# Risk, Return, Diversification

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1) Expected Return and Standard Deviation

Wilson holds a two stock portfolio that invests equally in Kelvera Industries and Old Glory Insurance Company (50% of his portfolio is in each stock). Each stock's expected return for next year will depend on market conditios. The stocks' expected returns if there are poor, average, or great market conditions are shown below:

Market Condition Probability Kelevra Industries Old Glory Insurance Co.

Poor 0.25 -12% -2%

Average 0.5 14% 6%

Great 0.25 44% 14%

a) What is the portfolio's expected return over the next year?

9.75%

10.00%

9.00%

10.50%

9.25%

b) What is the expected standard deviation of portfolio return?

13.10%

13.47%

12.38%

12.74%

11.67%

c) What is the coefficient of variation (CV) for the portfolio's expected return?

2) Portfolio expected return and risk

An analyst is examining the following two-stock portfolio:

Stock Portfolio Weight Expected Return Standard Deviation

Stock X 0.4 18.00% 35.00%

Stock Y 0.6 11.00% 35.00%

a) What is the portfolio's expected return?

15.20%

13.45%

13.80%

12.75%

13.10%

b) Suppose Stocks X and Yare perfectly, positively correlated (r = 1). What is the portfolio's standard deviation of returns?

0%

50%

70%

20%

35%

c) If you added randomly selected stocks to the portfolio, the portfolio's standard deviation would

d) If a portfolio has no firm-specific risk remaining, which of the following is the best estimate of the standard deviation of returns?

0%

70%

50%

20%

35%

e) The tradeoff between risk and return is a cornerstone concept in finance. If a security offers a higher expected return, it must have higher risk. Look at the two stocks described in this problem. They have the same risk, but one stock has a higher expected return. Does this example contradict the tradeoff between risk and return?

No

Yes

3. Diversification, risk, and return

Conrad holds a $20,000 portfolio that consists of four stocks. His investment in each stock, as well as each stock's beta, is shown below:

Stock Investment Beta Standard Deviation

Aramis Airlines $3,000 0.7 30%

Barrington Inc. $8,000 1.8 52%

Carrow & Co. $5,000 1.3 38%

Dartan Enterprise $4,000 0.3 33%

a) If all the stocks in the portfolio were equally weighted, which of these stocks would have the least amount of stand-alone risk?

Barrington Inc.

Carrow & Co.

Aramis Airlines

Dartan Enterprise

b) If all the stocks in Conrad's portfolio were equally weighted, which of these stocks would contribute the least risk to the portfolio?

Dartan Enterprise

Carrow & Co.

Aramis Airlines

Barrington Inc.

c) The risk-free rate is 5% and the market risk premium is 6%. What is the portfolio's beta and required return?

d) Conrad is thinking about reallocating the funds in his portfolio. He plans to sell his stake in Dartan Enterprises and put that money into Barrington Inc. Assuming the market is in equilibrium and Conrad changes his portfolio, how much will his portfolio's required return change?

1.56%

0.84%

1.68%

1.80%

1.08%

e) Suppose an analyst believes that the expected return on the portfolio is actually 14.80%. Does this analyst think the portfolio is undervalued, overvalued, or fairly valued?

Overvalued

Fairly Valued

Undervalued

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1. Expected Return and Standard Deviation

Wilson holds a two stock portfolio that invests equally in Kelvera Industries and Old Glory Insurance Company (50% of his portfolio is in each stock). Each stock's expected return for next year will depend on market conditios. The stocks' expected returns if there are poor, average, or great market conditions are shown below:

50% 50%

Market Condition Probability Kelevra Industries Old Glory Insurance Co.

Poor 0.25 -12% -2%

Average 0.5 14% 6%

Great 0.25 44% 14%

Market Condition Portfolio return

Poor -7.00% =50.% x -12.% + 50.% x -2.%

Average 10.00% =50.% x 14.% + 50.% x 6.%

Great 29.00% =50.% x 44.% + 50.% x 14.%

Market Condition Return Probability Return x Probability Difference Difference 2 Prob x Difference 2

Poor -7.00% 0.2500 -1.75% -17.50% 0.030625 0.007656

=(-7.%)-10.5% =-0.175^2 =0.25 x 0.030625

Average 10.00% 0.5000 5.00% -0.50% 0.000025 0.000012

=(10.%)-10.5% =-0.005^2 =0.5 x 0.000025

Great 29.00% 0.2500 7.25% 18.50% 0.034225 0.008556

=(29.%)-10.5% =(0.185)^2 =0.25 x 0.034225

Total= 1.00 10.5000% 0.016224

=-1.75% + 5.% + ( 7.25%) =0.007656 + 0.000012 + 0.008556

Expected return= 10.500%

Variance= 0.01622

Standard deviation=√Variance= 12.74% =√0.016224

Coefficient of variation= Standard deviation / Mean= 1.213 =12.74% / 10.5%

What is the portfolio's expected return over the next year?

9.75%

10.00%

9.00%

10.50%

9.25%

Answer: 10.50% (see calculations above)

What is the expected standard deviation of portfolio return?

13.10%

13.47%

12.38%

12.74%

11.67%

Answer: 12.74% (see calculations above)

What is the coefficient of variation (CV) for the portfolio's expected ...

#### Solution Summary

Answers questions on 1) Expected return and standard deviation, 2) Portfolio expected return and risk and 3)Diversification, risk, and return