Question

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

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

  1. What is the expected return for Stock A?
  1. What is the standard deviation for Stock A?
  1. 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?
  1. 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?

  1. 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?

Homework Answers

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%

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