CHAPTER 13

RETURN, RISK, AND THE SECURITY MARKET LINE

Answers to Concepts Review and Critical Thinking Questions

1. Some of the risk in holding any asset is unique to the asset in question. By investing in a variety of

assets, this unique portion of the total risk can be eliminated at little cost. On the other hand, there are

some risks that affect all investments. This portion of the total risk of an asset cannot be cost-lessly

eliminated. In other words, systematic risk can be controlled, but only by a costly reduction in

expected returns.

2. If the market expected the growth rate in the coming year to be 2 percent, then there would be no

change in security prices if this expectation had been fully anticipated and priced. However, if the

market had been expecting a growth rate different than 2 percent and the expectation was incorpo-

rated into security prices, then the governmentâ€™s announcement would most likely cause security

prices in general to change; prices would drop if the anticipated growth rate had been more than

2 percent, and prices would rise if the anticipated growth rate had been less than 2 percent.

3. a. systematic

b. unsystematic

c.both; probably mostly systematic

d. unsystematic

e.unsystematic

f.systematic

4. a. a change in systematic risk has occurred; market prices in general will most likely

decline.

b. no change in unsystematic risk; company price will most likely stay constant.

c.no change in systematic risk; market prices in general will most likely stay constant.

d. a change in unsystematic risk has occurred; company price will most likely decline.

e.no change in systematic risk; market prices in general will most likely stay constant.

5. No to both questions. The portfolio expected return is a weighted average of the asset returns, so it

must be less than the largest asset return and greater than the smallest asset return.

6. False. The variance of the individual assets is a measure of the total risk. The variance on a well-

diversified portfolio is a function of systematic risk only.

7. Yes, the standard deviation can be less than that of every asset in the portfolio. However, Î²p cannot be

less than the smallest beta because Î²p is a weighted average of the individual asset betas.

8. Yes. It is possible, in theory, to construct a zero beta portfolio of risky assets whose return would be

equal to the risk-free rate. It is also possible to have a negative beta; the return would be less than the

risk-free rate. A negative beta asset would carry a negative risk premium because of its value as a

diversification instrument.

9. Such layoffs generally occur in the context of corporate restructurings. To the extent that the market

views a restructuring as value-creating, stock prices will rise. So, itâ€™s not layoffs per se that are being

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cheered on. Nonetheless, Bay Street does encourage corporations to takes actions to create value,

even if such actions involve layoffs.

10. Earnings contain information about recent sales and costs. This information is useful for projecting

future growth rates and cash flows. Thus, unexpectedly low earnings often lead market participants

to reduce estimates of future growth rates and cash flows; price drops are the result. The reverse is

often true for unexpectedly high earnings.

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.

Basic

1. The portfolio weight of an asset is total investment in that asset divided by the total portfolio value.

First, we will find the portfolio value, which is:

Total value = 70($40) + 110($22) = $5,220

The portfolio weight for each stock is:

WeightA = 70($40)/$5,220 = .5364

WeightB = 110($22)/$5,220 = .4636

2. The expected return of a portfolio is the sum of the weight of each asset times the expected return of

each asset. The total value of the portfolio is:

Total value = $1,200 + 1,900 = $3,100

So, the expected return of this portfolio is:

E(Rp) = ($1,200/$3,100)(0.11) + ($1,900/$3,100)(0.16) = .1406 or 14.06%

3. The expected return of a portfolio is the sum of the weight of each asset times the expected return of

each asset. So, the expected return of the portfolio is:

E(Rp) = .50(.11) + .30(.17) + .20(.14) = .1340 or 13.40%

4. Here we are given the expected return of the portfolio and the expected return of each asset in the

portfolio, and are asked to find the weight of each asset. We can use the equation for the expected

return of a portfolio to solve this problem. Since the total weight of a portfolio must equal 1 (100%),

the weight of Stock Y must be one minus the weight of Stock X. Mathematically speaking, this

means:

E(Rp) = .122 = .14wX + .09(1 â€“ wX)

We can now solve this equation for the weight of Stock X as:

.122 = .14wX + .09 â€“ .09wX

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.032 = .05wX

wX = 0.64

So, the dollar amount invested in Stock X is the weight of Stock X times the total portfolio value, or:

Investment in X = 0.64($10,000) = $6,400

And the dollar amount invested in Stock Y is:

Investment in Y = (1 â€“ 0.64)($10,000) = $3,600

5. The expected return of an asset is the sum of the probability of each return occurring times the

probability of that return occurring. So, the expected return of the asset is:

E(R) = .3(â€“.08) + .7(.28) = .1720 or 17.20%

6. The expected return of an asset is the sum of the probability of each return occurring times the

probability of that return occurring. So, the expected return of the asset is:

E(R) = .2(â€“.05) + .5(.12) + .3(.25) = .1250 or 12.50%

7. The expected return of an asset is the sum of the probability of each return occurring times the

probability of that return occurring. So, the expected return of each stock asset is:

E(RA) = .10(.06) + .60(.07) + .30(.11) = .0810 or 8.10%

E(RB) = .10(â€“.2) + .60(.13) + .30(.33) = .1570 or 15.70%

To calculate the standard deviation, we first need to calculate the variance. To find the variance, we

find the squared deviations from the expected return. We then multiply each possible squared

deviation by its probability, then add all of these up. The result is the variance. So, the variance and

standard deviation of each stock is:

ÏƒA2 =.10(.06 â€“ .0810)2 + .60(.07â€“.0810)2 + .30(.11 â€“ .0810)2 = .00037

ÏƒA = (.00037)1/2 = .0192 or 1.92%

ÏƒB2 =.10(â€“.2 â€“ .1570)2 + .60(.13â€“.1570)2 + .30(.33 â€“ .1570)2 = .02216

ÏƒB = (.022216)1/2 = .1489 or 14.89%

8. The expected return of a portfolio is the sum of the weight of each asset times the expected return of

each asset. So, the expected return of the portfolio is:

E(Rp) = .20(.08) + .70(.15) + .1(.24) = .1450 or 14.50%

If we own this portfolio, we would expect to get a return of 14.50 percent.

9. a. To find the expected return of the portfolio, we need to find the return of the portfolio in each

state of the economy. This portfolio is a special case since all three assets have the same weight.

To find the expected return in an equally weighted portfolio, we can sum the returns of each

asset and divide by the number of assets, so the expected return of the portfolio in each state of

the economy is:

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