Question

There are two assets and three states of the economy, answer questions 11 to 15.  

State of Economy	Probability of State of Economy	Return of Stock A if State Occurs	Return of Stock B if State Occurs
Recession	0.30	-0.20	0.10
Normal	?	0.30	0.20
Boom	0.15	0.40	0.30

7. What is the expected return for Stock A?

8. What is the standard deviation for Stock A?

9. Suppose you have $50,000 total. If you put $20,000 in Stock A and the remainder in Stock B, what are the portfolio returns in each state?

10. Suppose you have $50,000 total. If you put $20,000 in Stock A and the remainder in Stock B, what will be the expected return of your portfolio?

11. Suppose you have $50,000 total. If you put $20,000 in Stock A and the remainder in Stock B, what will be the standard deviation of your portfolio?

Answer 1

Probability of Normal =1-0.30-0.15 =0.55

Expected Return for Stock A =0.30*-0.20+0.55*0.30+0.15*0.40=16.50%
Standard Deviation of A =0.30*(-0.20-16.50%)^2+0.55*(0.30-16.50%)^2+0.15*(0.40-16.50%)^2=5.83%


Weight of A =20000/50000=40%
expected Return in recession =40%*-0.20+60%*0.10 =-2%
expected Return in normal =40%*0.30+60%*0.20 =24%
expected Return in recession =40%*0.40+60%*0.30 =34%

Expected Return of portfolio =0.30*-2%+0.55*24%+0.15*34% =17.70%
Standard Deviation of Portfolio =(0.30*(-2%-17.70%)^2+0.55*(24%-7.70%)^2+0.15*(34%-17.70%)^2)^0.5 =17.39%