Question

Ken 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 therefore concerned about potential losses but recognizes that the S&P 500 Index could nevertheless move above its current 883 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 880 (just out of the money).
• The put can be financed by selling two 900 calls (further out-of-the-money) for every put purchased.
• Because the combined delta of the two calls (see the following table) is less than 1 (that is, 2 x .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.

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 927.

ii. Remained at 883 (no change).

iii. Declined by approximately 5% to 841.

(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

Short answer

a. (i) gain of $29 per index unit (ii) Loss of $1505 (iii) Put option will be exercised

b. (i) put delta will approach zero (ii) Delta of each will approach zero and the options will not be exercised (iii) call is out of the money

c. Call – 20,00%; Put – 22.00%

Step-by-step solution

Calculation of potential returns ‘a’ (i)

Each short call will payout $54 less the short option price of $27.20

Each put will lose the option price of $32.20

The gain for each strategy = $1854 - $1766 = $88

Therefore the gain = $88 -$59 = $29 per index unit

Calculation of potential returns ‘a’ (ii)

Since the option price from 1 short call was less $27.20

Versus

a cost of $32.20 on long put,

Therefore, there is a loss on the strategy of $5 x 301 = $1505

Calculation of potential returns ‘a’ (iii)

The put option will be exercised and the proceeds will be used to offset the purchase price and decline in portfolio value.

Explanation on the effect on hedge ratio ‘b’

i. The put delta will approach zero. While expiration of the call approaches and exercise becomes certain, the delta of the call will approach 1.0

ii. As expiration approaches, delta of each will approach zero and the options will not be exercised. Hence both options expire out of the money.

iii. As expiration approaches, the call gets out of the money. Delta approaches zero. On the other hand, he delta of the put approaches 1.0 as exercise happens.

Evaluation of pricing of put and call ‘c’

The call sells at an implied volatility (20.00%).

The put sells at an implied volatility (22.00%)

The call seems cheaper than the put.