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PART 1: MULTIPLE CHOICE QUESTIONS (5 POINTS EACH)

Question 1: Suppose a company’s return in the past three years has been -30%, 0%, and 30%. What is the
geometric average of these returns?

A. -30%
B. -3.10%
C. 0%
D. 3.10%
E. 30%


Question 2: Suppose we have done mean-variance analysis and drawn the investment opportunity set.
What happens to the Sharpe ratio of the tangency portfolio if we now introduce one more risky asset?

A. It increases
B. It stays the same
C. It decreases substantially if the new asset is highly correlated with one of the old assets
D. It becomes to equal to the expected return of the minimum variance portfolio
E. It stays the same or increases. The outcome depends on the asset’s expected return and its
correlation with existing assets.


Question 3: All things equal, diversification is most effective when

A. Asset returns are uncorrelated
B. Asset returns are positively correlated
C. Asset returns are high
D. Asset returns are negative correlated
E. Both B and C


Question 4: Which one of the following portfolios has the highest Sharpe ratio? The risk-free rate is 3%.

F. E(rA) = 10%, σA = 20%
G. E(rB) = 12%, σB = 24%
H. E(rC) = 14%, σC = 30%
I. E(rD) = 16%, σD = 34%
J. E(rE) = 18%, σE = 40%


Question 5: Your opinion is that a security has an expected rate of return of 10.6%. It has a beta of 1.2.
The risk-free rate is 4% and the market expected rate of return is 10%. According to the Capital Asset
Pricing Model, this security is

A. underpriced.
B. overpriced.
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C. fairly priced.
D. cannot be determined from data provided.
E. none of the above.


Question 6: The Arbitrage Pricing Theory (APT)…

A. tells us how to find common factors among returns
B. says that if any two securities have the same exposures to the common factors, they must have
the same expected returns
C. states that the CAPM is wrong
D. assumes there are abundant arbitrage opportunities
E. both A and B are correct


Question 7: The minimum variance portfolio of risky assets

A. has equal covariance with all individual assets
B. always has a lower expected return than the tangency portfolio
C. has the same or lower variance than all individual risky assets
D. all of the above
E. none of the above


Question 8: Discount rates are

A. actual rates of return
B. realized rates of return
C. historical average returns
D. expected returns
E. B and C


Question 9: Suppose you invest $10,000 into S&P 500 with the expectation that S&P will earn 0.8% per
month from now on. What do you expect your investment to be worth in 50 years?

A. About $15 thousand
B. About $470 thousand
C. About $740 thousand
D. About $980 thousand
E. About $1.2 million



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PART 2: SHORT ANSWER QUESTIONS


Question 10: Suppose you invest $10,000 in the S&P 500 with the expectation that it will earn 1% per
month from now on. What do you expect your investment to be worth in 5 years? (8 points)


Question 11: Suppose the world is described by a two factor APT model, that there are no arbitrage
opportunities, and that the returns on three base assets satisfy the equations below. What is the risk-free
rate? (15 points)
r1 = .13 + 2F1 + 2F2 + e1
r2 = .07 + F1 + e2
r3 = .15 + 2F1 + 3F2 + e3


Question 12: According to the CAPM, an asset may have an expected return below the risk-free rate, but
no asset can have an expected return below zero since everyone holds the market portfolio. Is this TRUE,
FALSE, or IT DEPENDS (briefly explain)? (10 points)


Question 13: The expected returns of A, Inc. and B Enterprises are 12% and 14%, respectively.
Furthermore, the variance-covariance matrix for these two stocks is given by the following:

A B
A 0.005 0.002
B 0.002 0.004
The risk-free rate is 6%. Compute the portfolio weights of the two stocks in the minimum variance portfolio.
(10 points)


Question 14: The following table gives you information about stocks A and B, and the risk-less asset



a) What is the expected return of a portfolio that invests 1/3 in A, 1/3 in B, and 1/3 in the risk-less
asset (10 points)


b) What is the standard deviation of the portfolio in part (a) (7 points)?