Question

Refers to the information below:

S&R index level today (t=0)	900
Forward price (T=3 months)	918
Annualized 3-month interest rate	8% p.a.
Call option Premium (Strike = 900)	62.57
Put option Premium (Strike = 900)	44.92
Dividend Yield	0%
S&R index level 3 months later	930

(i) What is your profit 3 months later if you have taken a long position on the stock at t=0?

(ii) What is your profit 3 months later if you have taken a short position on the stock at t=0?

(iii) What is your payoff 3 months later if you have taken a long position on the forward at t=0?

(iv) What is your profit 3 months later if you have taken a short position on the forward at t=0?

(v) What is your payoff 3 months later if you have taken a long position on the call option at t=0?

(vi) What is your profit 3 months later if you have taken a long position on the call option at t=0?

(vii) What is your maximum profit 3 months later if you have taken a long position on the call option at t=0?

(viii) What is your maximum loss 3 months later if you have taken a long position on the call option at t=0?

Answer 1

i) If a person is long on a stock, he will make profit only if the stock goes above the price at which he has taken a long position. In he given case, he was long at 930. Assuming he has hold the position till 3 months, the profit shall be 30 (930 close price - 900 cost)

ii) If a person is short on a stock, he will make profit only if the stock goes below the price at which he has taken a short position. In he given case, he was long at 930. Assuming he has hold the position till 3 months, the profit shall be -30 (900 cost - 930 closing)

iii & iv) Forward contract: A contract between two parties (buyer and seller) where the price and time shall be pre-determined. The counterparties has the obligation to fulfill the responsibilities.

Buyer of forward has a long position and seller of a forward has a short position.

If we are long position in a forward, we have agreed to buy the stock after 3 months at 918. We will make profit only if the stock goes above 918. The closing price of the stock was 930, but we have agreed to buy at 918 at the begining of contract. Profit shall be 930-918=12.

If you are short on this position we would make profit only if it closes below 918. Since the closing price was 930, the short position would end up with a loss of 12 (918-930).

Note: Forward is a zero sum game, which means loss to one party equals profit of the other in absence of any transaction costs.

v) Call Option: The holder of a call option has a right to exercise but not the obligation to purchase the underlying at a specified price after a specific time (say 3 months in this case) by paying a premium

In the given case, the holder of position pays a premium of 62.50 for a strike price of 900. Break-even point shall be strike price + Premium = 900+62.50= 962.50.

Since the index price 3 months later was 930. Call option value is worth 30 (930-900).

Profit = value of the option - Premium paid = 30-62.50 = -32.50

vi) Assuming the question is incorrect. It should be long on a put option

Put Option: The holder of a put option has a right to exercise but not the obligation to sell the underlying at a specified price after a specific time by paying a premium

In the given case, the holder of position pays a premium of 44.92 for a strike price of 600. Break-even point shall be strike price - Premium = 900-44.92=855.08.

Since the index price 3 months later was 930. The holder of a short position will lose the money that he has paid as premium.

Profit = 0 - 44.92 = 44.92

Since the index price 3 months later was 930. Call option value is worth 30 (930-900).

Profit = value of the option - Premium paid = 30-62.50 = -32.50

vii) The maximum profit for a long position in call option is unlimited because the upside potential for the stock is unlimited.It can go till infinity.

viii) The maximum loss for a long position in a call option is the premium paid because if the underlying goes below the strike price, the holder will not exercise the contract (holder has right but not obligation). So maximum loss shall be the premium paid i.e., in the given case it shall be 62.50.

Note: For all the questions above buyer is said to have long position and seller is said to hold short position.