1. You are given the following information on a stock fund.
a. Please compute the expected return and standard deviation for the stock fund.
Scenario Probability Rate of Return/Stock Fund
Recession 25.0% -7%
Normal 50% 12%
Boom 25.0% 28%
b. You plan to form a portfolio with 50% invested in the Stock Fund and 50% invested in T-bills (the risk-free asset). T-bill offers a return of 5%. What's the portfolio return and portfolio risk?
c. There is a Bond Fund which has a correlation coefficient of -1 with the Stock Fund mentioned in part a. The expected return and standard deviation for the Bond Fund are 6% and 10%, respectively. You plan to form a portfolio with the Stock Fund and the Bond Fund only (no T-bills in this part). What are the portfolio weights you need to choose such that the variance of the portfolio is minimized?
This provides an example of computing expected return, standard deviation, portfolio return and risk, and portfolio weights to minimize variance.