1. You know the following information about possible returns offered by two stocks, Umbrella and Resorts, next year.

Scenario Probability Return (X) Return (Y)

Rainy season 0.3 30% -10%

Sunny season 0.7 -20% 40%

Assume risk free rate is 5%.

(a) Assume that you invest 30% in stock X and 70% in stock Y. Is holding both stocks better than holding either stock? Support your answer with sufficient calculations.

(b) Assume that you invest 50% of your money in a portfolio (30% in stock X and 70% in stock Y) and the remaining 50% of your money in risk-free assets which offer a rate of 5%. What is the expected return and standard deviation of your investment portfolio?