Ken Webster manages a $400 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 therefore concerned about potential losses but recognizes that the S&P 500 Index could nevertheless move above its current 1,766 level.

Webster is considering the following option collar strategy:

• Protection for the portfolio can be attained by purchasing S&P 500 Index puts with a strike price of 1,760 (just out of the money).

• The put can be partially financed by selling an equal number of call options with strike price 1,800 (further out-of-the-money) for every put purchased.

• Because the combined delta of the call and put positions (see the following table) is greater than -1, (that is, -.44 -.30 = -.74), 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.

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 1,854.
ii. Remained at 1,766 (no change).
iii. Declined by approximately 5% to 1,682.
(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. Evaluate the pricing of each of the following in relation to the volatility data provided:
i. The put
ii. The call

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Characteristics 1,800 Call 1,760 Put S32.20 Option price $27.20 Option implied volatility 20% 22% Option's delta 0.30 -0.44 Notes: Ignore transaction costs. S&P 500 historical 30-day volatility = 21%. Time to option ex piration = 30 days.