Note: Due time/date for this homework is 4:30pm on February 5. Please make online submission at T-square.

0. Today you bought 100 shares of ABC Inc. at $100 per share. A year from now ABC will pay a dividend of $2 per share for sure. The price of ABC a year from now is uncertain and depends on the state of the economy. A year from now the economy will either be in a recession, a state of “normal” growth, or a boom with probabilities of 30%, 40%, and 30% respectively. After analyzing ABC you determine that the price of ABC a year from now in these various states of the economy will be: State of the Economy Recession Normal Growth Boom Price of ABC $80 $110 $130

What is the expected return over the next year to your investment in ABC?

What is the standard deviation of that return?

1. You are considering buying equity in a firm. If you purchase the equity, in one year you will receive $1.5 million with 40% probability and $1.2 million with 60% probability. Currently the yield on one year T-bills is 4%. Suppose that you require a risk premium of 10% to invest in the equity of this firm. In other words, your minimum required return on this investment is 14%.

(a) What is the most you would be willing to pay for the equity?

(b) If you pay this, what is the expected rate of return on your investment?

(c) What is the standard deviation of the return to your investment in the firm?

2. Based on your examination of the historical record, you calculate that the expected return on the S&P500 over the next year is 6% over T-bills with a standard deviation of 15%. Currently a T-bill with one year to maturity and face value of $10,000 is selling for $9,615. You have $1 million to invest and you will put all of your money in some combination of the S&P500 and one-year T-bills. Calculate the expected return and standard deviation of that return for 3 different portfolios. (a) Portfolio #1 is invested 100% in the S&P500.