The covariance of returns between Share A and Share B is 0.0243. Share A has exhibited historical returns with a mean of 12% and standard deviation of 18%. Over the same period, Share B had average returns of 21% with a standard deviation of 27%. Calculate the expected return and standard deviation of a portfolio consisting of $50,000 in Share A and $100,000 in Share B.

Consider Ford stock (F) with a current price of $20 per share and a standard deviation of returns of 15%.

General Motors (GM) stock has an expected return of 12% and a standard deviation of returns of 16%.

a) An investor expects to sell Ford stock in one year at $21 per share and expects the firm to pay a dividend of $1 per share at the end of the year. What is the expected total return and what is the dividend yield?

b) An investor holds a portfolio of F and GM with 80% of the portfolio in Ford. What is the standard deviation of this portfolio if Ford and GM have a correlation of -1?

c) Given the correlation of Ford and GM stock, can an investor construct a zero variance portfolio? If so, what are the weights on F and GM in this portfolio? If not, explain why?

d) Given your answer in c), what is the risk-free rate? Why?

Stocks A and B have the following historical returns.

Calculate the average return for each stock during the period 1998 through 2002. (8 marks)

Assume that someone held a portfolio consisting of 50 percent stock A and 50 percent stock B. What would have been the realized rate of return on the portfolio in each year from 1998 through 2002? What would have been the average return on the portfolio during this period?

(9 marks)

Calculate the standard deviation of returns for each stock and for the portfolio and explain what each figure mean. (8 marks)

Suppose that the standard deviation of returns from a typical share is about 0.55 (or 55%) a year. The correlation between the returns of each pair of shares is about 0.4. a. Calculate the variance and standard deviation of the returns on a portfolio that has equal investments in 2 shares, 3 shares, and so on, up to 10 shares. b. How large is the underlying market variance that cannot be diversified away? c. Assume that the correlation between each pair of stocks is zero. Calculate the variance and standard deviation of the returns on a portfolio that has equal investments in 2 shares, 3 shares, and so on, up to 10 shares.