# Risk and return on investment - Individual stocks and portfo

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?

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#### Solution Preview

See the attached file for complete solution. The text here may not be copied exactly as some of the symbols / tables may not print. Thanks

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?

Expected Return = Dividend yield + capiatl gain yield

A 14%

B 14%

C 14%

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

When the dividends are disbursed, then investors needs to reinvest the divident payments and incur transaction cost.

In the presence of capital gain tax, the capital gain on the stock is taxed when stock is sold in the market.

Thus, there is a trade of between higher capital gains and dividend gains. If the dividend gains are high, the trasaction

cost would be high but capital gain tax would be low and vice versa.

If the transaction costs are low (say nil), investor would prefer stock A. If capital gain tax is low(say nil), the investor would prefer stock c.

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

A B

Expected return 10% 14%

Standrad dviation 3.00% 5.00%

Correlation coefficient of the returns -0.1

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

Proportion of stock A 0.4

Proportion of Stock B 0.6

Expected return of portfolio 12.40%

b)What is the standard deviation of this portfolio?

Standard devistion of portfolio 3.12%

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 ...

#### Solution Summary

The post answers four questions related to security analysis and portfolio management. The first question explains how the mix between dividend yield and capital gain yield affects the investment decisions. In the second questions, we understand the concepts of portfolio risk and return. The same concepts are reiterated in question 3 and 4. The solution provides step-by-step process to help the students grasp the concepts.

SML, Expected Return, Beta

5) The rate on Treasury bills is 4 percent, and the equity risk premium is 10 percent. Use the SML to estimate the return on each of the above stocks.

Security Standard deviation Correlation with market

A 0.30 0.70

B 0.75 0.30

C 0.45 0.50

D 0.50 0.16

6) Maria has decided to invest $5,000 in each of the above stocks. Compute the expected return on the portfolio and the portfolio beta.

Security Standard deviation Correlation with market

A 0.30 0.70

B 0.75 0.30

C 0.45 0.50

D 0.50 0.16

(See attached file for full problem description with data charts)

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