FIN 532 Investments Mini
Philip H. Dybvig
Washington University in Saint Louis
October 23, 2000
This is a closed-book 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
B. Return Computations 40 points
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
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?
C. Mean-variance Optimization 30 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
after-tax return Which has a higher
after-tax return for an investor in the 30% tax bracket, a
Treasury Bond yielding 6% or an insured muni yielding 5%?
Before learning about BioTec stock, our optimal portfolio
had 75% in the index fund and 25% in T-Bills.
D. True and False 10 points
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.)
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
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
Black-Scholes call option pricing formula:
SN(x ) - BN(x ),
x = log(S/B)/sqrt(s T) + sqrt(s T)/2
x = log(S/B)/sqrt(s T) - sqrt(s T)/2.
Binomial option pricing:
Value = p V + p V
u u d d
p = (r-d)/(r(u-d))
p = (u-r)/(r(u-d))
Binomial replicating portfolio:
stock = (V - V )/(u-d)
bond = (uV - dV )/(u-d)