1. You have $9,000 to invest and are deciding between investing in an equity mutual fund and Treasury bills. The fund has an expected return of 10% and a standard deviation of returns of 23%. T-bills have a return of 2%

a. If you put 77% into the mutual fund, what is your expected return?

b. What is the standard deviation of returns?

c. Since you're risk-averse, you are only willing to tolerate a standard deviation of 10% on the complete portfolio. How much money should you put into T-bills (in $)?

d. What's the Sharpe ratio of the complete portfolio with _c=10%?

e. If you wanted to achieve an expected return of 6% for the complete portfolio instead, how much money would you have to invest in the mutual fund (in $)?

2. We know the following expected returns for stocks A and B, given different states of the economy:

State (s)	Probability	E(rA,s)	E(rB,s)
Recession	0.1	-0.04	0.02
Normal	0.5	0.11	0.05
Expansion	0.4	0.19	0.09

a. What is the expected return for stock A?

b. What is the expected return for stock B?

c. What is the standard deviation of returns for stock A?

d. What is the standard deviation of returns for stock B?

3. You've estimated the following expected returns for a stock, depending on the strength of the economy:

State (s)	Probability	Expected return
Recession	0.1	-0.05
Normal	0.5	0.06
Expansion	0.4	0.11

a. What is the expected return for the stock?

b. What is the standard deviation of returns for the stock?