Financial Management Chapter 06 IM 10th Ed

8/2/2019 Financial Management Chapter 06 IM 10th Ed

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CHAPTER 6

Risk andRates of Return

CHAPTER ORIENTATION

This chapter introduces the concepts that underlie the valuation of securities and their rates

of return. We are specifically concerned with common stock, preferred stock, and bonds. Wealso look at the concept of the investor's expected rate of return on an investment.

CHAPTER OUTLINE

I. The relationship between risk and rates of return

A. Data have been compiled by Ibbotson and Sinquefield on the actual returnsfor various portfolios of securities from 1926-2002.

B. The following portfolios were studied.

1. Common stocks of small firms

2. Common stocks of large companies

3. Long-term corporate bonds

4. Long-term U.S. government bonds

5. U.S. Treasury bills

C. Investors historically have received greater returns for greater risk-taking withthe exception of the U.S. government bonds.

D. The only portfolio with returns consistently exceeding the inflation rate has

been common stocks.II. Effects of Inflation on Rates of Return

A. When a rate of interest is quoted, it is generally the nominal or, observed rate.The real rate of interest represents the rate of increase in actual purchasingpower, after adjusting for inflation.


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B. Consequently, the nominal rate of interest is equal to the sum of the real rateof interest, the inflation rate, and the product of the real rate and the inflationrate.

III. Term Structure of Interest Rates

The relationship between a debt securitys rate of return and the length of time untilthe debt matures is known as the term structure of interest rates or the yield tomaturity.

IV. Expected Return

A. The expected benefits or returns to be received from an investment come inthe form of the cash flows the investment generates.

B. Conventionally, we measure the expected cash flow, X , as follows:

X =

Ni

XiP(Xi)

where N = the number of possible states of the economy.

Xi = the cash flow in the ith state of the economy.

P(Xi) = the probability of the ith cash flow.

V. Riskiness of the cash flows

A. Risk can be defined as the possible variation in cash flow about an expectedcash flow.

B. Statistically, risk may be measured by the standard deviation about theexpected cash flow.

C. Risk and diversification

1. Total variability can be divided into:

a. The variability of returns unique to the security (diversifiableor unsystematic risk)

b. The risk related to market movements (nondiversifiable orsystematic risk)

2. By diversifying, the investor can eliminate the "unique" security risk.The systematic risk, however, cannot be diversified away.

3. The market rewards diversification. We can lower risk withoutsacrificing expected return, and/or we can increase expected returnwithout having to assume more risk.

4. Diversifying among different kinds of assets is called asset allocation.Compared to diversification within the different asset classes, thebenefits received are far greater through effective asset allocation.

5. Risk and being patient


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a. An investor in common stocks must often wait longer to earnthe higher returns than those provided by bonds.

b. The capital markets reward us not just for diversifying, butalso for being patient. The returns tend to converge toward theaverage as we lengthen our holding period.

6. The characteristic line tells us the average movement in a firm'sstock price in response to a movement in the general market, such asthe stock market. The slope of the characteristic line, which has cometo be called beta, is a measure of a stock's systematic or market risk.The slope of the line is merely the ratio of the "rise" of the linerelative to the "run" of the line.

7. If a security's beta equals one, a 10 percent increase (decrease) inmarket returns will produce on average a 10 percent increase(decrease) in security returns.

8. A security having a higher beta is more volatile and thus more risky

than a security having a lower beta value.

9. A portfolio's beta is equal to the average of the betas of the stocks inthe portfolio.

VI. Required rate of return

A. The required rate of return is the minimum rate necessary to compensate aninvestor for accepting the risk he or she associates with the purchase andownership of an asset.

B. Two factors determine the required rate of return for the investor:

1. The risk-free rate of interest which recognizes the time value of

money.

2. The risk premium which considers the riskiness (variability of returns)of the asset and the investor's attitude toward risk.

C. Capital asset pricing model-CAPM

1. The required rate of return for a given security can be expressed as

Requiredrate =

risk-freerate + beta x

market

return -risk-free

rate

or

kj = krf + j (km - krf)

2. Security market line

a. Graphically illustrates the CAPM.

b. Designates the risk-return trade-off existing in the market,where risk is defined in terms of beta according to the CAPMequation.


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ANSWERS TO

END-OF-CHAPTER QUESTIONS

6-1. Data have been compiled by Ibbotson and Sinquefield on the actual returns for the

following portfolios of securities from 1926-2002.

1. U.S. Treasury bills

2. U.S. government bonds

3. Corporate bonds

4. Common stocks for large firms

5. Common stocks for small firms

Investors historically have received greater returns for greater risk-taking with theexception of the U.S. government bonds. Also, the only portfolio with returns

consistently exceeding the inflation rate has been common stocks.6-2 When a rate of interest is quoted, it is generally the nominal or, observed rate. The

real rate of interest represents the rate of increase in actual purchasing power, afteradjusting for inflation. Consequently, the nominal rate of interest is equal to the sumof the real rate of interest, the inflation rate, and the product of the real rate and theinflation rate.

6-3 The relationship between a debt securitys rate of return and the length of time untilthe debt matures is known as the term structure of interest rates or the yield tomaturity. In most cases, longer terms to maturity command higher returns or yields.

6-4. (a) The investor's required rate of return is the minimum rate of return necessary

to attract an investor to purchase or hold a security.(b) Risk is the potential variability in returns on an investment. Thus, the greater

the uncertainty as to the exact outcome, the greater is the risk. Risk may bemeasured in terms of the standard deviation or by the variance term, which issimply the standard deviation squared.

(c) A large standard deviation of the returns indicates greater riskiness associatedwith an investment. However, whether the standard deviation is large relativeto the returns has to be examined with respect to other investmentopportunities. Alternatively, probability analysis is a meaningful approach tocapture greater understanding of the significance of a standard deviation

figure. However, we have chosen not to incorporate such an analysis into ourexplanation of the valuation process.

6-5. (a) Unique risk is the variability in a firm's stock price that is associated with thespecific firm and not the result of some broader influence. An employeestrike is an example of a company-unique influence.

(b) Systematic risk is the variability in a firm's stock price that is the result ofgeneral influences within the industry or resulting from overall market or


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economic influences. A general change in interest rates charged by banks isan example of systematic risk.

6-6. Beta indicates the responsiveness of a security's returns to changes in the marketreturns. Beta is multiplied by the market risk premium and added to the risk-free rateof return to calculate a required rate of return.

6-7. The security market line is a graphical representation of the risk-return trade-off thatexists in the market. The line indicates the minimum acceptable rate of return forinvestors given the level of risk. Since the security market line results from actualmarket transactions, the relationship not only represents the risk-return preferences ofinvestors in the market but also represents the investors' available opportunity set.

6-8. The beta for a portfolio is equal to the weighted average of the individual stock betas,weighted by the percentage invested in each stock.

6-9. If a stock has a great amount of variability about its characteristic line (the graph ofthe stock's returns against the market's returns), then it has a high amount ofunsystematic or company-unique risk. If, however, the stock's returns closely follow

the market movements, then there is little unsystematic risk.

SOLUTIONS TO

END-OF-CHAPTER PROBLEMS

Solutions to Problems Set A

6-1A.

krf= .045 + .073 + (.045 x .073)

krf= .1213

or

12.13% = nominal rate of interest

6-2A.

krf= .064 + .038 + (.064 x .038)

krf= .1044

or10.44% = nominal rate of interest


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6-3A.(A) (B) (A) x (B) Weighted

Probability Return Expected Return Deviation

P(ki) (ki) k (ki - k)2P(ki)

.15 -1% -.15% 2.223%

.30 2 0.60% 0.217%

.40 3 1.20% 0.009%

.15 8 1.20% 3.978%

k= 2.85% 2 = 6.427% = 2.535%

No, Pritchard should not invest in the security. The level of risk is excessive for areturn which is less than the rate offered on treasury bills.

6-4A.

Common Stock A:

(A) (B) (A) x (B) WeightedProbability Return Expected Return Deviation


0.3 11% 3.3% 4.8%0.4 15 6.0 0.00.3 19 5.7 4.8

k = 15.0% 2 = 9.6%

= 3.10%

Common Stock B



0.2 -5% -1.0% 41.472%0.3 6 1.8 3.4680.3 14 4.2 6.3480.2 22 4.4 31.752

k = 9.4% 2 = 83.04% = 9.11%

Common Stock A is better. It has a higher expected return with less risk.


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6-5A.Common Stock A:



0.2 - 2% -0.4% 69.9%0.5 18 9.0 0.80.3 27 8.1 31.8

k = 16.7% 2 = 102.5% = 10.12%

Common Stock B:



0.1 4% 0.4% 2.704%0.3 6 1.8 3.0720.4 10 4.0 0.2560.2 15 3.0 6.728

k = 9.2% 2 = 12.76% = 3.57%

Common Stock A Common Stock Bk = 16.7% k = 9.2%

= 10.12% = 3.57%

We cannot say which investment is "better." It would depend on the investor'sattitude toward the risk-return tradeoff.

6-6A.

(a)

Required rate

of return =

Risk-free

rate + Beta

Market Risk

Premium

= 6 % + 1.2 (16% - 6%)

= 18%

(b) The 18 percent "fair rate" compensates the investor for the time value ofmoney and for assuming risk. However, only nondiversifiable risk is beingconsidered, which is appropriate.

6-7A. Eye balling the characteristic line for the problem, the rise relative to the run is about0.5. That is, when the S & P 500 return is eight percent Aram's expected returnwould be about four percent. Thus, the beta is also approximately 0.5 (4 8).


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6-8A.

Risk-FreeRate +

Expected Market - Risk-Free

Return Rate x Beta =

RequiredRate ofReturn

A 6.75% + (12% - 6.75%) x 1.50 = 14.63%B 6.75% + (12% - 6.75%) x 0.82 = 11.06%C 6.75% + (12% - 6.75%) x 0.60 = 9.90%D 6.75% + (12% - 6.75%) x 1.15 = 12.79%

6-9A.`


=Risk-Free

Rate + (Market Return - Risk-Free Rate) X Beta

= 7.5% + (11.5% - 7.5%) x 0.765

= 10.56%

6-10A. If the expected market return is 12.8 percent and the risk premium is 4.3 percent, theriskless rate of return is 8.5 percent (12.8% - 4.3%). Therefore;

Tasaco = 8.5% + (12.8% - 8.5%) x 0.864 = 12.22%

LBM = 8.5% + (12.8% - 8.5%) x 0.693 = 11.48%

Exxos = 8.5% + (12.8% - 8.5%) x 0.575 = 10.97%

6-11A.Asman Salinas

Time Price Return Price Return

1 $10 $302 12 20.00% 28 -6.67%3 11 -8.33 32 14.294 13 18.18 35 9.38

A holding-period return indicates the rate of return you would earn if you bought asecurity at the beginning of a time period and sold it at the end of the period, such asthe end of the month or year.


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6-12A.a. Zemin Market

Month kb (kb - k)2 kb (kb - k)

2

1 6.00% 16.00% 4.00% 8.03%

2 3.00 1.00 2.00 0.693 1.00 1.00 -1.00 4.694 -3.00 25.00 -2.00 10.035 5.00 9.00 2.00 0.696 0.00 4.00 2.00 0.69Sum 12.00 56.00 7.00 24.82

Averagemonthlyreturn

2.00% 1.17%

(Sum 6)

Annualizedaveragereturns

24.00% 14.04%

Variance 11.20% 4.97%

(Sum 5)

Standarddeviation 3.35% 2.23%

b.

Required

Rate ofReturn

= Risk-FreeRate + (Market Return - Risk-Free Rate) X Beta

= 8% + [(14% - 8%) X 1.54] = 17.24%

c. Zemin's historical return of 24 percent exceeds what we would consider a fairreturn of 17.24 percent, given the stock's systematic risk.

6-13A.

a. The portfolio expected return, kp, equals a weighted average of the

individual stock's expected returns.

kp = (0.20)(16%) + (0.30)(14%) + (0.15)(20%) + (0.25)(12%) +

(0.10)(24%)

= 15.8%


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b. The portfolio beta, p, equals a weighted average of the individual stock betas

p = (0.20)(1.00) + (0.30)(0.85) + (0.15)(1.20) + (0.25)(0.60) +

(0.10)(1.60)

= 0.95

c. Plot the security market line and the individual stocks

Beta

0.00

5.00

10.00

15.00

20.00

25.00

0. 00 0. 50 1. 00 1. 50 2. 00

1

4

3

2

5

PM

d. A "winner" may be defined as a stock that falls above the security market

line, which means these stocks are expected to earn a return exceeding whatshould be expected given their beta or systematic risk. In the above graph,these stocks include 1, 3, and 5. "Losers" would be those stocks fallingbelow the security market line, which are represented by stocks 2 and 4 ever

so slightly.

e. Our results are less than certain because we have problems estimating thesecurity market line with certainty. For instance, we have difficulty inspecifying the market portfolio.


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6-14A a.Market Mathews

Month Price kt (kt - k)2 Price kt (kt - k)

2

Jul-02 1328.72 34.50

Aug-02 1320.41 -0.63% 0.0002 41.09 19.10% 0.0170

Sep-02 1282.71 -2.86% 0.0013 37.16 -9.56% 0.0244

Oct-02 1362.93 6.25% 0.0031 38.72 4.20% 0.0003

Nov-02 1388.91 1.91% 0.0001 38.34 -0.98% 0.0050

Dec-02 1469.25 5.78% 0.0026 41.16 7.36% 0.0002

Jan-03 1394.46 -5.09% 0.0034 49.47 20.19% 0.0199

Feb-03 1366.42 -2.01% 0.0007 56.50 14.21% 0.0066

Mar-03 1498.58 9.67% 0.0080 65.97 16.76% 0.0114

Apr-03 1452.43 -3.08% 0.0014 63.41 -3.88% 0.0099

May-03 1420.60 -2.19% 0.0008 62.34 -1.69% 0.0060

Jun-03 1454.60 2.39% 0.0003 66.84 7.22% 0.0001Jul-03 1430.83 -1.63% 0.0005 66.75 -0.13% 0.0038

Sum 8.52% 0.0225 72.79% 0.1048

b)

Average monthly return 0.71% 6.07%Standard deviation 4.52% 9.76%

c)

-15.00%

-10.00%

-5.00%

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

-10.00% -5.00% 0.00% 5.00% 10.00% 15.00%

Market Index

Mathews


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d. Mathews returns seem to correlate to the market returns during the majorityof the year, but show great volatility.

6-15AStock 1



0.15 2% 0.30% 6.048%0.40 7 2.80 0.7290.30 10 3.00 0.8170.15 15 2.25 6.633

k = 8.35% 2 = 14.227% = 3.77%

Stock 2



0.25 -3% -0.75% 85.56%0.50 20 10.00 10.130.25 25 6.25 22.56

k = 15.50% 2 = 118.25%

= 10.87%Stock 3



0.10 -5% -0.50% 36.1%0.40 10 4.00 6.40.30 15 4.50 0.30.20 30 6.00 51.2

k = 14.00%

2

= 94.0% = 9.7%



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6-16A

Risk-FreeRate +




H 5.5% + (11% - 5.5%) x 0.75 = 9.63%T 5.5% + (11% - 5.5%) x 1.40 = 13.20%P 5.5% + (11% - 5.5%) x 0.95 = 10.73%W 5.5% + (11% - 5.5%) x 1.25 = 12.38%

6-17AWilliams Davis

Time Price Return Price Return1 $33 $192 27 -18.18% 15 -21.05%3 35 29.63 14 -6.67

4 39 11.43 23 64.29

6-18A

(a)

Required rate

of return =

Risk-free

rate + Beta

Market Risk

Premium

= 5 % + 1.2 (9% - 5%)

= 9.8%

(b)

Required rate

of return =

Risk-free

rate + Beta

Market Risk

Premium

= 5 % + 0.85 (9% - 5%)

= 8.4%

(c) If beta is 1.2:

Required rate = 5 % + 1.2 (12% - 5%)of return

= 13.4%If beta is 0.85:


= 10.95%


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SOLUTION TO INTEGRATIVE PROBLEM

1. Holding-period returns for Market, Reynolds Computer, and Andrews

Market Reynolds Computer Andrews

Price kt (kt - k)2 Price kt (kt - k)2 Price kt (kt - k)2

01May 1090.82 20.60 24.00

June 1133.84 3.94% 0.0007 23.20 12.62% 0.0067 26.72 11.33% 0.0065

July 1120.67 -1.16% 0.0006 27.15 17.03% 0.0158 20.94 -21.63% 0.0619

Aug 957.28 -14.58% 0.0251 25.00 -7.92% 0.0153 15.78 -24.64% 0.0778

Sept 1017.01 6.24% 0.0025 32.88 31.52% 0.0733 18.09 14.64% 0.0130

Oct 1098.67 8.03% 0.0046 32.75 -0.40% 0.0023 21.69 19.90% 0.0277

Nov 1163.63 5.91% 0.0022 30.41 -7.15% 0.0134 23.06 6.32% 0.0009

Dec 1229.23 5.64% 0.0019 36.59 20.32% 0.0252 28.06 21.68% 0.0340

02Jan 1279.64 4.10% 0.0008 50.00 36.65% 0.1037 26.03 -7.23% 0.0110

Feb 1238.33 -3.23% 0.0020 40.06 -19.88% 0.0592 26.44 1.58% 0.0003

Mar 1286.37 3.88% 0.0007 40.88 2.05% 0.0006 28.06 6.13% 0.0008

Apr 1335.18 3.79% 0.0006 41.19 0.76% 0.0014 36.94 31.65% 0.0806

May 1301.84 -2.50% 0.0014 34.44 -16.39% 0.0434 36.88 -0.16% 0.0012

June 1372.71 5.44% 0.0018 37.00 7.43% 0.0009 37.56 1.84% 0.0002

July 1328.72 -3.20% 0.0020 40.88 10.49% 0.0037 23.25 -38.10% 0.1710

Aug 1320.41 -0.63% 0.0004 48.81 19.40% 0.0224 22.88 -1.59% 0.0023

Sept 1282.71 -2.86% 0.0017 41.81 -14.34% 0.0353 24.78 8.30% 0.0026

Oct 1362.93 6.25% 0.0025 40.13 -4.02% 0.0072 27.19 9.73% 0.0042

Nov 1388.91 1.91% 0.0000 43.00 7.15% 0.0007 26.56 -2.32% 0.0031Dec 1469.25 5.78% 0.0021 51.00 18.60% 0.0201 24.25 -8.70% 0.0143

03Jan 1394.46 -5.09% 0.0040 38.44 -24.63% 0.0845 32.00 31.96% 0.0824

Febr 1366.42 -2.01% 0.0011 40.81 6.17% 0.0003 35.13 9.78% 0.0043

Mar 1498.58 9.67% 0.0071 53.94 32.17% 0.0769 44.81 27.55% 0.0591

Apr 1452.43 -3.08% 0.0019 50.13 -7.06% 0.0132 30.23 -32.54% 0.1281

May 1420.60 -2.19% 0.0012 43.13 -13.96% 0.0339 34.00 12.47% 0.0085

Sum 30.07% .0689 106.62% 77.95% .7958

2. AverageMonthlyReturn 1.25% 4.44% 3.25%

StandardDeviation 5.47% 16.93% 18.60%


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3. Reynolds vs Market

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-0.2 -0.1 0 0.1 0.2

Reynolds

Market

Andrews vs. Market

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-0.2 -0.1 0 0.1 0.2

Market

A

ndrews


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4 Reynoldss returns have a great amount of volatility with some correlation to themarket returns.

The same can be said of Andrews. The returns show a great amount of volatility thatfollowed the market returns only part of the time.

5. Monthly returns of a portfolio of equal amounts of Reynolds and Andrews.

Monthly

Returns2001 June 11.98%

July -2.32%

August -16.27%

September 23.08%

October 9.74%

November -0.41%December 21.02%

2002 January 14.70%

February -9.16%

March 4.09%

April 16.20%

May -8.28%

June 4.65%

July -13.81%

August 8.90%

September -3.00%October 2.84%

November 2.43%

December 4.95%

2003 January 3.66%

February 7.97%

March 29.87%

April -19.80%

May -0.75%

Average

return

3.84%

Standarddeviation

12.29%


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6.

We see in this new graph where both stocks are included as a single portfolio that therelationship of the stocks with the market approximates an average of the relationships takenalone. Note the reduction in volatility that occurs when risk is diversified even between justtwo stocks.

Reynolds and Andrews

-30.00%

-20.00%

-10.00%

0.00%

10.00%

20.00%

30.00%

40.00%

-20.00% -10.00% 0.00% 10.00% 20.00%

Market

50%Reynolds50%Andrews


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7. Monthly holding-period returns for long-term government bondsAnnualReturn

MonthlyReturn (ki - k)

2

2001 June 5.70% 0.48% 0.000000%

July 5.68% 0.47% 0.000001%

August 5.54% 0.46% 0.000004%September 5.20% 0.43% 0.000023%

October 5.01% 0.42% 0.000041%

November 5.25% 0.44% 0.000020%

December 5.06% 0.42% 0.000036%

2002 January 5.16% 0.43% 0.000027%

February 5.37% 0.45% 0.000012%

March 5.58% 0.47% 0.000003%

April 5.55% 0.46% 0.000004%

May 5.81% 0.48% 0.000000%

June 6.04% 0.50% 0.000005%

July 5.98% 0.50% 0.000003%

August 6.07% 0.51% 0.000006%

September 6.07% 0.51% 0.000006%

October 6.26% 0.52% 0.000016%

November 6.15% 0.51% 0.000009%

December 6.35% 0.53% 0.000022%

2003 January 6.63% 0.55% 0.000050%

February 6.23% 0.52% 0.000014%

March 6.05% 0.50% 0.000005%

April 5.85% 0.49% 0.000000%

May 6.15% 0.51% 0.000009%

Average

Monthly

Return 0.48%

Standard

Deviation 0.04%


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8. Monthly portfolio returns when portfolio consists of equal amounts invested inReynolds, Andrews, and long-term government bonds.

MonthlyReturns (ki - k)

2

2001 June 8.14% 0.0029July -1.39% 0.0017

August -10.69% 0.0180

September 15.53% 0.0164

October 6.63% 0.0015

November -0.13% 0.0008

December 14.15% 0.0131

2002 January 9.94% 0.0052

February -5.95% 0.0075

March 2.88% 0.0000

April 10.95% 0.0068

May -5.36% 0.0065June 3.27% 0.0000

July -9.04% 0.0138

August 6.10% 0.0011

September -1.83% 0.0021

October 2.07% 0.0000

November 1.79% 0.0001

December 3.48% 0.0001

2003 January 2.63% 0.0000

February 5.49% 0.0008

March 20.08% 0.0301April -13.04% 0.0248

May -0.33% 0.0009

Sum 65.36% 0.1542

ReturnMonthlyAverage

2.72%

Std. Dev.. 8.19%


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9. Comparison of average returns and standard deviations

Average StandardReturns Deviations

Reynolds 4.44% 16.93%

Andrews 3.25% 18.60%Government security 0.48% 0.04%Reynolds & Andrews 3.84% 12.29%Reynolds, Andrews, 2.72% 8.19%

& government securityMarket 1.25% 5.47%

From the findings above, we see that higher average returns are associated withhigher risk (standard deviations), and that by diversification we can reduce risk,possibly without reducing the average return.

10. Based on the standard deviations, Andrews has more risk than Reynolds, 18.60

percent standard deviation versus 16.93 percent standard deviation. However, whenwe only consider systematic risk, Andrews is slightly less risky--Reynolds's beta is1.96 compared to Andrews beta of 1.49. (The betas given here for Reynolds andAndrews come from financial services who calculate firms' betas. These are notconsistent with the graphs above where we see Andrews' returns as being moreresponsive to the general market. We are seeing the problem of using only 24months of returns as we have done.)

11.


=Risk-Free


Market Return = 1.25 % Average Monthly Return X 12 Months = 15%.

(The average returns for the market over a two-year period may be high or lowrelative to the longer-term past, and as a result should not be considered as typicalinvestor expectations. For instance, if we used information from Ibbotson &Sinquefield for the years 1926-2002, the market risk premiummarket return lessrisk-free ratewas 8.4 percent, and not the 19 percent that we use below. The point:Do not think two years fairly captures what we can expect in the future?)

Reynolds:23.64% = 6% + (15% - 6%) X 1.96

Andrews:

19.41% = 6% + (15% - 6%) X 1.49

And if we used the market premium of 8.4 percent:

Reynolds:22.46% = 6% + 8.4% X 1.96

Andrews:18.52% = 6% + 8.4% X 1.49


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Solutions to Problem Set B

6-1B.krf= .05 + .07 + (.05 x .07)krf= .1235

or12.35% = nominal rate of interest

6-2B.krf= .03 + .05 + (.03 x .05)krf= .0815or8.15% = nominal rate of interest

6-3B.(A) (B) (A) x (B) Weighted

Probability Return Expected Return DeviationP(ki) (ki) k (ki - k)

2P(ki)

.15 -3% -0.45% 4.788

.30 2 0.60 0.127

.40 4 1.60 0.729

.15 6 0.90 1.683

k = 2.65% 2 = 7.327% = 2.707%

No, Gautney should not invest in the security. The securitys expected rate of return

is less than the rate offered on treasury bills.

6-4B.Security A:



0.2 - 2% -0.4% 69.19%0.5 19 9.5 2.880.3 25 7.5 21.17

k = 16.6% 2 = 93.24% = 9.66%


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Security B:



0.1 5% 0.5% 2.704%0.3 7 2.1 3.0720.4 12 4.8 1.2960.2 14 2.8 2.888

k = 10.2% 2 = 9.96% = 3.16%

Security A Security B

k = 16.6% k = 10.2%

= 9.66% = 3.16%


6-5B.

Common Stock A:



0.2 10% 2.0% 2.89%0.6 13 7.8 0.380.2 20 4.0 7.69

k = 13.8% 2 = 10.96% = 3.31%

Common Stock B


P(ki) (ki) k (ki - k)2

P(ki)

0.15 6% 0.9% 5.67%0.30 8 2.4 5.170.40 15 6.0 3.250.15 19 2.85 7.04

k = 12.15% 2 = 21.13% = 4.60%


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Common Stock A is better. It has a higher expected return with less risk.

6-6B.

(a)

Required rate

of return =

Risk-free

rate + Beta

Market Risk

Premium

= 8 % + 1.5 (16% - 8%)= 20%

(b) The 20 percent "fair rate" compensates the investor for the time value ofmoney and for assuming risk. However, only nondiversifiable risk is beingconsidered, which is appropriate.

6-7B. Eye balling the characteristic line for the problem, the rise relative to the run is about1.75. That is, when the S & P 500 return is four percent Bram's expected returnwould be about seven percent. Thus, the beta is also approximately 1.75 (7 4).

6-8B.

Risk-FreeRate +

Expected Market

Return -Risk-Free

Rate x Beta =


A 6.75% + (12% - 6.75%) x 1.40 = 14.10%B 6.75% + (12% - 6.75%) x 0.75 = 10.69%C 6.75% + (12% - 6.75%) x 0.80 = 10.95%D 6.75% + (12% - 6.75%) x 1.20 = 13.05%

6-9B.

RequiredRate of

Return=

Risk-Free

Rate+ (Market Return - Risk-Free Rate) X Beta

= 7.5% + (10.5% - 7.5%) x 0.85

= 10.05%6-10B. If the expected market return is 12.8 percent and the risk premium is 4.3 percent, the

riskless rate of return is 8.5 percent (12.8% - 4.3%). Therefore;

Dupree = 8.5% + (12.8% - 8.5%) x 0.82 = 12.03%

Yofota = 8.5% + (12.8% - 8.5%) x 0.57 = 10.95%

MacGrill = 8.5% + (12.8% - 8.5%) x 0.68 = 11.42%

6-11B.O'Toole Baltimore

Time Price Return Price Return1 $22 $452 24 9.09% 50 11.11%3 20 -16.67% 48 -4.00%4 25 25.00% 52 8.33%


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A holding-period return indicates the rate of return you would earn if you bought asecurity at the beginning of a time period and sold it at the end of the period, such asthe end of the month or year,


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6-12B.(a) Sugita Market

Month kt (kt - k)2 kt (kt - k)

2

1 1.80% 0.01% 1.50% 0.06%

2 -0.50 5.68 1.00 0.063 2.00 0.01 0.00 1.564 -2.00 15.08 -2.00 10.565 5.00 9.71 4.00 7.566 5.00 9.71 3.00 3.06Sum 11.30 40.20 7.50 22.86

Averagemonthlyreturn

1.88% 1.25%

(Sum 6)

Annualizedaveragereturns

22.60% 15.00%

Variance 8.04% 4.58%(Sum 5)

Standarddeviation 2.84% 2.14%

b.


=Risk-Free


= 8% + [(15% - 8%) X 1.18] = 16.26%

c. Sugita's historical return of 22.6 percent exceeds what we would consider afair return of 16.26 percent, given the stock's systematic risk.

6-13B

a. The portfolio expected return, kp, equals a weighted average of theindividual stock's expected returns.

kp = (0.10)(12%) + (0.25)(11%) + (0.15)(15%) + (0.30)(9%) +

(0.20)(14%)

= 11.7%


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b. The portfolio beta, p, equals a weighted average of the individual stock betas

p = (0.10)(1.00) + (0.25)(0.75) + (0.15)(1.30) + (0.30)(0.60) +(0.20)(1.20)

= 0.90

c. Plot the security market line and the individual stocks

Beta

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

0. 00 0. 20 0. 40 0. 60 0. 80 1. 00 1. 20 1. 40

12

3

4

5

M

P

d. A "winner" may be defined as a stock that falls above the security market

line, which means these stocks are expected to earn a return exceeding what

should be expected given their beta or systematic risk. In the above graph,these stocks include 1, 2, 3, and 5. "Losers" would be those stocks fallingbelow the security market line, that being stock 4.

e. Our results are less than certain because we have problems estimating thesecurity market line with certainty. For instance, we have difficulty inspecifying the market portfolio.


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6-14Ba) Market Hilarys

Month Price kt (kt - k)2 Price kt (kt - k)

2

Jul-02 1328.72 21.00

Aug-02 1320.41 -0.63% 0.0002 19.50 -7.14% 0.0211

Sep-02 1282.71 -2.86% 0.0013 17.19 -11.85% 0.0369

Oct-02 1362.93 6.25% 0.0031 16.88 -1.80% 0.0084

Nov-02 1388.91 1.91% 0.0001 18.06 6.99% 0.0000

Dec-02 1469.25 5.78% 0.0026 24.88 37.76% 0.0924

Jan-03 1394.46 -5.09% 0.0034 22.75 -8.56% 0.0254

Feb-03 1366.42 -2.01% 0.0007 26.25 15.38% 0.0064

Mar-03 1498.58 9.67% 0.0080 33.56 27.85% 0.0419

Apr-03 1452.43 -3.08% 0.0014 43.31 29.05% 0.0470

May-03 1420.60 -2.19% 0.0008 43.50 0.44% 0.0048

Jun-03 1454.60 2.39% 0.0003 43.50 0.00% 0.0054Jul-03 1430.83 -1.63% 0.0005 43.63 0.30% 0.0050

Sum 8.52% 0.0225 88.42% 0.2948

b)Return

MonthlyAverage0.71% 7.37%

Standard deviation 4.52% 16.37%


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c)

d. The Hilarys returns for the last six months of 2002 and the first six monthsof 2003 were partially correlated, but with a lot of the variance in the stocksreturns, clearly not explained by the marketas would be expected.

-20.00%

-10.00%

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

-10.00% -5.00% 0.00% 5.00% 10.00% 15.00%

Market

Hilary's


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6-15B

Stock A



0.10 -4% -0.40% 16.384%0.30 2 0.60 13.8720.40 13 5.20 7.0560.20 17 3.40 13.448

k= 8.80% 2 = 50.76% = 7.125%

Stock B



0.13 4% 0.52% 13.658%0.40 10 4.00 7.2250.27 19 5.13 6.0920.20 23 4.60 15.31

k = 14.25% 2 = 42.285% = 6.503%

Stock C



0.20 -2% -0.40% 27.145%0.25 5 1.25 5.4060.45 14 6.30 8.5150.10 25 2.50 23.562

k = 9.65% 2 = 64.628% = 8.039%

Stock B has a higher expected rate of return with less risk than Stocks A and C.


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6-16B

Risk-Free

Rate +




K 5.5% + (11% - 5.5%) x 1.12 = 11.66%G 5.5% + (11% - 5.5%) x 1.30 = 12.65%B 5.5% + (11% - 5.5%) x 0.75 = 9.63%U 5.5% + (11% - 5.5%) x 1.02 = 11.11%

6-17BWatkins Fisher

Time Price Return Price Return1 $40 $272 45 12.50% 31 14.81%

3 43 -4.44 35 12.904 49 13.95 36 2.86

6-18B

(a)

Required rate

of return =

Risk-free

rate + Beta

Market Risk

Premium

= 4% + 0.95 (7% - 4%)= 6.85%

(b) Required rate

of return = Risk-free

rate + Beta Market Risk

Premium

= 4 % + 1.25 (7% - 4%)

= 7.75%

(c) If beta is 0.95:


= 9.7%If beta is 1.25:


= 11.5%

Documents

Financial Management Chapter 06 IM 10th Ed