Fin 550 Week 10 Homework.

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•Chapter 22: Problems 3(a-d), 5(a-d), 7(a-c), 10(a-b), and 12

3. Assuming that a one- year call option with an exercise price of $ 38 is available for the stock of the DEW Corp., consider the following price tree for DEW stock over the next year:

Now S1 S2 One Year

42

40

38.40

a. If the sequence of stock prices that DEW stock follows over the year is $ 40.00, $ 42.00, $ 40.32, and $ 38.71, describe the composition of the initial riskless portfolio of stock and options you would form and all the subsequent adjustments you would have to make to keep this portfolio riskless. Assume the one- year risk- free rate is 6 percent.

b. Given the initial DEW price of $ 40, what are the probabilities of observing each of the four terminal stock prices in one year? ( Hint: In arriving at your answer, it will be useful to consider ( 1) the number of different ways that a particular terminal price could be achieved and ( 2) the probability of an up or down movement.)

b. Given the initial DEW price of $ 40, what are the probabilities of observing each of the four terminal stock prices in one year? ( Hint: In arriving at your answer, it will be useful to consider ( 1) the number of different ways that a particular terminal price could be achieved and ( 2) the probability of an up or down movement.)

5. Consider the following questions on the pricing of options on the stock of ARB Inc.: a. A share of ARB stock sells for $ 75 and has a standard deviation of returns equal to 20 percent per year. The current risk- free rate is 9 percent and the stock pays two divi-dends: ( 1) a $ 2 dividend just prior to the option’s expiration day, which is 91 days from now ( i. e., exactly one- quarter of a year), and ( 2) a $ 2 dividend 182 days from now ( i. e., exactly one- half year). Calculate the Black- Scholes value for a European- style call option with an exercise price of $ 70. b. What would be the price of a 91- day European- style put option on ARB stock having the same exercise price? c. Calculate the change in the call option’s value that would occur if ARB’s management suddenly decided to suspend dividend payments and this action had no effect on the price of the company’s stock. d. Briefly describe ( without calculations) how your answer in Part a would differ under the following separate circumstances: ( 1) the volatility of ARB stock increases to 30 percent, and ( 2) the risk- free rate decreases to 8 percent.

7. Suppose the current value of a popular stock index is 653.50 and the dividend yield on the index is 2.8 percent. Also, the yield curve is flat at a continuously compounded rate of 5.5 percent. a. If you estimate the volatility factor for the index to be 16 percent, calculate the value of an index call option with an exercise price of 670 and an expiration date in exactly three months. b. If the actual market price of this option is $ 17.40, calculate its implied volatility coefficient. c. Besides volatility estimation error, explain why your valuation and the option’s traded price might differ from one another.

10. Melissa Simmons is the chief investment officer of a hedge fund specializing in options trading. She is currently back- testing various option trading strategies that will allow her to profit from large fluctuations— either up or down— in a stock’s price. An example of such typical trading strategy is straddle strategy that involves the combination of a long call and a long put with an identical strike price and time to maturity. She is considering the following pricing information on securities associated with Friendwork, a new Inter-net start- up hosting a leading online social network: Friendwork stock: $ 100 Call option with an exercise price of $ 100 expiring in one year: $ 9 Put option with an exercise price of $ 100 expiring in one year: $ 8

a. Use the above information on Friendwork and draw a diagram showing the net profit/ loss position at maturity for the straddle strategy. Clearly label on the graph the break-even points of the position. b. Melissa’s colleague proposes another lower- cost option strategy that would profit from a large fluctuation in Friendwork’s stock price: Long call option with an exercise price of $ 110 expiring in one year: $ 6 Long put option with an exercise price of $ 90 expiring in one year: $ 5 Similar to Part a, draw a diagram showing the net profit/ loss position for the above alter-native option strategy. Clearly label on the graph the breakeven points of the position.

12. In developing the butterfly spread position, we showed that it could be broken down into two call option money spreads. Using the price data for SAS stock options from Exhibit 22.17, demonstrate how a butterfly profit structure similar to that shown in Exhibit 22.30 could be created using put options. Be specific as to the contract positions involved in the trade and show the expiration date net payoffs for the combined transaction.

**•Chapter 24: Problems 3(a-d), 6(a-c), 8(a-c), and 10(a-c)**

**3. Consider the recent performance of the Closed Fund, a closed- end fund devoted to find-ing undervalued, thinly traded stocks:**

**Period NAV Premium/ Discount**

0 $10.00 0.0%

1 11.25 -5.0

2 9.85 +2.3

3 10.50 -3.2

4 12.30 -7.0

Here, price premiums and discounts are indicated by pluses and minuses, respectively, and Period 0 represents Closed Fund’s initiation date. a. Calculate the average return per period for an investor who bought 100 shares of the Closed Fund at the initiation and then sold her position at the end of Period 4. b. What was the average periodic growth rate in NAV over that same period? c. Calculate the periodic return for another investor who bought 100 shares of Closed Fund at the end of Period 1 and sold his position at the end of Period 2. d. What was the periodic growth rate in NAV between Periods 1 and 2?

6. Suppose that at the start of the year, a no- load mutual fund has a net asset value of $ 27.15 per share. During the year, it pays its shareholders a capital gain and dividend dis-tribution of $ 1.12 per share and finishes the year with an NAV of $ 30.34.

a. What is the return to an investor who holds 257.876 shares of this fund in his ( non-taxable) retirement account?

b. What is the after- tax return for the same investor if these shares were held in an ordi-nary savings account? Assume that the investor is in the 30 percent tax bracket.

c. If the investment company allowed the investor to automatically reinvest his cash dis-tribution in additional fund shares, how many additional shares could the investor ac-quire? Assume that the distribution occurred at year end and that the proceeds from the distribution can be reinvested at the year- end NAV.

**8. Mutual funds can effectively** charge sales fees in one of three ways: front- end load fees, 12b- 1 ( i. e., annual) fees, or deferred ( i. e., back- end) load fees. Assume that the SAS Fund offers its investors the choice of the following sales fee arrangements: ( 1) a 3 per-cent front- end load, ( 2) a 0.50 percent annual deduction, or ( 3) a 2 percent back- end load, paid at the liquidation of the investor’s position. Also, assume that SAS Fund averages NAV growth of 12 percent per year.

a. If you start with $ 100,000 in investment capital, calculate what an investment in SAS would be worth in three years under each of the proposed sales fee schemes. Which scheme would you choose?

b. If your investment horizon were 10 years, would your answer in Part a change? Demonstrate.

c. Explain the relationship between the timing of the sales charge and your investment horizon. In general, if you intend to hold your position for a long time, which fee arrangement would you prefer?

10. Peter and Andrea Mueller have built up their $ 600,000 investment portfolio over many years through regular purchases of mutual funds holding only U. S. securities. Each pur-chase was based on personal research but without consideration of their other holdings. They would now like advice on their

Type Market Sector Beta Percent of Total

Andrea’s company stock Stock Small- cap growth 1.40 35

Blue- chip growth fund Stock Large- cap growth 1.20 20

Super- beta fund Stock Small- cap growth 1.60 10

Conservative fund Stock Large- cap value 1.05 2

Index fund Stock Large- cap index 1.00 3

No- dividend fund Stock Large- cap growth 1.25 25

Long- term zero-coupon fund Bond Government — 5

Evaluate the Muellers’ portfolio in terms of the following criteria:

a. Preference for “ minimal volatility”

b. Equity diversification

c. Asset allocation ( including cash flow needs)

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