Investment key

8/20/2019 Investment key

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Chapter 4

Mutual Funds

Concept Questions

1. Mutual funds are owned by fund shareholders. A fund is run by the fund manager, who is hired bythe fund’s directors. The fund’s directors are elected by the shareholders.

2. A rational investor might pay a load because he or she desires a particular type of fund or fundmanager for which a no-load alternative does not exist. More generally, some investors feel you getwhat you pay for and are willing to pay more. Whether they are correct or not is a matter of somedebate. Other investors simply are not aware of the full range of alternatives.

3. The NAV of a money market mutual fund is never supposed to change; it is supposed to stay at aconstant $1. It never rises; only in very rare instances does it fall. Maintaining a constant NAV is possible by simply increasing the number of shares as needed such that the number of shares is

always equal to the total dollar value of the fund.

4. A money market deposit account is essentially a bank savings account. A money market mutual fundis a true mutual fund. A bank deposit is insured by the FDIC, so it is safer, at least up to themaximum insured amount.

5. ETFs are very popular with active traders since they allow an investor to use margin to purchase theasset. They also provide the ability to short sell, and they are continuously priced. In contrast, mutualfunds have only end-of-day pricing. For periodic investors who are investing small amounts, mutualfunds may be a better choice since the commissions associated with investing in ETFs would becostly.

6. In an up market, the cash balance will reduce the overall return since the fund is partly invested inassets with a lower return. In a down market, a cash balance should help reduce the negative returnsfrom stocks or other instruments. An open-end fund typically keeps a cash balance to meetshareholder redemptions. A closed-end fund does not have shareholder redemptions so very littlecash, if any, is kept in the portfolio.

7. 12b-1 fees are designed to pay for marketing and distribution costs. It does not really make sense thata closed-end fund charges 12b-1 fees because there is no need to market the fund once it has beensold at the IPO and there are no distributions necessary for the fund since the shares are sold on thesecondary market.

8. You should probably buy an open-end fund because the fund stands ready to buy back shares at

NAV. With a closed-end fund another buyer must make the purchase, so it may be more difficult tosell at NAV. We should note that an open-end fund may have the right to delay redemption if it sochooses.

9. Funds that accumulate a long record of poor performance tend to not attract investors. They are often

simply merged into other funds. This is a type of survivor bias, meaning that a mutual fund family’stypical long-term track record may look pretty good, but only because the poor performing funds didnot survive. In fact, several hundred funds disappear each year.


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10. With a high water mark, the fund manager must overcome any losses before performance fees

can be taken. So, a “bad” return year is not ignored.

Core Questions

NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple

steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is

found without rounding during any step in the problem.

1. NAV = $20.73

2. Load = 6.53%

3. NAV = $17.59; Market value of assets = $337,728,000

4. Initial shares = 50,000. Final shares = 51,250, and final NAV = $1 because this is a money marketfund.

5. Total assets = $2,614,400; NAV = $52.29

6. NAV = $50.09

7. Offering price = $52.73

8. = 32.73%

9. NAV = $21.81; = – 11.74%

10. = 12.53%

Intermediate

11. Turnover = X/$3,400,000,000 = .42; X = $1,428,000,000. This is more than the $1.25 billion in sales,so the turnover with the sales figure is $1,250,000,000 / $3,400,000,000 = .368.In addition to the standard commission costs, there are two other potential costs associated withexcess turnover. First, added trading causes gains to be realized sooner, thereby increasing taxliability. Second, if the trade provider has a soft dollar arrangement, there will be added costs.

12. Management fee = $15,300,000Miscellaneous and administrative expenses = $10,200,000

13. Initial NAV = $44.75Final NAV = $47.46Sale proceeds per share = $46.51Total return = -1.25%You lost -1.25% even thought the fund’s investments grew by 8%! The various fees and loads sharplyreduced your return.


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Note, there is another interpretation of the solution. To calculate the final NAV including fees, wewould first find the final NAV excluding fees with an 8 percent return, which would be:

NAV excluding fees = $48.33

Now, we can find the final NAV after the fees, which would be:

Final NAV = $47.39

Notice this answer is $0.07 different than our original calculation. The reason is the assumption behind the fee withdrawal. The second calculation assumes the fees are withdrawn entirely at the endof the year, which is generally not true. Generally, fees are withdrawn periodically throughout theyear, often quarterly. The actual relationship between the return on the underlying assets, the feescharged, and the actual return earned is the same as the Fisher equation, which shows the relationship between the inflation, the nominal interest rate, and the real interest rate. In this case, we can write therelationship as:

(1 + Return on underlying assets) = (1 + Fees)(1 + Return earned)

As with the Fisher equation, effective annual rates must be used. So, we would need to know the periodic fee withdrawal and the number of fee assessments during the year to find the exact final NAV. Our first calculation is analogous to the approximation of the Fisher equation, hence it is themethod of calculation we will use going forward, that is:

Return earned = Return on underlying assets – Fees

Assuming a small fee (which we hope the mutual fund would have), the answer will be closest to theactual value without undue calculations.

14. Yr 1: There is no performance fee since the manager had a negative return. So, the only year 1 fee is

the 2% management fee: =$15,000.

Yr 2: The management fee is taken out at the beginning of the year on the new balance, so it is:= 13,230

The performance fee is 20% of everything over the $750,000 high water mark.= $777,924= $5,584.80

15. The cost of the ETF is = $55The cost of the mutual fund is = $57.50

16. After 3 years: (For every dollar invested)

Class A: = $1.22191Class B: = $1.24380After 20 years:Class A: = $5.32106Class B: = $4.89962

17. R = 8.19%R = 5.59%


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18. National municipal fund: after-tax yield = 3.22%Taxable fund: after-tax yield = 3.08% New Jersey municipal fund: after-tax yield = 3.40%Choose the New Jersey fund.

19. Municipal fund: after-tax yield = 3.5%

Taxable fund: after-tax yield = 3.51% New Jersey municipal fund: after-tax yield = 3.40%Choose the taxable fund.

20. NAV = $16.72Shares outstanding = 33,492,823For closed-end funds, the total shares outstanding are fixed, just as with common stock (assuming nonet repurchases by the fund or new share issues to the public).

21. NAV at IPO = $9.20 P = $8.56The value of your investment is= $42,800, a loss of $7,200 in one day.

CFA Exam Review by Schweser

1. a

The biggest disadvantage of the fund of funds is the extra layer of fees. Style drift could impact both individual hedge funds and a fund of funds. Benchmark availability is probably more of anissue for individual funds.

2. b

Arbitrage funds usually focus on mergers, spin-offs, takeovers, or convertibles, buying onesecurity and shorting a related one to take advantage of differences in prices.

3. a

Many alternative assets (i.e., hedge funds) provide high returns and are tax-friendly. However,most are not easy to value and are difficult to track closely over short periods of time.

4. b

Benchmarks are available for commodities, real estate, private equity, and hedge funds, thoughnot all of them are easy to interpret. There would be no such benchmark for an individual,

privately held firm such as Kelly.


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Chapter 8

Behavioral Finance and the Psychology of Investing

Concept Questions

1. There are three trends at all times, the primary, secondary, and tertiary trends. For a market timer, thesecondary, or short-run trend, might be the most important, but, for most investors, it is the primary,or long-run trend that matters.

2. A support area is a price or level below which a stock price or market index is not likely to drop. Aresistance area is a price or level above which a stock price or market index is not likely to rise.

3. Mental accounting is when investors treat each investment separately as opposed to considering theoverall wealth of their portfolios. This bias may induce investors to sell winners too early and keeplosers too long.

4. Plan participants often use the 1/n heuristic for their asset allocation. So, if someone allocates evenlyacross all choices, the asset class with the most choices will receive the largest allocation.

5. Men are generally more overconfident than women. This leads to excessive trading, which generallyresults in lower returns.

6. The illusion of knowledge suggests that you believe the information you hold is better than that held by other investors. Therefore, you become overconfident and believe your investment choices are better.

7. At the time the theory was developed, large companies in the U.S. were either involved in themanufacturing of goods or the transportation of them (primarily railroads). The basic idea behind the

Dow theory is that these activities are fundamentally related, so the two averages must move in thesame direction over time.

8. The least likely limit to arbitrage is firm-specific risk. For example, in the 3Com/Palm case, the stocksare perfect substitutes after accounting for the exchange ratio. An investor could invest in a riskneutral portfolio by purchasing the underpriced asset and selling the overpriced asset. When the prices of the assets revert to an equilibrium, the positions could be closed.

9. A contrarian investor goes against the crowd. For example, when investors are bullish, a contrarianwould argue the market is overbought and short sell. Conversely, when investors are pessimistic, acontrarian would begin purchasing stocks.

10. Consider support and resistance lines. If it is agreed the resistance line is $90, what would a rationalinvestor do when the stock price reaches $89 (or some other suitable close price)? The investor wouldsell the stock. This means the new resistance line is $89. Now, an investor would sell at $88. Thislogic implies the support and resistance lines would collapse on each other.


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11. An up gap, where the low stock price today is higher than the high stock price from the previous day,is a bullish signal. A down gap, where the high price today is lower than the low price from the previous day is a bearish signal. Of course, gap traders also believe that the stock must eventually

“cover the gap”, that is, trade in the stock price the gap missed .

12. As long as it is a fair coin the probability in both cases is 50 percent as coins have no memory.

Although many believe the probability of flipping a tail would be greater given the long run of heads,this is an example of the gambler’s fallacy.

13. Prospect theory argues that investors are willing to take more risk to avoid the loss of a dollar thanthey are to make a dollar profit. Also, if an investor has the choice between a sure gain and a gamblethat could increase or decrease the sure gain, the investor is likely to choose the sure gain. The focuson gains and losses, combined with the tendency of investors to be risk-averse with regard to gains, but risk-taking when it comes to losses, is the essence of prospect theory. A fully rational investor (inan economic sense) is presumed to only care about his or her overall wealth, not the gains and lossesassociated with individual pieces of that wealth.

14. Frame dependence is the argument that an investor’s choice is dependent on the way the question is posed. An investor can frame a decision problem in broad terms (like wealth) or in narrow terms (likegains and losses). Broad and narrow frames often lead the investor to make different choices. While itis human nature to use a narrow frame (like gains and losses), doing so can lead to irrationaldecisions. Using broad frames, like overall wealth, results in better investment decisions.

15. A noise trader is someone whose trades are not based on information or financially meaningfulanalysis. Noise traders could, in principle, act together to worsen a mispricing in the short-run. Noisetrader risk is important because the worsening of a mispricing could force the arbitrageur to liquidateearly and sustain steep losses.

Solutions to Questions and Problems

NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this

solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem.

Core Questions1. Adv./Dec. Cumulative

Monday 232 232Tuesday 705 937Wednesday 230 1167Thursday 1958 3125

Friday 73 3198

2. Arms ratio

Monday 0.967Tuesday 0.760Wednesday 1.343Thursday 0.730

Friday 1.029


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3. AMZN GOOG

March $58.30 $328.06

April 65.68 341.53

May 72.92 360.67June 77.32 387.09

July 80.72 411.60

August 82.47 427.29

September 83.54 442.10

October 86.77 466.86

November 97.79 497.88

December 116.03 538.32

4. AMZN GOOG

March $61.54 $333.02

April 69.56 344.79

May 76.72 378.32

June 77.65 402.16

July 82.19 416.59

August 84.12 435.17


October 90.07 481.35

November 108.30 517.00

December 125.97 560.66

5. AMZN GOOG

March $59.92 330.54

April 67.62 343.16

May 74.82 369.50

June 77.49 394.62

July 81.46 414.10

August 83.29 431.23


October 88.42 474.11

November 103.04 507.44

December 121.00 549.49


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6. MSI

1 0.5207

2 0.5620

3 0.6116

4 0.5868

5 0.6446

If the MSI is used as a contrarian indicator, since the indicator is headed upward, the generalsentiment is increasingly bearish. Thus, as a contrarian the market appears to be headed upward.

7. Price Up/DownPrice times

VolumePositive Money

Flow Negative Money

Flow Net Money

Flow

$70.12

$70.14 + 133,266 133,266

$70.13 – 98,182 98,182

$70.09 – 126,162 224,344

$70.05 – 147,105 371,449

$70.07 + 189,189 322,455

$70.03 – 210,090 581,539

Money flow at the end of the day – $259,084

In this case, the money flow is a bearish signal.

8. Simple Exponential

11/2/2009 - -

11/3/2009 - - 11/4/2009 1,044.96 1,045.73

11/5/2009 1,052.88 1,059.76

11/6/2009 1,060.81 1,065.06

11/9/2009 1,076.34 1,084.71

11/10/2009 1,085.13 1,089.07

11/11/2009 1,094.87 1,096.69

11/12/2009 1,092.92 1,090.08

11/13/2009 1,093.08 1,093.28

The reason to calculate the moving average on an index is the same for an individual stock. It can

give an indication of whether the market as a whole is moving upward or downward compared to itsrecent past. If the index closed above the 3-day moving average, it would be a buy indicator.

9. There appears to be a support level at about $25. The resistance level may be about $30, although thestock did break through for a period. A support level is a level below which the stock or market isunlikely to go. A resistance level is a level above which the stock or market is likely to rise.


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10. Adv./Dec. Cumulative Arms ratio

Monday 2,011 2,011 0.545Tuesday 1,790 3,801 0.836Wednesday 172 3,973 1.081Thursday 1,375 5,348 0.904

Friday 641 5,989 0.998

11. Price Up/DownPrice times

VolumePositive Money

Flow Negative Money

Flow Net Money

Flow

$61.85

$61.81 - $61,810 $61,810

$61.82 + 86,548 $86,548

$61.85 + 80,405 166,953

$61.84 - 49,472 111,282

$61.87 + 68,057 235,010

$61.88 + 86,632 321,642

$61.92 + 37,152 358,794

$61.91 - 74,292 185,574

$61.93 + 99,088 457,882

Money flow at the end of the day $272,308

Since the price was relatively stable and the money flow was positive, this is likely a bullish signal.

Intermediate Questions

12. Primary support = $42 – [($42 – 26)(.382)] = $35.89

Secondary support = $42 – [($42 – 26)(.618)] = $32.11


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13. 3-day 5-day

10/26/09 - -

10/27/09 - -

10/28/09 23.08 -

10/29/09 22.97 -

10/30/09 22.68 22.9011/2/09 22.57 22.72

11/3/09 22.41 22.60

11/4/09 22.50 22.56

11/5/09 22.77 22.60

11/6/09 23.04 22.82

11/9/09 23.28 22.98

11/10/09 23.35 23.17

11/11/09 23.49 23.41

11/12/09 23.70 23.54

11/13/09 23.80 23.62

Series1

Series3


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14. Date 3-day 5-day

10/26/09 $- $-

10/27/09 $- $-

10/28/09 22.91 $-

10/29/09 22.99 $-

10/30/09 22.47 22.5311/2/09 22.51 22.56

11/3/09 22.46 22.55

11/4/09 22.53 22.55

11/5/09 23.00 22.97

11/6/09 23.19 23.12

11/9/09 23.28 23.15

11/10/09 23.39 23.32

11/11/09 23.62 23.61

11/12/09 23.81 23.76

11/13/09 23.77 23.69

Series1

Series3


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15. Week Put/Call Ratio

1 1.1490

2 1.1234

3 1.1069

4 1.0965

The put/call ratio is a measure of investor sentiment about the future direction of the market. Puts area bet that the market (or stock) will move down and calls are a bet the market (or stock) will moveupwards. The put/call ratio is the number of down bets divided by the number of up bets. A ratiogreater than one indicates more investors believe the market (or stock) will move down than thenumber of investors who believe the market will move up. It is a bearish signal. From these numbers,it appears more investors believe the market will move down in the future. Of course, there arecaveats. First, the put/call ratio can be used as a contrarian indicator. Second, even though a largenumber of calls may indicate that investors believe the stock (or market) will increase in value,options are a derivative asset. So, there is another investor selling the call for a premium who also believes he will also make money on the transaction.

CFA Exam Review by Schweser

1. a

Tom believes that on the basis of his five-year record that he can continue to outperform a benchmark. His record could be due to luck and/or he may not be reporting his shortcomings.

2. c

As an overconfident investor, Higgins will tend to underestimate risk and overestimate the impactof an event, which will likely lead to a negative surprise in the future.

3. a

Because she dislikes losses so much, she is willing to take more risk to make up the losses in her portfolio.

4. c

Jack believes that just because a firm’s environmental policy is good that the firm’s stock will bea good investment. He ignores valuation.

5. c

These investors will use their experiences, inferences, and heuristics to form decisions, whileignoring fundamental characteristics.


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Chapter 10

Bond Prices and Yields

Concept Questions

1. Premium (par, discount) bonds are bonds that sell for more than (the same as, less than) their face or par value.

2. The face value is normally $1,000 per bond. The coupon is expressed as a percentage of face value(the coupon rate), so the annual dollar coupon is calculated by multiplying the coupon rate by$1,000. Coupons are normally paid semi-annually; the semi-annual coupon is equal to the annualcoupon divided by two.

3. The coupon rate is the annual dollar coupon expressed as a percentage of face value. The currentyield is the annual dollar coupon divided by the current price. If a bond’s price rises, the coupon rate

won’t change, but the current yield will fall.

4. Interest rate risk refers to the fact that bond prices fluctuate as interest rates change. Lower couponand longer maturity bonds have greater interest rate risk.

5. For a premium bond, the coupon rate is higher than the yield. The reason is simply that the bondssell at a premium because it offers a coupon rate that is high relative to current market requiredyields. The reverse is true for a discount bond: it sells at a discount because its coupon rate is toolow.

6. A bond’s promised yield is an indicator of what an investor can expect to earn if (1) all of the bond’s promised payments are made and (2) market conditions do not change. The realized yield is theactual, after-the-fact return the investor receives. The realized yield is more relevant, of course, but it

is not knowable ahead of time. A bond’s calculated yield to maturity is the promised yield.

7. The yield to maturity is the required rate of return on a bond expressed as a nominal annual interestrate. For noncallable bonds, the yield to maturity and required rate of return are interchangeableterms. Unlike YTM and required return, the coupon rate is not used as the interest rate in bond cashflow valuation, but is a fixed percentage of par over the life of the bond used to set the coupon payment amount. For the example given, the coupon rate on the bond is still 10 percent, and theYTM is 8 percent.

8. Since the yield increased, the price of the bond will decrease. This can be explained in two ways.First, any new bonds will have a 15 percent coupon rate in order to sell at par since that is the marketinterest rate. Investors will pay less for a 9 percent coupon bond since they can buy a bond with a 15 percent coupon rate. Second, the decrease in price is a function of the time value of money. The price of the bond is the present value o the coupon payments plus the present value of the principal.In any present value calculation, the present value declines when the interest rate increases.


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9. a. Bond price is the present value term when valuing the cash flows from a bond; YTM is theinterest rate used in valuing the cash flows from a bond. They have an inverse relationship.

b. If the coupon rate is higher than the required return on a bond, the bond will sell at a premium,since it provides periodic income in the form of coupon payments in excess of that required byinvestors on other similar bonds. If the coupon rate is lower than the required return on a bond,

the bond will sell at a discount, since it provides insufficient coupon payments compared to thatrequired by investors on other similar bonds. For premium bonds, the coupon rate exceeds theYTM; and for discount bonds, the YTM exceeds the coupon rate. For bonds selling at par, theYTM is equal to the coupon rate.

c. Current yield is defined as the annual coupon payment divided by the current bond price. For premium bonds, the current yield exceeds the YTM; for discount bonds the current yield is lessthan the YTM; and for bonds selling at par value, the current yield is equal to the YTM. In allcases, the current yield plus the expected one-period capital gains yield of the bond must beequal to the required return.

10. A premium bond is one with a relatively high coupon, and, in particular, a coupon that is higher than

current market yields. These are precisely the bonds that the issuer would like to call, so a yield tocall is probably a better indicator of what is likely to happen than the yield to maturity (the oppositeis true for discount bonds). It is also the case that the yield to call is likely to be lower than the yieldto maturity for a premium bond, but this can depend on the call price. A better convention would beto report the yield to maturity or yield to call, whichever is smaller.



steps. Due to space and readability constraints, when these intermediate steps are included in this


Core Questions

1. P = $35(PVIFA4.55%, 24) + $1,000(PVIF4.55%, 24) = $848.55

2. P = $1,086 = $30(PVIFAR%,28) + $1,000(PVIFR%,28) ; R = 2.566%, YTM = 5.13%

current yield = $60.00/$1,086 = 5.52%

3. P = $41(PVIFA3.7%,26) + $1,000(PVIF3.7%,26) = $1,066.07

4. P = $36(PVIFA4.0%, 50) + $1,000(PVIF4.0%, 50) = $914.07

5. P = $902.30 = $30(PVIFAR%,24) + $1,000(PVIFR%,24) ; R = 3.616%, YTM = 7.23%

6. P = $1,047 = $41(PVIFAR%,29) + $1,000(PVIFR%,29) ; R = 3.829%, YTM = 7.66%

7. P = $928 = $37.50(PVIFAR%,18) + $1,000(PVIFR%,18) ; R = 4.334%; YTM = 8.67%

8. YTM = [($1,000/$289)1/40 – 1] × 2 = 6.30%


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9. YTC = [($500/$289)1/20 – 1] × 2 = 5.56%

10. YTC = [($475/$289)1/20 – 1] × 2 = 5.03%

Intermediate Questions

11. P = $938 = $C(PVIFA3.75%,20) + $1,000(PVIFA3.75%,20) ; C = $33.04coupon rate = 2(0.03304) = 6.61%

12. P = $42(PVIFA4.6%,18) + $1,000(PVIF4.6%,18) = $951.75

13. P = $920 = $37.50(PVIFAR%,46) + $1,000(PVIFR%,46) ; R = 4.142%; YTM = 8.28%

14. Assuming a $1,000 face value, the current price of the bond is $1,000 / (1.03)40 = $306.56. Twoyears later the bond has 18 years to maturity and the same price, so the new yield to maturity must be [($1,000/$306.56)1/36 – 1] × 2 = 6.68%.

15. If held to maturity, a zero-coupon bond will always have a realized yield equal to its original yield tomaturity, which in this case is 6 percent.

16. P: P0 = $40(PVIFA3%,30) + $1,000(PVIF3%,30) = $1,196.00

P1 = $40(PVIFA3%,28) + $1,000(PVIF3%,28) = $1,187.64

P5 = $40(PVIFA3%,20) + $1,000(PVIF3%,20) = $1,148.77

P10 = $40(PVIFA3%,10) + $1,000(PVIF3%,10) = $1,085.30

P14 = $40(PVIFA3%,2) + $1,000(PVIF3%,2) = $1,019.13

P15 = $1,000

D: P0 = $40(PVIFA5%,30) + $1,000(PVIF5%,30) = $846.28

P1 = $40(PVIFA5%,28

) + $1,000(PVIF5%,28

) = $851.02

P5 = $40(PVIFA5%,20) + $1,000(PVIF5%,20) = $875.38

P10 = $40(PVIFA5%,10) + $1,000(PVIF5%,10) = $922.78

P14 = $40(PVIFA5%,2) + $1,000(PVIF5%,2) = $981.41

P15 = $1,000

All else held equal, the premium over par value for a premium bond declines as maturity isapproached, and the discount from par value for a discount bond declines as maturity isapproached. This is sometimes called the “pull to par.”

17. If both bonds sell at par, the initial YTM on both bonds is the coupon rate, 6 percent. If the YTMsuddenly rises to 8 percent, then:

PA = $30(PVIFA4%,10) + $1,000(PVIF4%,10) = $918.89

PB = $30(PVIFA4%,30) + $1,000(PVIF4%,30) = $827.08

∆PA% = (918.89 – 1,000)/1,000 = – 8.11%

∆PB% = (827.08 – 1,000)/1,000 = – 17.29%


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If the YTM suddenly falls to 4 percent, then:

PA = $30(PVIFA2%,10) + $1,000(PVIF2%,10) = $1,089.83

PB = $30(PVIFA2%,30) + $1,000(PVIF2%,30) = $1,223.96

∆PA% = (1,089.83 – 1,000)/1,000 = + 8.98%

∆PB% = (1,223.96 – 1,000)/1,000 = + 22.40%

All else the same, the longer the maturity of a bond, the greater is its price sensitivity to changesin interest rates.

18. Initially, at a YTM of 7 percent, the prices of the two bonds are:

PJ = $20(PVIFA3.5%,20) + $1,000(PVIF3.5%,20) = $786.81

PK = $40(PVIFA3.5%,20) + $1,000(PVIF3.5%,20) = $1,071.06

If the YTM rises from 7 percent to 9 percent:

PJ = $20(PVIFA4.5%,20) + $1,000(PVIF4.5%,20) = $674.80

PK = $40(PVIFA4.5%,20) + $1,000(PVIF4.5%,20) = $934.96

∆PJ = (674.80 – 786.81)/786.81 = – 14.24%∆PK = (934.96 – 1,071.06)/1,071.06 = – 12.71%

If the YTM declines from 7 percent to 5 percent:

PJ = $20(PVIFA2.5%,20) + $1,000(PVIF2.5%,20) = $922.05

PK = $40(PVIFA2.5%,20) + $1,000(PVIF2.5%,20) = $1,233.84

∆PJ = (922.05 – 786.81)/786.81 = + 17.19%∆PK = (1,233.84 – 1,071.06)/1,071.06 = + 15.20%

All else the same, the lower the coupon rate on a bond, the greater is its price sensitivity tochanges in interest rates.

19. Current yield = .0920 = $100/P0 ; P0 = $100/.0920 = $1,086.96

P0 = $1,086.96 = $50[ (1 – (1/1.043) Nx2

) / .043 ] + $1,000/1.043 Nx2 N = 9.07 yrs.

20. The maturity is indeterminate; a bond selling at par can have any maturity length.

21. a. P0 = $1,080 = $30(PVIFAR%,20) + $1,000(PVIFR%,20) ; R = 2.487%, YTM = 4.97%

This is the rate of return you expect to earn on your investment when you purchase the bond.


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b. Price when sold = $30(PVIFA3.487%,16) + $1,000(PVIF3.487%,16) = $940.99

Future value of reinvested interest payments = $30(FVIFA2.487%,4) = $124.55Realized return = ($940.99 – 1,080 + 124.55) / $1,080 = – 1.34%. On a per year basis, the rate isequal to -0.67%.

22. The yield to call can be computed as:

P = $1,080 = $50(PVIFAR%,10) + $1,100(PVIFR%,10) ; R = 4.778%, YTC = 9.56%

Since the bond sells at a premium to par value, you know the coupon rate must be greater than theyield. Thus, if interest rates remain at current levels, the bond issuer will likely call the bonds torefinance (at a lower coupon rate) at the earliest possible time, which is the date when call protection ends. The yield computed to this date is the YTC, and it will always be less than theYTM for premium bonds with a zero call premium. In the present example,

P = $1,080 = $50(PVIFAR%,50) + $1,000(PVIFR%,50) ; R = 4.589%, YTM = 9.18%

where if the bond is held until maturity, no call premium must be paid. Note that using the sameanalysis, a break-even call premium can also be computed:

P = $1,080 = $50(PVIFA4.59%,10) + ($1,000 + X)(PVIF4.59%,10) ; X = $74.62

Thus, if interest rates remain unchanged, the bond will not be called if the call premium is greaterthan $74.62.

23. P = $935.50 = $35(PVIFAR%,12) + $1,000(PVIFR%,12) ; R = 4.195%, YTM = 8.390%

Duration = (1.04195/.0839) – [(1.04195 + 6(.07 – .08390)) / (.08390 + .07(1.0419512 – 1))]Duration = 4.961years

Modified duration = 4.961/(1.04195) = 4.761 years

24. Estimated percent change in price = – 4.761 (.02) = – .09522 = (P1/P0) – 1

so P1 = (1 – .09522)($935.50) = $846.42

Actual P1 = $35(PVIFA5.195%,12) + $1,000(PVIF5.195%,12) = $851.41

25. Dollar value of an 01 = (4.761/100) × $935.50 × .01 = $0.445

26. P = $1,060.50 = $37.50(PVIFAR%,16) + $1,000(PVIFR%,16) ; R = 3.224%, YTM = 6.447%

Duration = (1.03224/.06447) – [(1.03224 + 8(.075 – .06447)) / (.06447 + .075(1.0322416 – 1))]Duration = 6.223 years



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Dollar value of an 01 = (6.029/100) × $1,060.50 × .01 = $0.642

Yield value of a 32nd = 1 / (32 × 0.642) = 0.049 basis points

27. Duration = (1.045/.09) – [(1.045 + 11(.08 – .09)) / (.09 + .08(1.04522 – 1))] = 7.374 years


28. Duration = (1.035/.07) – [(1.035 + 11(.08 – .07)) / (.07 + .08(1.03522 – 1))] = 7.653 years


For an option free bond, at a lower YTM, the duration is higher.

29. Duration = (1.035/.07) – [(1.035 + 19(.08 – .07)) / (.07 + .08(1.03538 – 1))] = 10.498 years


30. Initial price = $40(PVIFA3.5%, 38) + $1,000(PVIF3.5%,38) = $1,104.21If interest rates rise .25%:

Estimated percent change in price = – 10.143(.0025) = – .02536 = (P1/P0) – 1

so P1 = (1 – .02536)($1,104.21) = $1,076.21

Actual P1 = $40(PVIFA3.625%,38) + $1,000(PVIF3.625%,38) = $1,076.71

If interest rates rise 1%:


so P1 = (1 – .1014)($1,104.21) = $992.21

Actual P1 = $40(PVIFA4.0%,38) + $1,000(PVIF4.0%,38) = $1,00.00

If interest rates rise 2%:Estimated percent change in price = – 10.143(.02) = – .2029 = (P1/P0) – 1

so P1 = (1 – .2029)($1,104.21) = $880.21


If interest rates rise 5%:


so P1 = (1 – .5071)($1,104.21) = $544.22


While duration gives an effective estimate for small interest rate changes, duration does not produce

a good estimate of the price change for large interest rate changes.

31. Zero coupon YTM = $949 = $1,000 / (1 + r); r = 5.37%Two year spot rate: $1,020 = $75/(1 + .0537) + $1,075/(1 + r 2)

2 ; r 2 = 6.44%Three year spot rate: $1,029 = $85/(1 + .0537) + $85/(1 + .0644)2 + $1,085/(1 + r 2)

3; r 3 = 7.50%

32. P = $65/(1 + .0420) + $65/(1 + .0450)2 + $65/(1 + .0490)3 + $1,065/(1 + .0510)4 = $1,051.06

P = $1,051.06 = $65(PVIFAR%,4) + $1,000(PVIFR%,4) ; YTM = 5.06%


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Chapter 13

Performance Evaluation and Risk Management

Concept Questions

1. The Sharpe ratio is calculated as a portfolio’s risk premium divided by the standard deviation of the portfolio’s return. The Treynor ratio is the portfolio risk premium divided by the portfolio’s betacoefficient.

2. A common weakness of both the Jensen alpha and the Treynor ratio is that both require an estimateof beta, which can differ a lot depending on the source, which in turn can lead to a mismeasurementof risk adjusted return.

3. Jensen’s alpha is the difference between a stock’s or a portfolio’s actual return and that which is predicted by the CAPM. A positive alpha implies returns above the SML line (as drawn using theCAPM).

4. An advantage of the Sharpe ratio is that a beta estimate is not required; however, the Sharpe ratio isnot appropriate when evaluating individual stocks because it uses total risk rather than systematic.

5. To determine significance, one might use the t -statistics or p-values from a regression estimate.Beyond this, the information ratio will standardize alpha to account for the volatility in the estimate.Also, a high R-squared will give some degree of confidence to the alpha estimate. Lastly, adherenceto GIPS standards may give confidence to the estimate of one firm over another.

6. A Sharpe optimal portfolio is the portfolio with the highest possible Sharpe ratio given the availableinvestments. This portfolio has the characteristic of having the highest possible return for the leastamount of risk.

7. The Markowitz efficient frontier is closely related to the Sharpe ratio. The Markowitz efficientfrontier tells us which portfolios are efficient (highest return for a given level of risk), but the Sharpemodel helps to identify which of these efficient portfolios is actually the best.

8. After establishing the desired probability (x), the VaR statistic provides the minimum loss youwould receive x% of the time. As an example, given:

Prob(R – .20) = 5%we would expect at least a 20% loss in one out of twenty periods (5% of the time).

9. This is equivalent to saying that 5% of the time the minimum loss is 20%, similar to the previousanswer .

10. For sector funds or investments that only cover a portion of the market (e.g., value or growth), amore specific index may provide a better standard for judging performance.


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steps. Due to space and readability constraints, when these intermediate steps are included in this


Core Questions

1. 54% 2/12 = 22.05%

2. 9.20% / 1/12 = 31.87%

3.

Portfolio Sharpe ratio Treynor ratio Jensen's alpha

X 0.27586 0.0640 0.50%

Y 0.29167 0.0636 0.40%

Z 0.28571 0.0533 – 0.50%

Market 0.31579 0.0600 0.00%

4. IR = 0.50% / 11.40% = 0.0439

5. R-squared gives the percentage of the fund’s return driven by the market, which is: 0.752 = 56.25%

6. TE = 1.4% / 0.20 = 7.0%

7. Prob(R .10 – 1.645(.28)) = 5%Prob(R – .3606) = 5%

8. Prob(R (.18/12) – 1.96(.44)(1/12)1/2) = 2.5%

Prob(R – .2339) = 2.5%

9. E( R) = (.10 + .18)/2 = .14

= (.52 .28

2 + .52 .442)1/2 = .2608

Prob(R (.14/12) – 1.96(.2608)(1/12)1/2) = 2.5%

Prob(R – .1359) = 2.5%

10. For a portfolio with two investments having zero correlation, the Sharpe ratio would be calculated as

follows:

)x(x

R -)E(R x)E(R x ratioSharpe

1/22B

2B

2S

2S

f BBSS

11. ))]R ,)(Corr(R )((.2(.5)(.5).5[.5

R -).5E(R ).5E(R ratioSharpe

1/2BSBS

2B

22S

2

f BS


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12. Any portfolio of the two securities will also have the same expected return.

1/22B

2B

2S

2S

f B

1/22B

2B

2S

2S

f S

)x(x

R -)E(R

)x(x

R -)E(R ratioSharpe

13. Prob(R .11 – 2.326(.54)) = 1%Prob(R – 1.1462) = 1%This number does not make sense since it is impossible to lose more than 100% in a stock.

14. Prob(R .11 + 2.326(.54)) = 1%

Prob(R + 1.3662) = 1%While this is a large return, it is plausible, and even possible. Since it is not possible for a stock tolose more than 100% but it is possible for a stock to gain more than 100%, stock returns are not trulynormal.

15. E( R) = (.10 + .18) / 2 = .1400

= [(.52)(.262) + (.52)(.622) + 2(.5)(.5)(.26)(.62)(.5)]1/2 = .3915

Prob(R (.1400/12) – 1.645(.3915)(1/12)1/2) = 5%Prob(R – .1742) = 5%

16. E( R) = (.10 + .18) / 2 = .1400

= [(.52)(.262) + (.52)(.622) + 2(.5)(.5)(.26)(.62)( – .5)]1/2 = .2696

Prob(R (.1400/12) – 1.645(.2696)(1/12)1/2) = 5%

Prob(R – .1164) = 5%

17. E( R) = .14

= [(.3332)(.302) + (.3332)(.402) + (.3332)(.502) + 2(.333)(.333)(.30)(.40)(0) +2(.333)(.333)(.30)(.50)(0) + 2(.333)(.333)(.40)(.50)(0)]1/2 = .2357

Prob(R .14 – 2.326(.2357)) = 1%

Prob(R – .4083) = 1%

18. wA = [(.12 – .05)(.482) – (.15 – .05)(.29)(.48)(.25)] / {(.12 – .05)(.482) + (.15 – .05)(.292)

– (.12 – .05 + .15 – .05)[(.29)(.48)(.25)]}wA = .6792wB = .3208E(R P) = .6792(.12) + .3208(.15) = .1296

= [(.67922)(.292) + (.32082)(.482) + 2(.6792)(.3208)(.29)(.48)(.25)]1/2 = .2787

Sharpe ratio = (.1296 – .05)/.2787 = .2857

Prob(R .1296 – 1.960(.2787)) = 2.5%

Prob(R – .4166) = 2.5%

19. Sharpe = (.0546 - .0240) / .1505 = .2034Treynor = (.0546 - .0240) / .88 = .0350

20. Jensen’s alpha = .0546 – [.0240 + (.0196 - .0240)(0.88)] = 3.45%Information ratio = 3.45% / 4.14% = 0.8321

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