1. The optimal risky portfolio is _____.

above the efficient frontier

found at the point of tangency between the line through the risk-free asset and the efficient frontier

the portfolio with the smallest variance

the portfolio with the greatest expected return

below the efficient frontier

2. You've done some security analysis and generated the following data for two stocks and Treasury bills:

Security	Stock A	Stock B	T-bills
Expected return (%)	12	8	2
Standard deviation	0.2	0.12	0
Correlation with stock A	1	0.5	0

a. What is the weight of stock A in the optimal risky portfolio?

b. What is the Sharpe ratio of the optimal risky portfolio (ORP)?

3. You have $7,000 to invest. You've done some security analysis and generated the following data for three stocks and Treasury bills, including weights in the optimal risky portfolio (ORP) from doing Markowitz portfolio optimization:

Security	Stock A	Stock B	Stock C	T-bills
Expected return (%)	12	11	5	1
Variance	0.04	0.03	0.02	0
Beta	1.2	1.5	0.8	0
Weight in ORP (%)	44	18	38	0

a. If you want to achieve an expected return of 8% for the complete portfolio, how much money should you invest in stock B (in $)?

b. What is the ratio of the Sharpe ratio of the complete portfolio to the Sharpe ratio of the ORP?

4. The efficient frontier _____.

Check all that apply:

offers the minimum standard deviation for a given return OR offers the maximum return for a given standard deviation

is strictly concave

is that part of the feasible set above the minimum variance portfolio

plots the portfolios that are not dominated by some other portfolio

5. The return statistics for two stocks and T-bills are given below:

	A	B	C	D
1		Stock A	Stock B	T-bills
2	Expected return	0.053	0.075	0.03
3	Standard deviation	0.24	0.31
4	Correlation	0.9

a. What is the Sharpe ratio of the optimal risky portfolio?