Chapter 5 Risk and Portfolio Management

TRUE/FALSE

T 1. The tendency of individual stock prices to move together is one source of systematic risk.

F 2. Systematic risk is reduced through diversification.

T 3. A portfolio consisting of securities whose returns are highly correlated is not truly diversified.

F 4. While diversification decreases risk, it also increases the chance of a large gain.

F 5. A diversified portfolio requires the securities of at least fifty firms.

T 6. In a world of certainty, there would be no risk.

F 7. Portfolio risk is the summation of business and financial risk.

F 8. Diversification reduces reinvestment rate risk.

T 9. Investors must bear the systematic risk associated with fluctuating securities prices.

T 10. Unsystematic risk refers to factors that are unique to the specific asset.

T 11. Unsystematic risk considers how firms finance their assets and the nature of their operations.

T 12. The negative relationship between interest rates and securities prices is the source of interest rate risk.

F 13. Inflation, which is a general decline in prices, is the source of financial risk.

T 14. Exchange rate risk refers to fluctuations in the prices of foreign currencies (i.e., foreign exchange).

T 15. Investors may reduce risk by constructing diversified portfolios but not eliminate risk.

F 16. Reinvestment rate risk results from higher stock prices in the future.

F 17. By accepting more risk, the investor will increase the realized return.

T 18. Investors seek to minimize risk for a given return.

F 19. The informed investor can expect consistently to outperform the market.

T 20. The dispersion around a stock’s return is one measure of risk.

F 21. If a stock’s return has a large standard deviation, that suggests the stock has little risk.

F 22. If the return on two stocks is highly and positively

correlated (i.e., correlation coefficient = +1.0), combining these stocks will reduce the risk associated with the portfolio.

F 23. If a stock has a beta of 1.0, it is risk‑free stock.

F 24. Low beta stocks tend to generate higher returns in rising markets.

F 25. If a beta coefficient is 1.7, that implies the return on the stock tends to be less volatile than the return on the market.

T 26. A portfolio’s beta coefficient tends to be stable over time.

T 27. During a rising market, stocks with greater beta coefficients may be preferred.

T 28. The numerical value of beta for the market equals 1.

T 29. Portfolios that offer the highest return for a given

level of risk are “efficient.”

F 30. The “efficient frontier” relates all the combinations of risk and return that represent the same level of satisfaction.

T 31. The beta of a portfolio is a weighted average of each asset’s beta coefficient.

F 32. Arbitrage is the act of buying a high priced asset in one market and simultaneously selling it in another market at a lower price.

T 33. Arbitrage pricing theory is a multi-variable model used to explain securities returns.

MULTIPLE CHOICE

b 1. Unsystematic risk is

- the risk associated with movements in stock prices
- reduced through diversification
- higher when interest rates rise
- the risk of loss of purchasing power

c 2. The expected return on an investment in stock is

- the expected dividend payments
- the anticipated capital gains
- the sum of expected dividends and capital gains
- less than the realized return

b 3. Diversification reduces

- systematic risk
- unsystematic risk
- market risk
- purchasing power risk

c 4. Unsystematic risk

- is increased through diversification
- is reduced when markets fluctuate less
- is affected by the nature of how a firm finances

its operations

- increases during periods of volatile interest

rates

d 5. Sources of risk to an investor include

- loss when funds are reinvested at lower rates
- fluctuations in securities markets
- the financing decisions of the firm
- 1 and 2
- 1 and 3
- 2 and 3
- all of the above

c 6. Exchange rate risk refers to fluctuations in

- the prices of stocks on the New York Stock

Exchange

- the values of bonds and other debt instruments
- the price of one currency relative to other

currencies

- a decline in the value of an investor’s portfolio

when securities are sold

- 7. Reinvestment rate risk refers to fluctuations in
- a stock’s price
- a stock’s dividend
- rates earned when funds are reinvested
- the cost of an investment

- 8. Sources of risk include
- fluctuating exchange rates
- a firm’s financing decisions
- higher interest rates
- loss of purchasing power
- 1 and 2
- 2 and 3
- 2 and 4
- all four

a 9. Sources of unsystematic risk include

- the firm’s financing decisions
- the firm’s operations
- fluctuating market prices
- 1 and 2
- 1 and 3
- 2 and 3
- all of the above

d 10. Portfolio risk encompasses

- a firm’s financing decisions
- interest rate risk
- loss of purchasing power
- 1 and 2
- 1 and 3
- 2 and 3
- all of the above

d 11. If the dispersion around a stock’s return increases

- the expected return decreases
- the standard deviation decreases
- the stock’s price increases
- the stock’s risk increases

c 12. For diversification to reduce risk,

- the returns on the individual securities should

be highly correlated

- the prices of the stocks should be stable
- the returns on the individual securities should

be negatively correlated

- one firm should offer dividends and the other

should offer capital gains

a 13. Beta coefficients

- are a measure of systematic risk
- relate the return on an individual security to

the return on the market

- measure the variability of as asset’s return
- 1 and 2
- 1 and 3
- 2 and 3
- all of the above

c 14. Beta coefficients of 1.3 indicate

- the stock has more unsystematic risk
- the stock has less unsystematic risk
- the stock is more volatile than the market
- the stock is less volatile than the market

d 15. Investors who want to bear less risk should acquire

stocks whose beta coefficients are

- greater than 1.5
- greater than 1.0
- less than 1.0
- less than 0.5

c 16. An efficient portfolio

- maximizes risk for a given return
- minimizes risk for a given return
- maximizes return for a given level of risk
- minimizes return for a given level of risk
- 1 and 3
- 1 and 4
- 2 and 3
- 2 and 4

a 17. The efficient frontier in portfolio theory

- indicates the highest return for a given risk
- illustrates the optimal trade-off between long and

short-term capital gains

- quantifies systematic and unsystematic risk
- identifies the optimal portfolio for the investor

c 18. The security market line does not

- indicate the relationship between risk and return
- relate the market return and beta to a stock’s

return

- identify the optimal portfolio for the investor
- use beta coefficients as a measure of risk

b 19. According to the arbitrage pricing theory, the return

on a stock

- is not related to the expected return on the stock
- depends on the stock’s responsiveness to

unexpected changes

- is reduced through the construction of diversified

portfolios

- equals the market return if the expected rate of

inflation is realized

PROBLEMS

- What is the expected return on a stock that pays a 4 percent annual dividend and whose price is expected to appreciate annually at 6 percent?

- a. What is the expected return on a portfolio consisting of an equal amount invested in each stock?

Stock Expected Return

A 15%

B 10

C 22

D 14

- What is the expected return on the portfolio if 50 percent of the funds are invested in stock C, 30 percent in stock A, and 20 percent in Stock D?

- (This problem illustrates the computation of beta coefficients may be solved using a statistics program or Excel.) The returns on the market and stock A and stock B are as follows:

Period Market Stock A Stock B

1 10% 9% 12%

2 15 25 25

3 ‑3 6 5

4 7 12 6

5 4 ‑1 9

6 ‑5 ‑10 1

7 ‑8 ‑7 5

8 13 15 ‑1

9 15 23 12

10 3 9 10

Compute the beta coefficient for each stock and interpret the results of the computations.

- Given the following information:

Expected return on Stock A .12 (12%)

Standard deviation of return .1

Expected return on Stock B .20 (20%)

Standard deviation of return .6

Correlation coefficient of the

returns on Stock A and Stock B .2

- What are the expected returns and standard deviations of the following portfolios:
- 100 percent of funds invested in Stock A
- 100 percent of funds invested in Stock B
- 50 percent of funds invested in each stock?

- What would be the impact if the correlation coefficient were ‑0.6 instead of 0.2?

SOLUTIONS TO PROBLEMS

- Expected return = dividend yield + capital gains

= 4% + 6% = 10%

(Be certain that the student understands the concept of a total return and not just a dividend yield or a capital gain. Total return is the sum of these two sources of return.)

- a. The expected return is the sum of the individual asset’s expected return weighted by its proportion in the portfolio. If equal amounts are invested in each asset, the expected return on the portfolio is

A: .15 x .25 = .0375

B: .10 x .25 = .0250

C: .22 x .25 = .0550

D: .14 x .25 = __.0350__

.1525 = 15.25%

- If different amounts are invested in the various assets, the portfolio’s expected return becomes:

A: .15 x .30 = .0450

C: .22 x .50 = .1100

D: .14 x .20 = __.0280__

.1830 = 18.3%

By investing more in the stock that offers the highest expected return (and presumably the most risk), the investor increases the expected return of the portfolio.

- The following answers were derived using a computer program such as Excel.

Stock A’s beta coefficient: 1.25 (R2 = 0.81)

Stock B’s beta coefficient: 0.45 (R2 = 0.26)

The betas indicate that the return on Stock A was more volatile than the market. The return, however, on Stock B was less volatile. You may wish to point out that the coefficient of determination indicates that only a small proportion of the volatility of Stock B appears to be explained by movements in the market.

- a. The expected returns and standard deviations when 100 percent of funds invested in Stock A or Stock B are given in the problem. The only calculation required by the student is the expected return on the portfolio when funds are equally divided between the two stocks. That return is (.5)(.12) + (.5)(.2) = .16 = 16%.

The crux of this problem is the calculation of the standard deviation of the portfolio consisting of the two stocks. I have found some students will construct a weighted average of the two standard deviations. This is incorrect since it fails to consider the relationship between the two stocks. The calculation of the standard deviation of the portfolio when the correlation coefficient is 0.2 is

[(.5)2(.1)2 + (.5)2(.6)2 + (2)(.5)(.5)(.1)(.6)(.2)].5 = .314

- If the correlation coefficient were ‑0.6, the standard deviation of a portfolio equally weighted between the two stocks is

[(.5)2(.1)2 + (.5)2(.6)2 + (2)(.5)(.5)(.1)(.6)(-.6)].5 = .273

Since the returns on the two stocks are now negatively correlated, the standard deviation of the portfolio is reduced which indicates the portfolio is less risky.

Summary if correlation coefficient is 0.2:

Return Standard Deviation

All in stock A 12% .1

All in stock B 20% .6

50% in A and B 16% .314

Summary if correlation coefficient is -0.6:

Return Standard Deviation

All in stock A 12% .1

All in stock B 20% .6

50% in A and B 16% .273

Category: Business Studies

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