Ken Webster manages an $800 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 3,532 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 3,520.

• The put can be approximately financed by selling one 3,600 strike-price call for every put purchased.

• Because the combined delta of the call and put positions (see following table) is greater than

−1 (i.e., −.44 − .30 = −.74), the options position will not lose more than the underlying stock portfolio will gain if the market advances.

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

Characteristics 3,600 Call 3,520 Put Option price $68.20 $64.40 Option implied volatility 22% 24%

Option’s delta 0.30 −0.44 Notes:

• Ignore 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 3,708.

ii. Remained at 3,532 (no change).

iii. Declined by approximately 5% to 3,364.

(No calculations are necessary.)

b. Discuss the effect on the hedge ratio (delta) of each option as the S&P 500 approaches the level of each of the potential outcomes listed in part (a).

c. How will the pricing of each of the following respond to an increase in stock volatility?
i. The put.
ii. The call. p-69