Investment Analysis Package – Part 1 - Theories

Professor Raad Jassim

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Content:

Chapter 2 Margin Requirements 2-10

Chapter 24 Index Calculation 11-13

Chapter 7 Risk & Return / Markowitz 14-21

Chapter 16 Bonds 22-26

Industry Analysis 27-32

Stocks 34-36

Options 37-41

Solutions to selective chapters 46-110

Post-problems solutions 111

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Loan Value and Margin Requirements

Canadian securities

Security Loan Value Margin Requirement

Option eligible ($5.00+) 70% 30%

Listed ($3.00+) 50% 50% Listed ($3.00-) 0% 100%

Canadian Dealer’s Network 0% 100%

Warrants 50% 50%

Loan Value and Margin Requirement

Security Loan Value Margin Requirement

Mutual funds ($3.00+) 50% 50% Mutual funds ($3.00-) 0% 100%

Gov. of Canada bonds 96% 4% Prov. & Municipal bonds 90% 10% Corporate bonds 85% 15%

US T-bonds 96% 4%

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How does margin work?

How do you calculate the margin requirement on a purchase?

- # of shares x Price x Margin requirement

Example 1:

- We are buying 100 TD Waterhouse @ $23.00 - 100 x $23.00 x 30% = $690.00

This is the margin requirement to buy this stock.

Remember that TD Waterhouse is option eligible and trades above $5.00

Example 2:

- We want to buy 1000 shares of Cognicase @ $19.00. COG is not option eligible. - 1000 x $19.00 x 50% = $9500

This is the margin requirement on this trade. You are borrowing the remaining $9500 from TD Waterhouse.

Example 3:

- You want to buy $25,000 face value of a Quebec Provincial Strip bond @ $95 - 25,000 x $95/100 x 10% = $2375

Again, this amount is your margin requirement. The $21,375 balance is borrowed from TD Waterhouse.

Don’t forget to make sure that the annual yield on the bond you’re buying is at least the cost of borrowing. (7% in this example)

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Margin Account Rates

President account:

Canadian debit:

$0 - $99,999 - Prime + 0.75% = 7.00%

$100,000+ - Prime = 6.25%

US debit:

$0 – $24,999 - Prime + 1.00% = 9.25%

$25,000 – $99,999 - Prime + 0.75% = 9.00%

$100,000+ - Prime + 0.50% = 8.75%

What if the market goes down?

If the price of the stock you bought on margin drops, its loan value decreases.

This might result in a margin call.

A margin call is an amount of money a client has to come up with in order to keep its holding.

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Short selling margin requirement

Equities Listed ($3.00+) 150% Option eligible ($5.00+) 130% VSE and ASE ($3.00+) 175%

Bonds Government 110% Corporate not allowed

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Limit order - Book of specialist

1)

Limit buy Limit sell $ Shares $ Shares 49.75 500 50.25 100 49.50 800 51.50 100 49.25 300 54.75 300 49 200 58.25 100

48.50 600

A) Market – buy order for 100 @ what price the fill? - $50.25 B) Next Market buy-order? - $51.50 C) As a specialist would you inventory? - Increase

2) Stop-loss of BCE to sell 100 shares @ $55 Current price @ $62 At what price will you sell if price drop to $50?

a. 50 b.55 c. 54.875 d. Cant’ tell

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Below maintenance margin (Mm): Investor must do something:

1. Sell some shares or 2. Send cash 3. Value of securities no longer support loan 4. MM determines what investor must do

Above initial margin (Im): Investor May:

1. Do nothing 2. Buy additional shares with no additional cash 3. Increase loan amount 4. IM determines what investor may do

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Given:

You Short 100 shares @ $50

Dividends of $1/share are paid

You cover position @ $40

Profit = $900

Given:

You short 100 shares @ $50

Dividends of $1/shares are paid

You cover position @ $60

Loss = ($1,100)

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No Margin:

Purchase 100 shares @ $50

Sell 100 shares @ $70 in 1 year:

Profit = $2,000

Return = $2,000/$5,000 = 40%

Margin:

Purchase 200 shares @ $50

(Borrow $5000 @ 9%)

Interest = $450

Sell 200 shares @ $70 in 1 year:

Profit = $3,550

Return = $3,550/$5,000 = 71%

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No Margin:

Purchase 100 shares @ $50

Sell 100 shares @ $30 in 1 year:

Loss = $2,000

Return = ($2,000)/$5,000 = (40%)

Margin:

Purchase 200 shares @ $50

(Borrow $5000 @ 9%)

Interest = $450

Sell 200 shares @ $30 in 1 year:

Profit = $4,450

Return = ($4,450)/$5,000 = (89%)

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Measure of Return & Risk

HPR (Holding period return) = Ending value of inv. Beginning value of inv.

Ex. You commit $200 for one year @ end you get 220

HPR = 220/200 = 1.10 In % term on annual basis

HPY (holding period yield) = HPR - 1 = 1.10 – 1= 10%

Annual HPR = HPR1/n (n: no. of years)

Ex. Initial Inv. $250 $350 after 2 years

HPR = 350/250 = 1.4

Annual HPR = 1.4½ =1.1832

=1.1832-1 = 18.32%

Computing mean historical returns:

1. AM (arithmetic mean) = Σ HPY/n 2. GM (geometric mean) = [(HPR1)x(HPR2)…..(HPRn)] 1/n -1

Ex:

Year Initial Value End Value HPR HPY 1 100 115 1.15 0.15 2 115 138 1.20 0.20 3 138 110.4 0.80 -0.20

GM = [1.15 x 1.20 x 0.8]1/3 -1 = 3.353%

AM = [0.15 + 0.20 + (-0.20)] = 5% 3

Compare

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AM biased upward ex: Year Initial inv. End inv. HPR HPY 1 50 100 2 1 2 100 50 0.5 -0.5 AM= [1+ (-0.5)] = 50 = 0.25 = 25% 2 2 GM= [2 x 0.5]1/2 -1 = 11/2 -1 = 0%

If inflation in the market the portfolio

Calculating expected rates of return: An investor expects a certain rate of return for his future investment. The historical data is used as a benchmark for the possibility of future return. A 10% RR expectation could yield a range of -10% +25%

The investor assigns probability values to all possible return

E(Ri) expected return = Σ (probability of return)x(possible return)

E(Ri) =(1)(0.05) = 0.05

E(Ri) = (-0.15)(0.2)+(0.15)(-0.2)+(0.7)(0.1)=0.07

-0.05 0 0.05 0.10 RR

0.25

0.5

0.75

1

Prob./

-0.2 -0.1 0 RR

0.2

0.4

0.6

0.8

Prob./

0.1 0.2

Ex.1: Single condition 

Ex.2: Multiple conditions 

= P1R1 +P2R2…PnRn

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Measure the risk of expected rates of return

Investors quantify dispersion (instead of graph presentation) using statistical techniques: Variance & standard deviation to compare risk & return for alternative investments.

Variance 2) = Σ (probability) x (possible return – expected return)²

= Σ(Pi) [Ri- E(Ri)]²

Ex1: 2 =1(0.05-0.05)² = 1 x 0 = 0 No variance, no risk

Ex2: 2 = 0.15(0.2-0.07)² + 0.15(-0.20-0.07) + 0.7(0.1-0.07)² = 0.0141 The greater the dispersion the greater the risk

Standard deviation ( = √ 2 or √ Σ Pi[Ri-E(Ri)]² = 0.11874

Coefficient of variation (CV) = S.D. E(R) Used in an unadjusted 2 or Data misleading

Ex:

Inv. A Inv. B E(R) 0.07 0.12

0.05 0.07

By observation Inv. B is riskier than Inv. A using CV

CVA = 0.05 = 0.714 0.07

CVB= 0.07 = 0.583 0.12

Inv. B less riskier than Inv. A

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Bonds

Fabozzi (Chapter 7 – Fabozzi text)

Debt securities (with no embedded options – callable, putable, convertible) have the following fundamental Price/Yield relationship:

Callable bonds:

1. Call option gives the holder the right to purchase @ fixed price in future 2. The right to purchase rests with issuer 3. Below yield Y’: Investors anticipate that firms (issuer) may call bond 4. Investor receive call price 5. Bond’s market price is bonded by call price 6. Reinvestment risk : investor will have to invest @ rate. Both coupon & principal 7. Negative convexity

Yield  Price 

Y’ Yield

Price

Convexity Negative

Option free bond

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Putable bonds:

1. Option gives holder the right to sell bond @ a fixed price in the future 2. Right to sell rest with investor 3. Investor has the right to sell bonds @ put strike price 4. Above Y’ investor begin to anticipate put bonds back to issuer

Duration Macaulay:

1st derivative of bond’s price function with yield (math)

To find price volatility find value of duration

1) Duration is a measure of bond’s sensitivity to change in yield i.e. Estimating interest rate risk. [Ave. Mat. Of C.F., math: weighted ave. time

2) Modified duration calculation = Y - Y+ 2 V0 (∆ Ex. 15 yrs (option-free) bond, c=7%, trading @ par I.R. 50bp, P=95.58 [n=15, put = 7, fv= 100, I/Y = 7.5, CPT PV= 95.586] I.R 50 bp, P= 104.701 M.D. = 104.7 – 95.58 2(100)(0.005) 3) Estimating price change with M.D : ex 150bp Estimate = (-1) x D x (∆ = (-1) 8.845 x (150%) = 13.2675 Actual = [n= 15, pmt = 7, fv = 100, I/Y = 7% - 1.5 % CPT PV = 115.0561 4) Effective duration calculation (option adjusted): ex. Assume bond callable @102.5 Duration = 102.5 – 95.856 2(100)(0.005) 5) Portfolio duration = Dba Pba + Dbb Pbb

Pp Pp

Yield

Price

Option free bond

Putable bond

Value of put option

= 8.845 

=6.644 vs. 8.845 

Pba: price of bond a, Dba: Duration Pbb: price bond b, Dbb: Duration Pp: Price of portfolio

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Bond Pricing theorems: (Assume 1 coupon payment/year)

1) If bond price P0 , Yield & the reverse, ex:

5 yrs bond, P0 = $1000, c = $80 If P0= $1100, Y = 5.76% If P0= $900, Y = 10.68%

2) If bond yield does not change over its life, size of premium or discount towards maturity to par value, as its life gets shorter.

Ex. If P0 = $883.31, y=9%

P0, a year later = $902.81, y=9% (coupon 6%)

3) If yield stable over its life, size of premium & discount will decrease @ an increasing rate, accelerate towards maturity.

Ex. P5 (issued today) = $883.31 (different from par) = $116.69 P4 = $902.81 = $97.19

P3 = $924.06 = $75.94

4) If yield , P0 , by an amount > corresponding fall in P0, that occur if there were an equal-sized Y.

Ex: 1% yield P0 $42.12 (increase)

1% yield P0 $39.93 (decrease)

5) If coupon rate is high % change P0 owing to yield change is smaller.

Ex. Bond D, C = 9%, y=7% : P0 change = 3.889% Bond C, C = 7%, y=7% : P0 change = 3.993% Convexity:

1 & 4 theorems led to bond valuation called convexity

19.50%

19.50%

Time

Price

P5 P3 P2 P1 P0P4

Premium

Par

Discount

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How to immunize: Ex: A portfolio manager is required to have one cash flow of $1,000,000 in 2 years. Bond available 1 yr & 3 yr How much should be invested in each issue? The D of portfolio of bonds = weighted average of D. of individual bonds. W1 + W3 = 1 (W1 x 1) + (W3 x 2.78) = 2 W1, W3 are proportions of funds to be invested in 1, 3 yrs. bonds W1 = 0.4382 ie 43.82% of funds W3 = 0.5618 i.e 56.18% PV of P1 = $972.73 (c = 7%) PV of P3 = $950.25 (c = 8%) PV of 1,000,000 @ 10% Y for Yr 2 = 1,000,000 = 826,446 1.102

Types of passive bond management strategies

1) Net worth immunization: Matching duration of assets, liabilities Problems: Commercial banks mismatch of maturities – short term deposits &bank loans Bank search strategy may have equal duration – different terms

2) Target date immunization: Duration = horizon date Pension plan to provide firm income for retirement to avoid I.R. change

3) Cash flow matching and dedication: A. Cash flow matching (single period) B. Dedication (multi periods)

Manager select 0 and/or coupon bond: where cash flow = obligation This strategy avoids (-) impacts of I.R. changes as goals are always met.

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Contingent immunization calculation

Combination active and passive strategy Min. required return must be immunized, manage the surplus Given: $10 million portfolio 2-year horizon date In 2 years, portfolio value must be at least $11 million (could be 12 million) Current interest rate = 10% $11M (1.1)² Could actively manage $10M – $9.09 M = $0.91M. If lose that entire amount, immunize at that point.

If you do not lose that amount, you do not immunize & earn more than minimum require return

= $9.09 M, immunized would give minimum required return 

Yield

Price

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11

10

Trigger point

Immunize 2 yrs

Portfolio

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Before starting stock analysis, investor should look

1. Macroeconomic 2. Industry analysis

Top-down analysis A. Global economy: diversification – systematic & unsystematic

Risk: A.1 info on foreign firms A.2 disclosure A.3 accounting standards A.4 political risk A.5 exchange rate risk Ex. Emerging market, mutual funds

B. Domestic Micro-economy 1. Gross domestic product (G+S production) 2. Employment: workforce (working and actively searching) 3. Inflation rate, CPI, standard living 4. Interest rates - household, business 5. Budget deficit diff. gov. spending + revenue 6. Sentiment – optimism & pessimism of consumer & producer, willingness to produce & consume Ex. If nation’s economy is auto production For domestic usage & export If car replacement longer impact GDP, employment, …. Potential emerging of new industry ex. parts

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Federal Government Policy 1) Fiscal policy The federal government`s spending and tax actions (demand-side economics) 2) Monetary policy The manipulation of the money supply (demand-side economics)

A. Open market operations of the FRS (buying/selling US government bonds) Buying bonds increases the money supply Selling bonds decreases the money supply

B. Altering the discount rate. Short term rate charges to banks, rate signals expansionary policy

C. Altering the reserve requirement. Cash of bank deposits with fed 3) Supply side economics Increase productivity; decease taxes. Investment work

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Interest rate

1. Supply of funds from savers. Households 2. Demand of funds from businesses to finance: Physical plant, equipment,

inventories….etc.

3. Gov. Net. Supply. Demand for funds as modified by actions of fed res bank Monetary: I.R. & MS Fiscal: Gov. spending +taxes Budget deficit: difference between gov. rev. & gov. spending. Large gov. borrowing force up I.R Crowd out private borrowing Private borrowing & inventory chocking off

Demand corp. firms

E

E`

Gov. action budget deficit Supply households

Fund

I.R

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The Business Cycle: is the repetitive cycle of recession & recovery

1. The peak : is the transition from the end of an expansion to the start of a contraction 2. The through: occurs “ the bottom of a recession as the economy enters a recovery 3. Cyclical industries: are sensitive to state of economy. @through before recovery

attractive investment Firms: produce consumer durable: automobile

4. Defensive industries: industries produce basic necessities of life, food producers, pharmaceuticals, public utilities. In recession they outperform cyclical firms low betas

The problem is to I.D: peaks & throughs Economy in actual recession?

5. Growth company : experience above average growth in sales & earning than economy

Y>IRR (cost of capital). Retain large % earning to invest in above average projects. Identified after results out to the public. Efficient market theory N/A, info net ave.

Undervalued/fairly valued. Search for them before IPO

6. Speculative companies: Assets involve risk Large chance to lose, small chance to gain Return: 1) low 2) nonsexist 3) negative Loto 6/49 better, penny stocks

Time

GDP

Recession Recovery

1 

2 

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SIC Codes and industry life cycle

A. SIC Codes

15 Building contractors 152 Residential building contractors 1521 Single – family residential building contractors

B. Industry life cycle

- New tech - Firm leader change - Market saturate (-) growth - New product - Stable - Growth < econ. - No info (IPO) - Growing econ. - Difficult to predict

(Success/fail)

Time

Sales

Growth Risk Div Rapid & increasing growth

0 Div stable growth

Minimal or negative growth

Div Slowing growth

Start-up Consolidation Relative decline Maturity

0

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C. Sensitivity to the business cycle

1. Sensitivity of sales: is a major determinant, if industry is cyclical or defensive.

If product is a basic necessity of life, low-cost item relatively unaffected by B.C. If product is a consumer durable, expensive item affected by B.C.

2. Operating leverage: Relationship between variable and fixed cost.

- Firms F.C. are sensitive to B.C. because costs will be incurred regardless of the level of

production & sales - Firms V.C will reduce cost with production

3. Financial leverage: Debt vs. equity financing

Debt – payment to bondholders are fixed, must be met regardless of earnings

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The Graham-Rea Model (highest reward-to-risk)

1934 Benjamin Graham book security analysis Future earning as determinant of stock’s value 1974 Benjamin Graham & James Rea repudiated the above principles because of: Market is efficient (more than previous) Alternate approach: Certain stocks of certain firms may have inefficiencies to spot Examine financial statements, compare stock value to AAA bonds Rewards & risks yes & no answers Rewards Q.

1) Is P/E < ½ reciprocal AAA bond yield? Ex: if y=12%, recip = 1/0.12 = 8.3, 8.3/2=4.16, P/E,4.16

2) Is P/E<40% of its 5 yrs P/E average (P/E current year) 3) Is dividend yield > 2/3 AAA bond yield? 4) IS P0<2/3 book value per share? B.y= tot. Assets = tot. Debt/ out. Shares 5) IS P0<2/3 Net current Asset value/share? Curr. A- total debt/ out. Shares

Risk Q. 6) Is debt/equity>1? Total debt/total equity 7) Is current ratio>2? C.R = Current Assets/Current liabilities 8) Is total debt<2 net current assets?( Current assets= current-total debt) 9) Has E/S growth of last 10 yrs average min 7% per year?

E0 (earnings last year) = E-10(earnings 10 years ago)(1+g)10 E0 = E-10(1+g)10 if yes

10) In #9 more than 8 were less than -5% (steady earning) Method of selecting stocks (undervalued) to buy Remove all stock with YES answer to Q.6 Remove stocks that do not provide Yes to Q1, Q3 or Q5

To sell: If stocks 50% or 2 years passed since purchase Revisit the questions to eliminate stocks.

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The quest for value

Bennett Stewart, EVA & MVA Stern Stewart Bennett idea with regards to E/share:

- Myth: accounting clever presentation / dressing up! - Cutting to R&D, avoid acquisition to avoid goodwill & amortization - Differ expenses that could lead to performance

Market needs earnings? No Value EVA: (Economic value added) Capital budgeting

- Refuse (-) projects & investment companies - Measure Value & performance - Improve management skills - Max return + R&D - Liquidate unproductive assets & capital: land, rail.. - Retire line of credit

NOPAT (Net operating profit after tax) EVA (earning = NOPAT – cost of capital (WACC) Capital: equity, debt, all sources of money (credit line) Cost Cost is minimum required by shareholders >WACC Ex. EVA, EVA = 25Mil – 26 Mil = (-1) Reject-proj.

Ex: Two companies profit 1 million each A B Capital 5 million 10million

Ex: TSE: 145 companies surveyed 65 (-) EVA MVA = MKT value – capital = PV of all future EVA MVA= EVA + EVA ….. N. (1+K)1 (1+K)2

Corp return r MV c Capital

= If 5% = ? 15% 1

MV= 0.33 

If 30% = 2 15% 1

MV= 2 

Compare 

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Basic Option Terminology 1) Call: buyer has the right to purchase underlying asset 2) Put: buyer has right to sell underlying asset 3) Writer(seller) of call option: Commitment to sell underlying asset 4) Writer of put option: the commitment to buy underlying asset 5) Writing a covered call: own the underlying stock

Writing a naked call: not owning the underlying stock 6) Buyer and sell have opposite price expectations 7) Premium is the price of the contract. (intrinsic + time) 8) Options may be: exercised, traded in the open market, allowed to expire worthless.

American vs. European options 1) An American option contract allows the owner to exercise the right to buy or sell the

underlying asset on or before the expiration date. 2) A European option contract allows the owner to exercise the right to buy or sell the

underlying asset on the expiration date only. In general, American options are more valuable, due to increased flexibility. Virtually all option contracts traded in the U.S are American option contracts.* *Exception is foreign currency options and stock index options traded in the CBOE

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To estimate fair value of C or P: The Binomial Option Pricing Model (used for European) European options: Can be exercised only on expiration date / stocks pay no dividends American options: Can be exercised anytime during their life. BOPM can be used if modified / pays dividend $100

To value a call option: A portfolio with: Up Down Current price Stock 125 80 100 Bond 108.33 108.33 100 Call 25 0 ? Replicating the portfolio with appropriate combination of stock & bond can lead to a fair value of option EQ1: 125Ns + 108.33 Nb = 25 Up EQ2: 80Ns + 108.33 Nb = 0 Down (Ns: # of shares, Nb: bond) Ns = 0.5556, Nb = -0.4103 x 100 = $14.53 @ time: current V0 = 0.5556 x 100 – 0.4103 x 100 = $ 14.53 Buy stock Short sell bond V0 = NsPs +NbPb (Ps: $stock, Pb: $bond) Smart investor will recognize: once V0 is established then

1) If option overpriced say selling @ 20 the profit will be $5.47 (write the call for 20-14.53) 2) If option underpriced say selling @ 10 the profit will be $4.53( buy the call, short the

stock, invest in bond) 4.53 = [ -10 + (0.5556 x 100] – 41.03 Hedge ratio: the expected change in the value of an option for every $1 change in price of stock, the portfolio will change by Ns or 0.5556 The price of the Call will change by 0.5556 as well.

125 

80 

P0= 25 

P0 = 0 

Annual risk free = 8% 

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Shares to purchase h= POU – POD= 25-0 = 0.5556 or delta PSU – PSD 125-80 (S-sell bond) B = PV(hPSD-POD) = PV(0.5556 x 8- 0) = 44.45 = 41.03 1.0833. V0 = hPs-B, h & B are hedge ratio & current value = 14.53 of bond (short position) $5.47 = $20 – (0.5556 x 100) + $41.02 Semiannual analysis 100 The model requires year-end price, several answers or prices can be expected eg. 125, 100, 80 @ year end. 1) 111.8 Calc: h = 25- 0 125-100

B = PV (1 x 100 – 0) = 100 1.0408

V0 = 1 x 111.8 – 96.08 = 15.72

S.S.C  Buy S.    Pay loan 

111.8 

89.49 

125  P0 = 25 

80     P0 = 0 

100  P0 = 0 

= 1

1.04 x 10.4 = 1.0816 

6 M = 1.0408 

V0 = hPs - B

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2) 89.44, Calc = 0, intuition! 3) If 100 We can have quarterly or monthly calculation h = 15.72 – 0

111.8 – 89.44

B = PV (0.703 x 89.44) = 80.4

V0 = 0.703 x 100 – 60.4 = 9.9

Put Option H.R = 0 – 20 125-80

B = PV (-hPSU – POD) = -51.28 (bond to be purchased)

To replicated the put option 1) S. Short 0.444 share of stock 2) Purchase bond 51.28

Put option value to replicate portfolio = -44.44 + 51.28 = $ 6.84

Vop = hPs – B 

        = ‐hPs –(‐B) outflow for purchase 

 

Put-call Parity

The relationship of: European put & call hedge ratio: for same exercise price + Expiration date:

Hc – 1 = hp , 0.5556 – 1 = 0-0.4444

Buy a put & the stock = Buy a call & invest PV of risk free assets

6.84 + 100 = 14.53 + 92.31

Pp + Ps         = Pc + E 

       eRT  

 

(Protective put ; Married Put) 

 

111.8 

89.44 

P0 = 15.72 

P0 = 0 @ t= 0  V0 = 9.89 

= 0.70 

= -0.444 100 125 P0 = 0

80 P0 = 20

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Stock’s Risk from historical prices  

Rt = ln Pst    Ex. Pst = 107, Pst-1= 105 (the 53 week)  Pst – 1 Next week = 1, This week = 2

= Ln 107 = 1.886% Return for one week 105

LN: natural logarithm continuously compound return

Find 52 weekly returns n

Estimate stock’s Ave. return RAV = 1 ∑ (if 6 period - ) n

S2 = 1 ∑ 2 pre-period variance could be 1 week or one day n – 1

Variance: - 2 = 5252 - Some analysts give more weight to recent market value than historical data

Market consensus of a stock’s risk

Implicit volatility: Pc = Vc option priced fairly in market

Mkt $ = fair value

For same expiration date find 0 ex:

35 1

45 2

50 3

By using Vc = N(d1)Ps – E N(d2) formula or groups of diff. expiration date estimate eRT

See P695 Fig 206 for intrinsic call & time value of Black-Scholes value curve (Fig 208 for put)

Put call parity in Black-Scholes: Pp = E N(-d2) – Ps N (-d2) eRT

Pp = Pc + E – Ps eRT

Flex options: CBOE: contracts on indices (by institution), investor specify E&T

Average then