# Final Exam FIN 529 Investments Mini

Philip H. Dybvig
Washington University in Saint Louis
February 27, 1997

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 three types of investment. (For example, Treasury Bond would be one type.)

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2. What would be choice variables in a typical simple portfolio problem?

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3. What is the main trade-off in the CAPM?

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4. What is ERISA?

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5. Name a common performance benchmark.

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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 \$2 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 equities and 60% in bonds. Over the month, the bonds returned 1% and the equities returned 10%. What was the portfolio return 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 \$315,000. At that time, there was a cash infusion of \$185,000, increasing the fund to \$500,000. In the final month of the quarter, the market was down and the portfolio value fell to \$495,000. What was the unitized return over the quarter?

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4. after-tax return What is the break-even tax rate for a comparison between an untaxed municipal bond yielding 6% and a taxable Treasury bond yielding 8%?

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C. Portfolio Insurance Computation 30 points

A Simple Example in One Period

Riskless bond (interest rate is 50%):

```100 --- 150
```

Stock (underlying portfolio):

```    |- 125
50 -|
|-  50
```

Insured portfolio and put (floor = 95, insurance paid for separately):

```    |-  125              |- 0
? -|                 ? -|
|-  95               |- 45
```
1. What is the cost of the insurance (the put)?

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2. What portfolio of the stock and the bond replicates the put? (I suggest that you verify your answer by making sure the replication works whether the stock goes up or down.)

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3. What are the holdings in stocks and bonds of the insured portfolio including both the underlying portfolio and the put?

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D. True and False 10 points

1. Using historical mean returns for individual stocks is the most reliable method for obtaining mean returns to be used in mean-variance analysis.

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2. The main benefit of diversification is an increase in average expected return above that of the typical stock in the portfolio.

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3. According to the CAPM, investors are rewarded for taking on market level risk but not for taking on idiosyncratic (security-specific) risk.

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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. In the paper ``Why Should Older People Invest Less in Stocks than Younger People?'' (by Jagannathan and Kocherlakota), it is argued that the sensible answer to the question in the title is that over a long horizon, substantial amounts of risk can be eliminated.

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## Some useful formulas

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
```      r-d
p  = ------
u   r(u-d)
```

and
```      u-r
p  = ------.
d   r(u-d)
```

Binomial replicating portfolio:

```        V  - V
u    d
stock = -------
u-d
```

and
```        uV  - dV
d     u
bond =  ---------
r(u-d)
```