1)
(30 points) Jack is a portfolio manager in a mutual fund. He finds two different stocks.
Stock A and Stock B. He does not know what the returns of these stocks will be next month.
However he has some expectations. He knows the states of the economy and the associated
probabilities of these states for next month. He also identifies the returns of these stocks in three
different states as presented in the table below.
State
Probability
Return of Stock A
Return of Stock B
Boom
0.30
15%
18%
Neutral
0.40
10%
5%
Recession
0.30
12%
10%
a. Jack has additional $500,000 to invest in the portfolio. He plans to invest $150,000 in Stock
A and the rest in Stock B. Calculate the expected return and standard deviation of the portfolio.
b. When he is calculating the portfolio return and standard deviation Jack realizes that it might
not be a good idea to invest in both of these stocks. It will be better to choose one of these
stocks to invest. Briefly discuss why it is better if he chooses one of these stocks and state
which stock he should choose.
c. Jack's colleague Susan tells him that there is another stock; Stock C. Stock C has 13.50%
expected return and 2.97% standard deviation. The correlation coefficient of Stock C's return
with Stock A's return is 0.85. If Jack decides to invest $200,000 to Stock A and $300,000 to
Stock C and form a new portfolio then calculate the expected return and standard deviation of
this new portfolio.
d. Jack also gets additional information presented in the table.
Stock A Stock B Stock C
Market
Risk Free
Expected Return
13.50%
15.00%
2.5%
Standard Deviation
2.97%
3.87%
Correlation with the market 0.561
0.575
0.911
If Jack decides not to form a portfolio then decide which stock (Stock A, B or C) he should
choose and briefly discuss why.
e. If Jack decides to invest in all of these stocks (A, B, and C) with equal amounts then
calculate the beta of the portfolio he forms.