Question

Assume that at t = 0 a stock has price S = $500 and that a call that matures at T with a strike price of X = $500 has

Assume at the option’s maturity, t = T, that S_T = $500.

Assume that at t = 0 that investor #1 buys 100 shares of stock and sells them at t = T.

Assume that at t = 0 investor #2 buys one call option on the same stock & exercises it at t = T.

When investor #2 breaks even at T, what is the ROI (return on investment) for investor #1?

		10%
		None of these numbers are correct
		0%
		5%
		2%

Answer 1

Stock price at time t = 0 i.e. today, S = $500

Strike price of stock, X = $500

Stock price at time t = T i.e. maturity, ST = $500

Investor 1 : bought 100 shares of stock at t = 0 at stock price S = $500.

Sale price of stock at t = T is $500

Total investment = 100 shares x $500 = $500,000

Net proceeds from sale = 100 shares x $500 = $500,000

Hence, investor 1 hasn't earned any return or suffered any loss on investment i.e. he just break even on his investment.

Investor 2 : bought 1 call option on the same stock at t = 0 at X = $500

Stock price at time t = T i.e. maturity, ST = $500

He exercised the option on maturity at prevailing price i.e. $500. A buyer of call option gains when Market price is greater than Strike Price. In the given case market price equals strike price at maturity hence, no return was earned by investor 2.

Hence, ROI of both the investors is 0%