# Question

Ken Webster manages a $ 100 million equity portfolio benchmarked to the S& P 500 index. Over the past two years, the S& P 500 Index has appreciated 60 percent. Webster believes the market is overvalued when measured by several traditional fundamental/ economic indicators. He is concerned about maintaining the excellent gains the portfolio has experienced in the past two years but recognizes that the S& P 500 Index could still move above its current 668 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 665 (just out of the money).

• The put can be financed by selling two 675 calls (further out of the money) for every put purchased.

• Because the combined delta of the two calls is less than 1 ( i. e., 2 3 .36 5 .72), the options will not lose more than the underlying portfolio will gain if the market advances.

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 percent to 701.00

ii. Remained at 668 (no change)

iii. Declined by approximately 5 percent to 635.00 (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

• Protection for the portfolio can be attained by purchasing an S& P 500 Index put with a strike price of 665 (just out of the money).

• The put can be financed by selling two 675 calls (further out of the money) for every put purchased.

• Because the combined delta of the two calls is less than 1 ( i. e., 2 3 .36 5 .72), the options will not lose more than the underlying portfolio will gain if the market advances.

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 percent to 701.00

ii. Remained at 668 (no change)

iii. Declined by approximately 5 percent to 635.00 (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

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