Chapter 2



Risk and Return

These Formulas given on exam.

Two risky assets

E(Rp) = w1 R1 + w2 R2

σp2 = w12 σq2 + w22 σ22 + 2w1w2 ρ12 σ1σ2 ; note to find σp, take square root of σp2

One risk-free and Market

E(Rp ) = Rf + σp[(Rm-Rf)/σm]

E(Rp) = w1 Rf + w2 Rm

w1 + w2 = 1 where w1 is % in risk-free asset and w2 is % in risky asset.

σp = w2 σ2

CAPM: E(Rp) = rf + β(Rm-rf)

σi2 = Σ[Ri - E(Ri)]2/(n-1)

σi,m = Σ{[Ri - E(Ri)][Rm - E(Rm)]}/n-1

β = (ρi,m * σi)/σm or β = σi,m / σm2

ρim = σim/σiσm

ρ2 or r-square = Explained Var./Total Var. = (βi2 * σm2)/σi2

Review Problems

1. You buy Cisco stock for $50 a share. Cisco’s stock rises to $100 the next year. The following year, Cisco’s stock falls back to $50 a share.

A. What was your arithmetic return over the two years?

B. What was your geometric return over the two years?

2. You are given the following estimates for Stock’s A and B.

|State of Economy |Probability |A |B |

|Poor |0.25 |-5% |-8% |

|Normal |0.5 |8% |10% |

|Good |0.25 |12% |22% |

A. What are the expected returns for stock’s A and B respectively?

B. What are the standard deviations for stock’s A and B respectively?

C. Which stock is riskier?

D. Approximately two thirds of the time, the returns for A and B should be within what ranges respectively?

Answers to Review Problems

1.

A. The arithmetic return is simply (100% + -50%/2) = 25%.

B. The geometric return is [(1+1.0)*(1-.50)]^.5 – 1 = 0%.

2.

A. The expected return for A is .25(-5) + .5(8) + .25(12) = 5.75% and the expected return for B is .25(-8) + .5(10) + .25(22) = 8.5%

B. The standard deviation for A is the square root of [25(-5-5.75)^2 + .5(8-5.75)^2 + .25(12-5.75)^2] = 6.42% and the standard deviation for B is the square root of [.25(-8-8.5)^2 + .5(10-8.5)^2 + .25(22-8.5)^2] = 10.62%.

C. Stock B is riskier since its standard deviation of returns is higher. It is a more volatile stock and thus should offer greater expected return.

D. Two thirds of the time, returns should be within +/- 1 standard deviation of the expected return. Thus for stock A, the range is 5.75% +/- 6.42% or between –.67 and 12.17%. For stock B, the range is 8.5% +/- 10.62% = -2.12 and 19.12.

Review Problems

3. You have decided to invest 40% of your wealth in McDonalds which has an expected return of 15% and a standard deviation of 15%, and 60% of your wealth in GE which has an expected return of 9% and a standard deviation of 14%.

a. What is the expected return of your portfolio?

b. If the correlation between McDonalds and GM is 0.5, what is the standard deviation of your portfolio?

c. If you wanted an expected return of 13%, what percentage should you invest in McDonalds?

d. Based on your percentages in part c, what would the standard deviation of this portfolio be?

4. The table below gives the amount invested and betas for three stocks.

|Stock |Amount Invested |Beta |

|GM |$10,000 |1.0 |

|IBM |$10,000 |1.2 |

|WMT |$20,000 |0.7 |

a. Using the CAPM, if the expected return for the market is 9% and the risk-free rate is 3%, what is the expected return for each stock?

b. What is the beta for this portfolio based on the invested amounts?

c. Using the CAPM, what is the expected return for this portfolio?

Answers to Review Problems

3.

a. E(R) = .4(15) + .6(9) = 11.4%

b. The square root of [.42 * .152 + .62 * .142 + 2(.4)(.6)(.5)(.15)(.14)] = 12.51%

c. 13 = w1(15) + (1-w1 )9 where w1 = amount in McDonalds. Solving for w1 = 67%

d. The standard deviation of the portfolio in part c would be the square root of [.672 * .152 + .332 * .142 + 2(.67)(.33)(.5)(.15)(.14)] = 13.1%.

4.

a. E(R) = rf + B[E(Rm) – rf], so E(GM) = 3 + 1(9 – 3) = 9%, E(IBM) = 3 + 1.2(9 – 3) = 10.2%, E(WMT) = 3 + .7(9 – 3) = 7.2%.

b. Beta for a portfolio equals the weighted sums of the individual betas. In this case, beta for portfolio = 0.25(1) + 0.25(1.2) + .5(0.7) = 0.9.

c. E(Return for portfolio) = 3 + 0.9*(9-3) = 8.4%.

Multiple Choice Group A

CFA

Use the following data to answer the next two questions.

The annual rate of return for JSI’s common stock has been:

| |1989 |1990 |1991 |1992 |

|Return |14% |19% |-10% |14% |

CFA

1. What is the arithmetic mean of the rate of return for JSI’s common stock over the four years?

a. 8.62%

b. 9.25%

c. 14.25%

d. None of the above

CFA

2. What is the geometric mean of the rate of return for JSI’s common stock over the four years?

a. 8.62%

b. 9.25%

c. 14.21%

d. Cannot be calculated due to the negative return in 1991

CFA

3. An analyst estimates that a stock has the following probabilities of return depending on the state of the economy:

|State of Economy |Probability |Return |

|Good |0.1 |15% |

|Normal |0.6 |13% |

|Poor |0.3 |7% |

The expected return of the stock is:

a. 7.8%

b. 11.4%

c. 11.7%

d. 13.0%

CFA

Use the following expectations on Stocks X and Y to answer the following three questions

| |Bear Market |Normal Market |Bull Market |

|Probability |0.2 |0.5 |0.3 |

|Stock X |-20% |18% |50% |

|Stock Y |-15% |20% |10% |

CFA

4. What are the expected returns for Stocks X and Y?

| |Stock X |Stock Y |

|a. |18% |5% |

|b. |18% |12% |

|c. |20% |11% |

|d. |20% |10% |

CFA

5. What are the standard deviations of returns on Stocks X and Y?

| |Stock X |Stock Y |

|a. |15% |26% |

|b. |20% |4% |

|c. |24% |13% |

|d. |28% |8% |

CFA

6. Assume that of your $10,000 portfolio, you invest $9,000 in Stock X and $1,000 in Stock Y. What is the expected return on your portfolio?

a. 18%

b. 19%

c. 20%

d. 23%

7. If you buy an PG&G stock which has an expected return of 8% and a standard deviation of 12%, approximately 2/3 of the time you should expect to earn between

a. 8% and 12%

b. 0% and 24%

c. –12% and 12%

d. –4% and 20%

Answers to Multiple Choice B

1. b 6. b

2. a

3. b 7. d

4. d

5. c

Multiple Choice Group B

1. Which of the following is a source of unsystematic risk?

a. Interest rates

b. Business cycle

c. Energy Prices

d. Introduction of a bad product

CFA

2. In the context of capital market theory, unsystematic risk:

a. is described as unique risk.

b. refers to nondiversifiable risk.

c. remains in the market portfolio

d. refers to the variability in all risky assets caused by marcroeconomic and other aggregate market-related variables.

CFA

3. Consistent with capital market theory, systematic risk:

I. refers to the variability in all risky assets caused by macroeconomic and other aggregate market-related variables.

II. is measured by the coefficient of variation of returns on the market portfolio.

III. refers to nondiversifiable risk.

a. I only

b. II only

c. I and III only

d. II and III only (2 minutes)

CFA

4. An investor is considering adding another investment to a portfolio. To achieve the maximum diversification benefits, the investor should add an investment that has a correlation coefficient with the existing portfolio closest to:

a. –1.0

b. –0.5

c. 0.0

d. +1.0

CFA

5. The security market line depicts:

a. A security’s expected return as a function of its systematic risk.

b. The market portfolio as the optimal portfolio of risky securities.

c. The relationship between a security’s return and the return of the index.

d. the complete portfolio as a combination of the market portfolio and the risk-free asset.

CFA

6. Which of the following statements about the security market line (SML) is false?

a. Properly valued assets plot exactly on the SML

b. The SML leads all investors to invest in the same portfolio of risk assets.

c. The SML provides a benchmark for evaluating expected investment performance.

d. The SML is a graphic representation of the relationship between expected return and beta.

7. The slope of the Security Market Line will increase if

a. the risk free rate increases

b. the required return from the market portfolio increases

c. the average beta increases

d. if the risk premium decreases.

CFA

8. The Markowitz efficient frontier is best described as the set of portfolios that has:

a. the minimum risk for every level of return.

b. proportionally equal units of risk and return.

c. the maximum excess rate of return for every given level of risk.

d. the highest return for each level of beta based on the capital asset pricing model.

CFA

9. According to the CAPM, what is the rate of return of a portfolio with a beta of 1?

a. Between Rm and Rf

b. The risk-free rate, Rf

c. Beta * (Rm – Rf)

d. The return on the market, Rm

CFA

10. What is the expected return of a zero-beta security?

a. Market rate of return.

b. Zero rate of return.

c. Negative rate of return.

d. Risk-free rate of return.

CFA

11. Capital asset pricing theory asserts that expected returns are best explained by:

a. Economic factors

b. Specific risk

c. Systematic risk

d. Diversification

The table is for the next two questions:

The following table shows risk and return measures for two portfolios.

| |Average Annual |Standard | |

|Portfolio |Rate of Return |Deviation |Beta |

|R |11% |10% |0.50 |

|S&P 500 |14% |12% |1.00 |

CFA

12. When plotting portfolio R on the preceding table relative to the SML, portfolio R lies:

a. On the SML.

b. Below the SML.

c. Above the SML.

d. Insufficient data given.

13. If you place 25% of your wealth in Stock A which has a beta of 0.5 and 75% of your wealth in a stock that has a beta of 1.5, the beta of your portfolio will be

a. 1.0

b. 1.25

c. 1.5

d. Cannot tell without the knowing the correlation between the two stocks.

14. The higher the coefficient of determination (the R-square),

a. the higher the beta.

b. the more confidence one can have in the beta.

c. the lower the correlation coefficient.

d. the lower the beta.

15. A stock with a beta of 2 is

a. twice as risky as the average stock in the market.

b. will have twice the expected return as the average stock in the market.

c. will have twice the standard deviation as the average stock in the market.

d. will have twice the return as the risk-free rate.

Answers to Multiple Choice B

1. d 6. b 11. c

2. a 7. b 12. d

3. c 8. a 13. b

4. a 9. d 14. b

5. a 10. d 15. a

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