Problem 9.2

O ne year ago, Mr. Seth Cohen invested $10,400 in 200 shares of First Industries, Inc., stock and just received a dividend of $600. Today, he sold the 200 shares at $54.25 per share.

1. What was his capital gain?
2. What was his total dollar return?
3. What was his percentage return?
4. What was the stock's dividend yield?

Problem 9.7

Two years ago, General Materials and Standard Fixtures' stock prices were the same. Over the first year, General Materials' stock price increased by 10 % while Standard Fixtures' stock price decreased by 10 % . Over the second year, General Materials' stock price decreased by 10 % a nd Standard Fixtures' stock price increased by 10 % . Do these two stocks have the same prices today? Explain.

Problem 9.8

Using the returns for the period 1981 to 1985 listed below, calculate the five-year holding period return on the S&P 500 index.

Holding-period return (p. 8, 12)

Problem 9.13

The probability that the economy will contract is 0.2. The probability of moderate growth is 0.6, and the probability of a rapid expansion is 0.2. If the economy contracts, you can expect a return on your portfolio of 5 % . With moderate growth, your return will be 8 % . If there is a rapid expansion, your portfolio will return 15 % .

1. What is your expected return?
2. What is the standard deviation of the return?

Problem 10.2

Suppose you have invested only in two stocks, A and B . The returns on the two stocks depend on the following three states of the economy, which are equally likely to happen:

1. Calculate the expected return on each stock.
2. Calculate the standard deviation of returns on each stock.
3. Calculate the covariance and correlation between the returns on the two stocks.

Problem 10.5

Security F has an expected return of 12 % and a standard deviation of 9 % per year. Security G has an expected return of 18 % and a standard deviation of 25 % per year.

1. What is the expected return on a portfolio composed of 30 % of security F and 70 % of security G ?
2. If the correlation between the returns of security F and security G is 0.2, what is the standard deviation of the portfolio described in part ( a )?

Problem 10.13

There are three securities in the market. The following chart shows their possible payoffs.

1. What is the expected return and standard deviation of each security?
2. What are the covariances and correlations between the pairs of securities?
3. What is the expected return and standard deviation of a portfolio with half of its funds invested in security 1 and half in security 2 ?
4. What is the expected return and standard deviation of a portfolio with half of its funds invested in security 1 and half in security 3 ?
5. What is the expected return and standard deviation of a portfolio with half of its funds invested in security 2 and half in security 3 ?
6. What do your answers in parts ( a ), ( c ), ( d ), and ( e ) imply about diversification?

Cleveland Compressor and Pnew York Pneumatic are competing manufacturing firms. Their financial statements are printed below.

1. How are the current assets of each firm financed?
2. 
   Which firm has the larger investment in current assets? Why?
3. Which firm is more likely to incur carrying costs, and which is more likely to incur shortage costs? Why?

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