Andrew wants to invest in two securities Alpha and Omega and

Andrew 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%

Calculate expected returns and standard deviations of two securities.

Andrew 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

Expected return on Alpha = 3.75%

Standard dev = 12.44%

Expected return on Omega = 4%

Standard dev = 0%

weight of Omega = -1000/3000 = =1/3

weight of Alpha = 4/3

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

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