Ian Webster manages a $200 million equity portfolio benchmarked to the S&P 500 index. Webster believes the market is overvalued when measured by several traditional fundamental/economic indicators. He is concerned about potential losses but recognizes that the S&P 500 index could nevertheless move above its current 1136 level. Webster is considering the following option collar strategy:

Protection for the portfolio can be attained by purchasing an S&P 500 index put with a strike price of 1130 (just out of the money).

The put can be financed by selling two 1150 calls (farther out-of-the-money) for every put purchased.

Because the combined delta of the two calls (see following table) is less than 1 (that is, 2 * .36 = .72), the options will not lose more than the underlying portfolio will gain if the market advances.

The information in the following table describes the two options used to create the collar.

characteristics 1150 call 1130 put

option price 8,6$ 16,1$

option implied volatility 22% 24%

option's delta 0,36 -0,44

contracts needed for collar 602 301

notes:

ingnore transaction costs

S&P 500 historical 30-day volatility = 23%

Time to option expiration = 30 days

a. Describe the potential returns of the combined portfolio (the underlying portfolio plus the option collar) if after 30 days the S&P 500 index has:

i. risen approximately 5% to 1193.

ii. remained at 1136 (no change).

iii. declined by approximately 5% to 1080.

(No calculations are necessary.)

b. Discuss the effect on the hedge ratio (delta) of each option as the S&P 500 approaches the

level for each of the potential outcomes listed in part (a).

c. Evaluate the pricing of each of the following in relation to the volatility data provided:

i. the put

ii. the call