14.14 Covered call writing:
Current market price of the stock $61.50
Current market price of the call $5.75
Initial investment: $61.50 500 $30,750
a. If the stock price rises to $65 per share, the call options expire worthless:
Value of the call $0
Profit:
Holding period return (for three months):
=
= =
Total profit
HPR Initial investment
$5,025 16.34%
$30,750
b. For any price above $65, the loss on the call option will be exactly offset by the additional
c. The covered call position offers limited protection against a drop in stock price. The capital
14.15 Rick can either short RHL or use put options on RHLIf he is correct and the retail sector
14.16 a. LONG STRADDLE
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b. SHORT STRADDLE (you are the writer)
If the market falls by 750 points:
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Chapter 14 Options: Puts and Calls 274
c. Option straddles are extremely risky investment strategies; hence, an investor using this
strategy must completely understand the risk involved. For larger movements in the market,
14.17 The value of a call option using the Black-Scholes option-pricing model:
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14.18 The value of a call option using the Black-Scholes option-pricing model:
Solutions to Case Problems
Case 14.1 TheFranciscos’ Investment Options
This case is designed to show the student that more than one vehicle is sometimes available to investors
a. If Hector wants to invest in RPP for six months, he could use any of the vehicles mentioned: purchase
b. 1. Value of the first call ($50 exercise price):
Value of second call ($70 exercise price):
*Dividends will be received for only six months, or two quarters.
($3,000 * $800)
HPR (call with $50 exercise price) 275%
$800
($2,000 * $500)
HPR (call with $60 exercise price) 300%
$500
–
= =
–
= =
*Calculated in 2b.above.
Chapter 14 Options: Puts and Calls 276
c. Let’s examine this question on profitability in two different ways to show the benefits of leverage
with options. First, consider 100-share investments using each of the four vehicles and assuming
Hector is correct about the price appreciation, and the other figures in question 2 are correct.
Investment Vehicles
Per Share Common Stock $50 Call $60 Call
Dollar profits are highest for the common stock. However, recall that HPR is highest for the $60
call and that it requires the smallest investment. Now let us assume we put the same amount into
each investment, $5,750 (assuming we can purchase fractional options for illustration only).
Investments
Totals Common Stock $50 Call $60 Call
Investment $5,750 $5,750 $5,750
Dividends 120 0 0
Value in six months 8,000 21,563 23,000
Capital gain 2,250 15,813 17,250
Total profits $ 2,370 $15,813 $17,250
With equal dollar investment, the $60 call options would have the largest profit (in both dollar and
Thus, given risk-return considerations, we may want to consider another course of action. This
leads us back to the first illustration. In effect, we could consider the leverage attributes of calls
Unless current income and preservation of capitalare key investment objectives, which can be
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Case 14.2 Luke’s Quandary: To Hedge or Not to Hedge
This case illustrates a basic option strategy, hedging. Students review the hedging process and then analyze
the costs and benefits of a specific hedging situation.
a. Luke has an unrealized capital gain of 300 ($75 $40) $10,500, and he naturally wants to
protect the gain. One way to do this is to sell the stock and realize the actual gain. To do so in these
circumstances would mean Luke would have to pay taxes in the current year. He would benefit, for
b. If Luke purchases the three puts, the minimum before-tax profit he can realize is:
*Note:Because the put is an out-of-the-money option, its purchase price is made up exclusively of
investment premium and as such is a sunk cost.
c. If Luke purchases threeoptions and the stock price goes to $100, the market value of his investments
at the expiration date of the option would be:
*Note: The puts will be worthless upon expiration; Luke will lose the cost of the puts.
If the stock falls to $50, Luke will lose money on the stocks (from their current price of $75) but
make money on the puts:
Stock:
Puts:
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Chapter 14 Options: Puts and Calls 278
*Note: The instructor might want to emphasize that this is the same total profit we came up with in
part 2 (above). It is the minimum profit the investor will make regardless of how far the price of the
d. Because Luke is uncertain about the market, he should seriously consider the use of puts to hedge
the profit he has already made on his investment. If he is wrong and the stock price continues to go
up, there is really no limit to the amount of profit he can make. On the other hand, if the stock price
Answer to Chapter-Opening Problem
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