# Final Exam 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 length.)

1. Name two types of professionals on the buy side.
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2. What is probably a better investment of funds you will need within a month, a Treasury Bill or a corporate bond, and why?
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3. Describe one stock return anomaly.
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4. What are Treasury STRIPs?
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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?
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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?
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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?
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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?
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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%?
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C. Mean-variance Optimization 30 points

 mean return beta idiosyncratic std deviation total 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?
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2. What is our new optimal portfolio?
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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.)
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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.
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2. The main benefit of diversification is a decrease in volatility of returns below that of the typical stock in the portfolio.
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3. Most professional managers outperform their benchmarks.
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4. To first approximation, the optimal response to transaction costs is to trade less to avoid the costs.
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5. Portfolio insurance is designed to be an optimal way to beat the market.
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### 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 ),
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  = (r-d)/(r(u-d))
u
```
and
```p  = (u-r)/(r(u-d))
d
```
Binomial replicating portfolio:
```stock = (V  - V )/(u-d)
u    d
```
and
```bond = (uV  - dV )/(u-d)
d     u
```