Question 1 Ms Smith wants to invest in two securities Alpha

Question 1 Ms. Smith wants to invest in two securities, Alpha and Omega, and the relevant information is below: State of the Economy Probability Return on Alpha (%) Return on Omega (%) Bear 0.25 -15% 4% Moderate 0.5 5% 4% Bull 0.25 20% 4% a. Calculate expected returns and standard deviations of two securities.

b. Ms. Smith shorts $1,000 of Omega and invests all proceeds from this short sale as well as $3,000 of her own money into Alpha. What is the expected return and the standard deviation of her portfolio?

Solution

a.

Expected return on Alpha = 3.75%

Standard dev = 12.44%

Expected return on Omega = 4%

Standard dev = 0%

b/ weight of omega = -1/3

weght of Alpha = 4/3

expected return = 4/3 * 3.75% - 1/3*4% = 3.67%

standard dev = 4/3 * 12.44% = 16.59%