A large institutional investor is considering three Exchange Traded Funds:

Fund Expected Return Standard deviation Internet

ETF (Q) 11% 16%

Health Care ETF (H). 9% 12%

T-bill money-market ETF 4%

The two ETFs, Q, and H are uncorrelated.

1. Find the proportions of each asset, and the expected return and standard deviation of the tangency portfolio. 

2. What is the reward-to-variability (Sharpe) ratio of the best feasible capital allocation line?

3. Suppose this investor is highly risk-averse with a risk aversion coefficient equals to 8. 

a. What is the composition of the optimal portfolio in terms of all available funds? 

b. What are the expected return and standard deviation of your optimal portfolio? 

4. A less sophisticated investor would like to use only the Internet ETF and Health Care ETF, and require an expected return of 13%, what must be the investment proportions of her portfolio? Compare your result to the optimized portfolio in part 3.a. What do you conclude?