Q6. Portfolio Risk and Return

You have 100M to invest, and are considering a risk-free money market account that pays 4% return and a risky-stock investment that will generate 8% mean return and 20% stdev risk.

a. what is the excess return (aka risk premium) for stock investment?

b. what is sharpe ratio for the stock (excess return divided by stdev risk)?

c. what is the mean and stdev for the following portfolio:

0% in stock; 50% in stock; 100% in stock; 200% in stock; -50% in stock; -100% in stock; -200% in stock

(note: out of 100% of your funds, what is not invested in stock is in money market account.)

d. if you want to achieve 12% expected return, what is the allocation in stock you need? what if you only need 6% expected return?

e. what is the stdev risk associated with portfolio in part d?

f. if you can not tolerate more than 12% stdev risk, what is the maximum expected return you can make?

g. for the two investment allocations in part d, what are the chances that you will lose money? (losing money means portfolio return is less than 0)? what is the chance of doubling our money? (doubling means a portfolio net return of 100%)