HOMEWORK #2 (chapters 5, 6, and 8) All details of your work must be shown if a formula is used please show that as well.

1.) FIN307 stock has the following probability distribution of expected prices one year from now:

State Probability Price

1 .25 $50

2 .40 $60

3 .35 $70

If you require a risk premium of 5% and Rf is 4%. What is the price you are willing to pay today for FIN307? Assuming the stock will pay a dividend of $4 per share.

2.) Use the following information to answer questions a-d

You are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio, P, constructed with 2 risky securities, X and Y. The weights of X and Y in P are 0.60 and 0.40, respectively. X has an expected rate of return of 0.14 and variance of 0.01, and Y has an expected rate of return of 0.10 and a variance of 0.0081. The coefficient of correlation, rho, between X and Y is 0.45.

a. If you desire to form a portfolio with an expected rate of return of 0.11, what percentage of your money must you invest in the T-bill and P, respectively?

b. What would be the dollar values of your positions in X and Y, respectively, if you decide to hold 40% of your money in the risky portfolio and 60% in T-bills?

c. If you desire to form a portfolio with a standard deviation of 5.59%, what percentages of your money must you invest in the T-bill, X, and Y respectively

d. What would be the dollar value of your positions in X, Y, and the T-bills, respectively, if you decide to hold a portfolio that has an expected outcome of $1,200?

3.) A risky portfolio, P, is constructed with 2 risky securities, X and Y. The weights of X and Y in P are 0.60 and 0.40, respectively. X has an expected rate of return of 0.14 and variance of 0.01, and Y has an expected rate of return of 0.10 and a variance of 0.0081. The coefficient of correlation, rho, between X and Y is 0.45. What is the SR for the portfolio P? What is the change in SR if the coefficient of correlation is changed to -0.20? Assume TB rate is 5%.

4.) You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 5% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 60% and 40%, respectively. X has an expected rate of return of 14%, and Y has an expected rate of return of 10%. What will be the dollar values of your positions in X, Y, and Treasury bills, respectively, if you decide to hold a complete portfolio that has an expected return of 8%?

5.) You put half of your money in a stock portfolio that has an expected return of 14% and a standard deviation of 24%. You put the rest of your money in a risky bond portfolio that has an expected return of 6% and a standard deviation of 12%. The stock and bond portfolios have a correlation of .55 and TB or Rf is 2%. What is the SR of the resulting portfolio?