Dr. Sudhakar Raju
FN 6100
QUESTIONS FOR ASSIGNMENT 2
(This assignment is due by noon on Friday, Feb4. You may slide it under my office door
– Conway 311)
1.) You own a stock portfolio invested 25% in Stock Q, 20% in Stock R, 15% in Stock S,
and 40% in Stock T. The betas for these four stocks are 0.9, 1.4, 1.1, and 1.8,
respectively. What is the portfolio beta?
2.) You own a portfolio equally invested in a risk-free asset and two stocks. If one of the
stocks has a beta of .8 and the total portfolio is equally as risky as the market, what
must the beta be for the other stock in your portfolio?
3.) A stock has a beta of 1.10 and an expected return of 15%. A risk-free asset currently
earns 5%.
a) What is the expected return on a portfolio that is equally invested in the two
assets?
b) If a portfolio of the two assets has a beta of .6, what are the portfolio weights?
c) If a portfolio of the two assets has an expected return of 9%, what is its beta?
d) If a portfolio of the two assets has a beta of 2.20, what are the portfolio weights?
How do you interpret the weights for the two assets in this case?
4.) Stock Y has a beta of 1.45 and an expected return of
17%. Stock Z has a beta of .85 and an expected return of 12%. If the
risk-free rate is 6% and the market risk premium is 7.50%, are these stocks correctly
priced?
5.) In the previous problem, what would the risk-free rate have to be for the two stocks
to be correctly priced? (Note: A stock that is correctly priced will lie on the SML).
6.) You want to create an index portfolio (i.e. a portfolio that is equally as risky as the
market). You have $1,000,000 to invest. Given this information, fill in the following
table:
1
Asset
Investment
Beta
Stock A
$200,000
0.70
Stock B
$250,000
1.10
Stock C
?
1.60
Risk-free asset
?
?
7.) You have $100,000 to invest in a portfolio containing Stock X, Stock Y, and a risk-free
asset. You must invest all of your money. Your goal is to create a portfolio that has an
expected return of 12.50% and that has only 80% of the risk of the overall market. If
Stock X has an expected return of 28% and a beta of 1.60, Stock Y has an expected
return of 16% and a beta of 1.20, and the risk-free rate is 7%, how much money will you
invest in Stock X? How do you interpret your answer?
(One of the weights in this problem is negative. A negative weight means that the
position is “short” implying that you borrow the stock and hope to sell it later at a lower
price).
8.) Suppose you observe the following situation:
Security
Pete Corp.
Repete Co.
Beta
1.3
0.8
Expected Return
20%
14%
Assume these securities are correctly priced (i.e. stocks that are correctly priced will lie
exactly on the SML). Based on the CAPM, what is the expected return on the market?
What is the risk-free rate?
9.) Briefly discuss the following:
a.) The Efficient Frontier
b.) Draw a variance-covariance matrix for a 50 stock portfolio. How many variance terms
are there? How many covariance terms are there?
c.) Is there a shortcut that quickly estimates the risk of a 50 stock portfolio?
b.) What is beta? What factors affect beta? Can beta be negative?
e.) What are the 3 factors that affect the return on an asset?
2