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.)

  1. Name two types of professionals on the buy side.

    plan sponsor and fund manager (other answers are possible)

  2. 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.)

  3. Describe one stock return anomaly.

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

  4. 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.

  5. 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
  1. 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%
  2. 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%
  3. 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
  4. 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%?
         6% (1 - 30%) = 4.2% < 5%
                         ^     ^
                         |     |
                     T-Bond   Muni
    The muni is better.
C. Mean-variance Optimization 30 points

mean return beta idiosyncratic
std deviation
std deviation
1-year T-Bill 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 T-Bills.

  1. What are the portfolio weights for a position in BioTec with the market risk removed?
         long 100% BioTec + short 140% index fund + long 140% T-Bill
         ----------------   ---------------------   ----------------
                ^                     ^                    ^
                |                     |                    |
           base position        to remove the      investing proceeds
             in BioTec           market risk         from the short
  2. 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% T-Bills.

  3. 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 T-Bill to balance our budget.
D. True and False 10 points
  1. 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.)

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


  3. Most professional managers outperform their benchmarks.


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


  5. Portfolio insurance is designed to be an optimal way to beat the market.

    False. (Changing position in a portfolio-insurance strategy reflect a desire to shape the distribution of returns, not an attempt to time the market.)