Final Exam Answers
FIN 532 Investments Mini
Philip H. Dybvig
Washington University in Saint Louis
October 23, 2000
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.
plan sponsor and fund manager (other answers are possible)

What is probably a better investment of funds you will need
within a month, a Treasury Bill or a corporate bond, and
why?
A Treasury Bill is better because it is more liquid. (The Treasury
Bill is also less risky, but whether that makes it better depends on
your risk preferences.)

Describe one stock return anomaly.
The Weekend Effect: on average, stock prices fall over the weekend.
(Many other answers are possible.)

What are Treasury STRIPs?
A Treasury STRIP is a claim to interest or principal at a single date
that has been ``stripped'' out of a Treasury Bond or Note.

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?
The Jensen measure is more appropriate, because, unlike the Sharpe
measure, it does not penalize the manager for idiosyncratic volatility
that is irrelevant for the performance of the whole portfolio.
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?
45 + 10
  1 = 1.1  1 = 10%
50

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?
40% x 1% + 60% x (9%) = .4%  5.4% = 5%

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?
360,000 210,000
 x   1 = 1.2 x .75  1 = .9  1 = 10%
300,000 280,000

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%?
6% (1  30%) = 4.2% < 5%
^ ^
 
TBond Muni
The muni is better.
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?
long 100% BioTec + short 140% index fund + long 140% TBill
  
^ ^ ^
  
base position to remove the investing proceeds
in BioTec market risk from the short

What is our new optimal portfolio?
for the synthetic position described above:
mean XS return = 100% (12%  5%)  140% (10%  5%) + 140% (5%  5%)
= 0%
standard deviation = 40% (only BioTec's idiosyncratic risk remains)
Zero excess return and positive volatility implies we do not buy any
and instead we keep the original holding of 75% index fund and 25% TBills.

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.)
If Biotec had a larger beta, then its mean return would be insufficient
to compensate us for its market risk, and we would sell it short, buying
an additional amount of the index fund to restore the market risk and
buying a little less of the TBill to balance our budget.
D. True and False 10 points

Means computed using the CAPM tell us how much our portfolio should
differ from holding the market portfolio.
False. (If means are described by the CAPM, we hold the market portfolio
itself.)

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

Most professional managers outperform their benchmarks.
False.

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

Portfolio insurance is designed to be an optimal way to
beat the market.
False. (Changing position in a portfolioinsurance strategy reflect a
desire to shape the distribution of returns, not an attempt to time the
market.)