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?
(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?
24-3Consider the recent performance of the Closed Fund, a closed-end fund
devoted to finding undervalued, thinly traded stocks:
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
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
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
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
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
Put option with an exercise price of $100 expiring in one
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
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.