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 investors 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?

15:42

(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 Funds 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

options 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 options value

that would occur if ARBs management suddenly decided to suspend dividend

payments and this action had no effect on the price of the companys 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 options 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 stocks 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. Melissas colleague proposes another lower-cost option

strategy that would profit from a large fluctuation in friendworks 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.