# Expected return on portfolio; beta; riskier stock

You have the following information on the two securities in which you have invested

Expected Standard Security Amount

Return Probability Deviation Beta Invested

Kodak 15% .35 4.5% 1.20 $45,000

Xerox 12% .65 3.8% 0.98 $55,000

1) .. Which stock is riskier in a portfolio context? Which stock is riskier if you are not considering them in a portfolio? Explain. (5)

2) Compute the expected return on the portfolio. (5)

3) Compute the beta for the portfolio. (5)

4) Given the following information, Compute is the expected return on General Motors. (5)

Probability Expected Amount

Return Invested

0.2 -15 $5,000

0.3 20 8,000

0.4 25 10,000

0.1 40 15,000

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#### Solution Preview

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You have the following information on the two securities in which you have invested

Expected Return Probability Standard Deviation Security Beta Amount Invested

Kodak 15% 0.35 4.50% 1.2 $45,000

Xerox 12% 0.65 3.80% 0.98 $55,000

1) .. Which stock is riskier in a portfolio ...

#### Solution Summary

This post shows how to calculate the expected return on the portfolio, the beta for the portfolio and the expected return on General Motors. It discusses about the riskier stock in a portfolio context

Risk and return on investment - Individual stocks and portfolio

1. You are considering three stocks with the following expected dividends yields and gains:

Dividend Yield Capital Gain

A 14% 0%

B 8 6

C 0 14

a) What is the expected return on each stock?

b) How may transactions costs and capital gains taxes affect your choices?

2. You are given the following information concerning two stocks:

A B

Expected return 10% 14%

Standard deviation of the expected

Return 3.0 5.0

Correlation coefficient of the returns -.1

a) What is the expected return on a portfolio consisting of 40% in stock A and 60 % in stock B

b) What is the standard deviation of this portfolio?

c) Discuss the risk and return associated with investing (a) all your funds in stock A, (b) all your funds in stock B, and © 40 percent in A and 60 % in B. (This answer must use the numerical information in your answer derived above)

3. You are given the following information:

Expected return on stock A 12%

Expected return on stock B 20%

Standard deviation of returns:

Stock A 1.0

Stock B 6.0

Correlation coefficient of the returns on stock A&B +.2

a) What are the expected returns and standard deviations of a portfolio consisting of:

1) 100 % in stock A?

2) 100% in stock B?

3) 50 % in each stock?

4) 25% in stock A and 75% in stock B?

5) 75% in stock A and 25% in stock B?

b) Compare the above returns and risk associated with each portfolio.

c) Redo the calculations assuming that the correlation coefficient of the returns on the two stock is-0.6. What is the impact of this difference in the correlation coefficient?

4) What is the beta of a portfolio consisting of one share of each of the following stocks given their respective prices and beta coefficients?

Stock Price Beta

A $10 1.4

B 24 0.8

C 41 1.3

D 19 1.8

How would the portfolio beta differ if:

a) the investor purchased 200 shares of stock B and C for every 100 share of A and D?

b) equal dollar amounts were invested in each stock?