Question

Use the following stock and set of options to answer #1, # 2, and #3 below.

A stock, priced at $47.00, has 3-month call and put options with exercise prices of $45 and $50. The current market prices of these options are given by the following:

Exercise Price	Call	Put
45	$4.50	$2.20
50	$2.15	$4.80

1.   Assume that you feel that it is likely that the stock price will move up only very modestly over the next 3 months. (Use one option contract to scale your transactions.)

a) Which strategy do you recommend for this market forecast (using the above options), and what are the corresponding transactions for this strategy in the above options?

b) What is your maximum possible gain and loss, in dollars, if you hold this position to option expiration?

c) What is the breakeven terminal stock price, if you hold this position to option expiration?

d) What if you are correct, and the terminal stock price ends up at $51. What percentage return would you have earned, relative to your initial investment, on this strategy?

Answer 1

(a) As the investor is bullish on the stock, he should initiate a long position in the call option. As the expected upward movement is only modest, a long contract should be initiate for in-the-money call option. The investor will go long in $45 call option by paying a premium of $4.50

(b) Maximum possible gain in this naked call option strategy is unlimitied - As the stock price can rise to any level, the maximum possible gain is unlimited

Maximum possible loss is the premium paid which is $4.50 - this will happen if the stock price expires below $45 on expiry and the call expires worthless

(c) Break-even stock price = Exercise Price + Call Premium = $45 + $4.50 = $49.50

(d) If the stock price is $51 on expiry, the value of the call option will be $6 ($51-$45)

Percentage Return = ($6-$4.50)/$4.50) = 33.33%