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  1. Consider two stocks, A and B.

 

 

Expected return (%)

Standard deviation (%)

Stock A

24

28

Stock B

19

23

 

The returns on the two stocks have a positive correlation of 0.6. You are required to calculate the portfolio return and risk.

Suppose that the investor wants to reduce the portfolio risk to 15%. How much should the correlation coefficient be to bring the portfolio risk to the desired level?

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1. The diversification effect of a portfolio of two stocks: . A. increases as the correlation between the stocks declines. B. increases as the correlation between the stocks rises. C. decreases as the correlation between the stocks rises. D. Both A and C. E. None of the above. 2. Irene Adler is considering investing in the common stock of Holmes and Watson. The following data are available for the two securities. . ................... Expected Return ..... Standard Deviation Holmes .............. 0.12 ......................... 0.08 Watson ............. 0.19 .......................... 0.25 . If she invests 60% of her funds Holmes and 40% in Watson, and if the correlation of returns between these two securities is 0.45, what is the portfolio’s expected return and standard deviation? . A. 14.8% and 12.89% B. 13.6% and 11.03% C. 14.6% and 13.94% D. 14.4% and 11.03% E. 13.21% and 10.08% 3. What does a security bring to the risk of a well diversified portfolio? . A. It brings its standard deviation of possible returns. B. It brings its covariance with the other securities in the portfolio. C. It brings its total risk. D. It brings its unsystematic risk. 4. Diversification can effectively reduce risk. Once a portfolio is diversified, the type of risk remaining is: . A. individual security risk. B. riskless security risk. C. unsystematic risk D. systematic risk 5. Efficient portfolios are those, which offer: . A. Highest expected return for a given level of risk B. Highest risk for a given level of expected return C. The maximum risk and expected return D. All of the above

Consider the following case:

Andre is an amateur investor who holds a small portfolio consisting of only four stocks. The stock holdings in his portfolio are shown in the following table:

What is the expected return of Andre's stock portfolio?

a) 15.53%

b) 10.35%

c) 7.76%

d) 13.97

Suppose each stock in the preceding portfolio has a correlation coefficient of 0.4 (p=0.4) with each of the other stocks.  If the weighted average of the risk (standard deviation) of the individual securities in the partially diversified portfolio of four stocks is 40%, the portfolio's standard deviation () most likely is _______ 40 %.

Stock X and Stock Z both have an expected return of 10%. The standard deviation of the expected return is 8% for Stock X, and 12% for Stock Z. Assume that these are the only two stocks available in a hypothetical world.

A. Assume that the correlation between the returns of the two stocks is +1.

• What is the expected return and standard deviation of a portfolio containing 50% X and 50% Z?

• What is the optimal amount of Stock Z for an investor to hold in a portfolio (if the correlation is +1)?

B. Assume that the correlation between the returns of the two stocks is +0.1.

• What is the expected return and standard deviation of a portfolio containing 50% X and 50% Z?

• What is the optimal amount of Stock Z for an investor to hold in a portfolio (if the correlation is +0.1)?

C. Assume that the correlation between the returns of the two stocks is –1.

• What is the expected return and standard deviation of a portfolio containing 50% X and 50% Z?

• What is the optimal amount of Stock Z for an investor to hold in a portfolio (if the correlation is –1)?

D. If the Capital Asset Pricing Model is true, explain why it is possible for the two stocks to have the same expected return even though the standard deviation of the expected return is 8% for Stock X, and 12% for Stock Z. (What must be true about the types of risks facing the two companies for the given numbers to make sense?).

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