Question

Horst Schmidt is considering buying ten call options on Swiss franc on the Philadelphia Stock Exchange at a strike price of 54 cents per pound.  The contract size is SF62, 500.  The option will expire in three months.  The premium is 2.0 cents per pound.  Ignore the brokerage cost.  The spot rate is currently $.5400/SF and the three-month forward rate is $.5525/SF. Horst Schmidt believes that the most likely range for the spot pound in three months will be a low of $.5000/SF to a high of $.6200/SF, but the most likely value will be $.5900/SF.

1. Diagram the profit and loss position as perceived by Horst Schmidt.
2. Calculate what he would gain or lose at his expected range of future spot prices and at his expected future spot price.
3. Calculate and show on the diagram the breakeven future spot price

Answer 1

Solution:

Given Details,

Underlying currency: Swiss Franc
Expiration date: 3 months
Contract size: SF62,500
Excercise Price: $0.54/SF
Number of contracts: 10
Premium price: 2 cents/SF or $0.02

Total premium paid = Premium * contract size * no. of positions = 0.02 * 62,500 * 10 = $12,500

(1) Profit-Loss Diagram:

It is long call exposure so maximum loss is limited and equal to total premium paid of $12,500 whereas maximum profit will be unlimited. Following is the diagram:

(2) Gain or lose at his expected range of future spot prices and at his expected future spot price:

a) $.5000/SF (Low range)

Total premium paid = Premium * contract size * no. of positions = 0.02 * 62,500 * 10 = $12,500 (outflow)
As spot price < excercise price, call option will not be excercised.

Net Profit/Loss = -12500 = -$12,500. (Loss)

b) $.6200/SF (High range)

Total premium paid = Premium * contract size * no. of positions = 0.02 * 62,500 * 10 = $12,500 (outflow)
Excercise cost = Excercise price * contract size * no. of positions = 0.54 * 62,500 * 10 = $337,500 (outflow)
Spot sale = Spot price at that time * contract size * no. of positions = 0.6200 * 62,500 * 10 = $387,500 (Inflow)

Net Profit/Loss = 387500-12500-337500 = $37,500. (Profit)

c) $.5900/SF (Expected price)

Total premium paid = Premium * contract size * no. of positions = 0.02 * 62,500 * 10 = $12,500 (outflow)
Excercise cost = Excercise price * contract size * no. of positions = 0.54 * 62,500 * 10 = $337,500 (outflow)
Spot sale = Spot price at that time * contract size * no. of positions = 0.5900 * 62,500 * 10 = $368,750 (Inflow)

Net Profit/Loss = 36870-12500-337500 = $18,750. (Profit)

(3) Breakeven point:

Break even is at point where net profit is zero. Suppose B is break even point.

So, total inflow should we equal to total outflow at spot price of B.

Total outflow = Total premium paid + Excercise cost = 0.02 * 62,500 * 10 + 0.54 * 62,500 * 10 = $12,500 + $337,500 = $350,000 ------- eq(1)

Total inflow = Breakeven spot price * contract size * no. of positions = B * 62,500 * 10 = 625000 * B -------eq(2)

Equating equation 1 and 2

625000 * B = 350000

So, B = 350000/625000 = $0.56

Breakeven future spot price = $0.56/SF

Diagram: