Chapter 06 IM 10th Ed-MANAJEMEN KEUANGAN

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. We also 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 returns for 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 with the 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 purchasing power, after adjusting for inflation.

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

III. Term Structure of Interest Rates

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The relationship between a debt security’s rate of return and the length of time until the debt matures is known as the term structure of interest rates or the yield to maturity.

IV. Expected Return

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

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

= 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 expected cash flow.

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

C. Risk and diversification

1. Total variability can be divided into:

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

b. The risk related to market movements (nondiversifiable or systematic 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 without sacrificing expected return, and/or we can increase expected return without having to assume more risk.

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

5. Risk and being patient

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

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

6. The characteristic line tells us the average movement in a firm's stock price in response to a movement in the general market, such as

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the stock market. The slope of the characteristic line, which has come to 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 line relative to the "run" of the line.

7. If a security's beta equals one, a 10 percent increase (decrease) in market 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 in the portfolio.

VI. Required rate of return

A. The required rate of return is the minimum rate necessary to compensate an investor for accepting the risk he or she associates with the purchase and ownership 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

= + beta x

or

kj = krf + βj (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 CAPM equation.

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ANSWERS TOEND-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 the exception 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, after adjusting for inflation. Consequently, the nominal rate of interest is equal to the sum of the real rate of interest, the inflation rate, and the product of the real rate and the inflation rate.

6-3 The relationship between a debt security’s rate of return and the length of time until the debt matures is known as the term structure of interest rates or the yield to maturity. 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 be measured in terms of the standard deviation or by the variance term, which is simply the standard deviation squared.

(c) A large standard deviation of the returns indicates greater riskiness associated with an investment. However, whether the standard deviation is large relative to the returns has to be examined with respect to other investment opportunities. Alternatively, probability analysis is a meaningful approach to capture greater understanding of the significance of a standard deviation figure. However, we have chosen not to incorporate such an analysis into our explanation of the valuation process.

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

(b) Systematic risk is the variability in a firm's stock price that is the result of general influences within the industry or resulting from overall market or economic influences. A general change in interest rates charged by banks is an example of systematic risk.

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

6-7. The security market line is a graphical representation of the risk-return trade-off that exists in the market. The line indicates the minimum acceptable rate of return for investors given the level of risk. Since the security market line results from actual market transactions, the relationship not only represents the risk-return preferences of investors 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 of the stock's returns against the market's returns), then it has a high amount of unsystematic or company-unique risk. If, however, the stock's returns closely follow the market movements, then there is little unsystematic risk.

SOLUTIONS TOEND-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

or

10.44% = nominal rate of interest

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

Probability Return Expected Return DeviationP(ki) (ki) (ki - )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% = 2.85% 2 = 6.427%

= 2.535%

No, Pritchard should not invest in the security. The level of risk is excessive for a return 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

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

0.3 11% 3.3% 4.8%0.4 15 6.0 0.00.3 19 5 .7 4 .8

= 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

= 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

= 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

= 9.2% 2 = 12.76% = 3.57%

Common Stock A Common Stock B = 16.7% = 9.2%

= 10.12% = 3.57%

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

6-6A.(a) = + Beta

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

= 18%

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

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

6-8A.+ x Beta =

A 6.75% + (12% - 6.75%) x 1.50 = 14.63%

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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.`= + (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, the riskless 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 a security at the beginning of a time period and sold it at the end of the period, such as the end of the month or year.

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6-12A.a. Zemin Market Month k b (k b - ) 2 k b (k b - ) 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 .69 Sum 12.00 56.00 7.00 24.82

2.00% 1.17%(Sum ÷ 6)

24.00% 14.04%

Variance 11.20% 4.97%(Sum 5)

3.35% 2.23%

b. = + (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 fair return of 17.24 percent, given the stock's systematic risk.

6-13A.a. The portfolio expected return, p, equals a weighted average of the

individual stock's expected returns.

p = (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, ßp, equals a weighted average of the individual stock

betas

ßp = (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

Exp

ecte

d R

etur

n

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 what should be expected given their beta or systematic risk. In the above graph, these stocks include 1, 3, and 5. "Losers" would be those stocks falling below 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 the security market line with certainty. For instance, we have difficulty in specifying the market portfolio.

153

6-14A a. Market Mathews

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

Jul-02 1328.72 34.50Aug-02 1320.41 -0.63% 0.0002 41.09 19.10% 0.0170Sep-02 1282.71 -2.86% 0.0013 37.16 -9.56% 0.0244Oct-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% 0.0050Dec-02 1469.25 5.78% 0.0026 41.16 7.36% 0.0002Jan-03 1394.46 -5.09% 0.0034 49.47 20.19% 0.0199Feb-03 1366.42 -2.01% 0.0007 56.50 14.21% 0.0066Mar-03 1498.58 9.67% 0.0080 65.97 16.76% 0.0114Apr-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% 0.0060Jun-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)

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d. Mathews returns seem to correlate to the market returns during the majority of 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

= 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

= 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

= 14.00% 2 = 94.0% = 9.7%


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6-16A

+ x Beta =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%

6-17A Williams Davis

Time Price Return Price Return 1 $33 $192 27 -18.18% 15 -21.05%3 35 29.63 14 -6.674 39 11.43 23 64.29

6-18A(a) = + Beta

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

= 9.8%

(b) = + Beta

= 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 - )2 Price kt (kt - )2 Price kt (kt - )2

01May 1090.82 20.60 24.00June 1133.84 3.94% 0.0007 23.20 12.62% 0.0067 26.72 11.33% 0.0065July 1120.67 -1.16% 0.0006 27.15 17.03% 0.0158 20.94 -21.63% 0.0619Aug 957.28 -14.58% 0.0251 25.00 -7.92% 0.0153 15.78 -24.64% 0.0778Sept 1017.01 6.24% 0.0025 32.88 31.52% 0.0733 18.09 14.64% 0.0130Oct 1098.67 8.03% 0.0046 32.75 -0.40% 0.0023 21.69 19.90% 0.0277Nov 1163.63 5.91% 0.0022 30.41 -7.15% 0.0134 23.06 6.32% 0.0009Dec 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% 0.0110Feb 1238.33 -3.23% 0.0020 40.06 -19.88% 0.0592 26.44 1.58% 0.0003Mar 1286.37 3.88% 0.0007 40.88 2.05% 0.0006 28.06 6.13% 0.0008Apr 1335.18 3.79% 0.0006 41.19 0.76% 0.0014 36.94 31.65% 0.0806May 1301.84 -2.50% 0.0014 34.44 -16.39% 0.0434 36.88 -0.16% 0.0012June 1372.71 5.44% 0.0018 37.00 7.43% 0.0009 37.56 1.84% 0.0002July 1328.72 -3.20% 0.0020 40.88 10.49% 0.0037 23.25 -38.10% 0.1710Aug 1320.41 -0.63% 0.0004 48.81 19.40% 0.0224 22.88 -1.59% 0.0023Sept 1282.71 -2.86% 0.0017 41.81 -14.34% 0.0353 24.78 8.30% 0.0026Oct 1362.93 6.25% 0.0025 40.13 -4.02% 0.0072 27.19 9.73% 0.0042Nov 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% 0.0824Febr 1366.42 -2.01% 0.0011 40.81 6.17% 0.0003 35.13 9.78% 0.0043Mar 1498.58 9.67% 0.0071 53.94 32.17% 0.0769 44.81 27.55% 0.0591Apr 1452.43 -3.08% 0.0019 50.13 -7.06% 0.0132 30.23 -32.54% 0.1281May 1420.60 -2.19% 0.0012 43.13 -13.96% 0.0339 34.00 12.47% 0.0085Sum 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.

158

159

4 Reynolds’s returns have a great amount of volatility with some correlation to the market returns.

The same can be said of Andrews. The returns show a great amount of volatility that followed 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%

Standard deviation

12.29%

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6.

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

161

7. Monthly holding-period returns for long-term government bonds(ki - )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 in Reynolds, Andrews, and long-term government bonds.

(ki - )2

2001 June 8.14% 0.0029July -1.39% 0.0017August -10.69% 0.0180September 15.53% 0.0164October 6.63% 0.0015November -0.13% 0.0008December 14.15% 0.0131

2002 January 9.94% 0.0052February -5.95% 0.0075March 2.88% 0.0000April 10.95% 0.0068May -5.36% 0.0065June 3.27% 0.0000July -9.04% 0.0138August 6.10% 0.0011September -1.83% 0.0021October 2.07% 0.0000November 1.79% 0.0001December 3.48% 0.0001

2003 January 2.63% 0.0000February 5.49% 0.0008March 20.08% 0.0301April -13.04% 0.0248May -0.33% 0.0009Sum 65.36% 0.1542

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 with higher 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, when we only consider systematic risk, Andrews is slightly less risky--Reynolds's beta is 1.96 compared to Andrews’ beta of 1.49. (The betas given here for Reynolds and Andrews come from financial services who calculate firms' betas. These are not consistent with the graphs above where we see Andrews' returns as being more responsive to the general market. We are seeing the problem of using only 24 months of returns as we have done.)

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

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 low relative to the longer-term past, and as a result should not be considered as “typical” investor expectations. For instance, if we used information from Ibbotson & Sinquefield for the years 1926-2002, the market risk premium—market return less risk-free rate—was 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) (ki - )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 = 2.65% 2 = 7.327%

= 2.707%

No, Gautney should not invest in the security. The security’s 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

= 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

= 10.2% 2 = 9.96% = 3.16%

Security A Security B = 16.6% = 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

= 13.8% 2 = 10.96% = 3.31%

Common Stock B



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

= 12.15% 2 = 21.13% = 4.60%

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

6-6B.(a) = + Beta

166

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

= 20%

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

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

6-8B.+ 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. = + (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 Return 1 $22 $452 24 9.09% 50 11.11%3 20 -16.67% 48 -4.00%4 25 25.00% 52 8.33%

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

167

6-12B.(a) Sugita Market

Month k t (k t - ) 2 k t (k t - ) 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 .06 Sum 11.30 40.20 7.50 22.86

1.88% 1.25%(Sum ÷ 6)

22.60% 15.00%

Variance 8.04% 4.58%(Sum ÷ 5)

2.84% 2.14%

b.

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

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

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

6-13Ba. The portfolio expected return, p, equals a weighted average of the

individual stock's expected returns.

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

(0.20)(14%)

= 11.7%

168

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

betas

ßp = (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

Exp

ecte

d R

etur

n

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 falling below the security market line, that being stock 4.

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

169

6-14Ba) Market Hilary’s

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

Jul-02 1328.72 21.00Aug-02 1320.41 -0.63% 0.0002 19.50 -7.14% 0.0211Sep-02 1282.71 -2.86% 0.0013 17.19 -11.85% 0.0369Oct-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% 0.0000Dec-02 1469.25 5.78% 0.0026 24.88 37.76% 0.0924Jan-03 1394.46 -5.09% 0.0034 22.75 -8.56% 0.0254Feb-03 1366.42 -2.01% 0.0007 26.25 15.38% 0.0064Mar-03 1498.58 9.67% 0.0080 33.56 27.85% 0.0419Apr-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% 0.0048Jun-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) 0.71% 7.37%

Standard deviation 4.52% 16.37%

170

c)

d. The Hilary’s returns for the last six months of 2002 and the first six months of 2003 were partially correlated, but with a lot of the variance in the stock’s returns, clearly not explained by the market—as would be expected.

171

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

= 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

= 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

= 9.65% 2 = 64.628% = 8.039%

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

172

6-16B

+ x Beta =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%

6-17B Watkins Fisher

Time Price Return Price Return 1 $40 $272 45 12.50% 31 14.81%3 43 -4.44 35 12.904 49 13.95 36 2.86

6-18B(a) = + Beta

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

(b) = + Beta

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

= 7.75%

(c) If beta is 0.95:


= 9.7%If beta is 1.25:


= 11.5%

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Chapter 06 IM 10th Ed-MANAJEMEN KEUANGAN