Question

For an index, the $930 strike 6 months call premium is $45.34 and the $950 strike 6 months call is selling for $28.78. What is the maximum profit that an investor can obtain from a strategy employing a bull spread at strike prices 930 and 950 with these two call options over 6 months? Interest rates is 0.5% per month.

$2.44 B. $2.94 C. $37.06 D. $36.56

Answer 1

For a bull spread strategy, we would buy a call option at the lower strike price of $930 and sell a call option at the higher strike price of $950. As a result, we would pay a premium of $45.34 for buying the lower strike option and receive a premium of $28.78 for selling the higher strike option. Thus the net outgo of cash today would be $45.34 - $28.78 = $16.56.

Assuming that we financed the net cash outgo through borrowing at the specified interest rate of 0.5% per month, the net cash outgo at the maturity of these two options after 6 months would be $16.56 * (1+0.5%)^6 = $17.06.

If the spot value of the index at the maturity of the options is $950, then we would have made a profit of $20 on the call option exercised at the strike price of $930 (not adjusted for the premium paid). Also, there would be no outgo on the call option we sold since the strike price of the same is same as the market price on maturity date. Thus, adjusting for the above mentioned net cash outgo financed through borrowing at 0.5%/month interest rate, the net profit made would be $20 - $17.06 = $2.94.

We may explore the net profit at various market prices at maturity, but basis this bull spread strategy, the maximum profit that can be obtained is as calculated above i.e. $2.94 i.e. Option B.