Final Exam
FIN 532 Investments Mini
Philip H. Dybvig
Washington University in Saint Louis
October 23, 2000
This is a closedbook examination. Answer all questions as
directed. Mark your answers directly on the examination. There
are no trick questions on the exam. There are some formulas
from the course (including some you will not need) at the end
of the exam. Good luck!
A. General Concepts Short Anwer: 20 points (Answer
each question in no more than one sentence of ordinary
length.)

Name two types of professionals on the buy side.

What is probably a better investment of funds you will need
within a month, a Treasury Bill or a corporate bond, and
why?

Describe one stock return anomaly.

What are Treasury STRIPs?

Which is a better measure of performance of the
contribution of one of many managers to a big portfolio,
the Sharpe measure or the Jensen measure?
B. Return Computations 40 points

single security A stock had a price a
month ago of $50. Today the price is $45 and the stock has
paid a dividend of $10 during the month. What was the rate
of return over the month?

portfolio return A month ago, a portfolio
was invested 40% in a bond portfolio and 60% in an equity
portfolio. Over the month, the bonds increased in value by
1% and the equities decreased in value by 9%. What was the
return on the entire portfolio over the month?

unitization At the beginning of a quarter,
a portfolio was worth $300,000. Two months into the
quarter, the market was up and the fund had grown to
$360,000. At that time, there was a cash withdrawal of
$80,000, decreasing the fund to $280,000. In the final
month of the quarter, the market was down and the portfolio
value fell to $210,000. What was the unitized return over
the quarter?

aftertax return Which has a higher
aftertax return for an investor in the 30% tax bracket, a
Treasury Bond yielding 6% or an insured muni yielding 5%?
C. Meanvariance Optimization 30 points

mean return 
beta 
idiosyncratic
std deviation 
total
std deviation 
1year TBill 
5% 
0.00 
0.00 
0.00 
index fund 
10% 
1.00 
0.00 
0.30 
BioTec stock 
12% 
1.40 
0.40 
0.58 
Before learning about BioTec stock, our optimal portfolio
had 75% in the index fund and 25% in TBills.

What are the portfolio weights for a position in BioTec
with the market risk removed?

What is our new optimal portfolio?

If Biotec had a beta greater than 1.4 (but the same mean and
idiosyncratic variance), how would the holding change and
why? (Computation is optional on this part.)
D. True and False 10 points

Means computed using the CAPM tell us how much our portfolio should
differ from holding the market portfolio.

The main benefit of diversification is a decrease in
volatility of returns below that of the typical stock in
the portfolio.

Most professional managers outperform their benchmarks.

To first approximation, the optimal response to transaction
costs is to trade less to avoid the costs.

Portfolio insurance is designed to be an optimal way to
beat the market.
Some useful formulas
Jensen's alpha for a portfolio P:
mean(r r )  beta mean(r r )
P f P M f
Sharpe measure for a portfolio P:
mean(r r )/std(r )
P f P
BlackScholes call option pricing formula:
SN(x )  BN(x ),
1 2
where
2 2
x = log(S/B)/sqrt(s T) + sqrt(s T)/2
1
and
2 2
x = log(S/B)/sqrt(s T)  sqrt(s T)/2.
2
Binomial option pricing:
Value = p V + p V
u u d d
where
p = (rd)/(r(ud))
u
and
p = (ur)/(r(ud))
d
Binomial replicating portfolio:
stock = (V  V )/(ud)
u d
and
bond = (uV  dV )/(ud)
d u