Strayer FIn550 problems

PROBLEM 8: Mutual funds van 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 sakes fee arrangements: (1) a 3 percent 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[CT1] [CT2] you choose?

(b) 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?

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(c) Explain the relationship between the timing of the sales charges and your investment horizon, I you hold you position in a long time, which fee arrangement you prefer?

Problem 24-3Consider the recent performance of the Closed Fund, a closed-end fund devoted to finding 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?

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% per year. The current risk-free rate is 9% and the stock pays two dividends: (1) a 2% dividend just prior to the option’s expiration day, which is 91 days from now (i.e., exactly one half year). Calculate the black-Scholes value for European-style call option with an exercise price of $70.
b- What would be the price of a 91-day European-style 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%, and (2) the risk free rate decreases to 8%.

7- Suppose the current value of a popular stock index is 653.50 and the dividend yield on the index is 2.8%. Also, the yield curve is flat at a continuously compounded rate of 5.5%.

a. If you estimate the volatility factor for the index to be 16%, 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 profitfrom 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 internet 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 alternative option strategy. Clearly label on the graph the breakeven points of the position.