Question

1a. Suppose that Apple stock has an expected return of 10% and a standard deviation of returns of 25%. The risk-free rate on the economy (measured as the yield on a one-year Treasury bond) is 5%. What is the Sharpe ratio of Apple stock?.

1b. Suppose that the only risky asset you are interested in holding is Apple stock. However, you would prefer to hold a portfolio with more risk. Specifically, you would like to hold a portfolio with return standard deviation equal to 30%. What expected return can you achieve by mixing together Apple stock with the Treasury bond to achieve a portfolio with a 30% return standard deviation? (Please enter you answer to the nearest tenth; e.g. 52.6).

What weight do you need to put on Apple stock in your portfolio to achieve the 30% standard deviation?

What weight do you need to put on the Treasury bond in your portfolio to achieve the 30% standard deviation?

Answer 1

1.
What is the Sharpe ratio of Apple stock?.
=(10%-5%)/25%
2.
What weight do you need to put on Apple stock in your portfolio to achieve the 30% standard deviation?
=30%/25%=1.2 or 120.00%

What weight do you need to put on the Treasury bond in your portfolio to achieve the 30% standard deviation?
=1-1.2=-0.2 or -20.00%

What expected return can you achieve by mixing together Apple stock with the Treasury bond to achieve a portfolio with a 30% return standard deviation?
=1.2*10%-0.2*5%
=11.0000%