Andrew wants to invest in two securities, Alpha and Omega, and the relevant info
ID: 2823516 • Letter: A
Question
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?
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%
Explanation / Answer
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%
p(x) return p*x p*(x - mean)^2 0.25 -15% -0.0375 0.0087891 0.5 5% 0.025 0.0000781 0.25 20% 0.05 0.0066016