year that will go down in history as one of the worst years ever for the global economy. Recall that this was before the Fed obtained the authority to pay interest on reserves that happened in October of 2008. The numbers above are in $ billion. The target for the federal funds rate at the beginning of January, 2008, was 4.25% (those were the days!). In the space below, draw a reserve market diagram depicting these conditions and label as point A (assume that the Fed does perfect in terms of predicting reserve demand so that the actual funds rate is equal to its target rate). The discount rate in January 2008 was set at 4.5%.

(10 points for correct and completely labeled diagram)

142

b) (10 points) Let us update to January 2009. As you know, since the Fed has hit the 'zero bound' in December of 2008 where the official target for the federal funds rate is now and has been since December of 2008, a range: 0% - .25% or in words, zero to 25 basis points. In the space below, redraw the diagram as above with point A (from January 2008) and add a point B, that corresponds to the conditions on January 2009 (2009-01-01). Assume importantly and for simplicity, that the position of the reserve demand remains constant from January 2008 to January 2009. Assume also that the actual funds rate is at its upper bound of the target range. The discount rate was set at 50 basis points in January of 2009.

(10 points for correct and completely labeled diagram)

c. (10 points) If the Fed wants to raise the federal funds rate to 4.25% like it was in January, 2008, what type and how many open market operations would they need to conduct? What are the implications on the economy if the Fed pursued such a strategy.

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6. Merck Problem. (50 points total) - same as in previous exam 2.

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