Question

The current price of a stock is $72. Three-month call options with a strike price of $75 currently sell for $10. An investor with $9,000 to invest is considering the following three investment strategies:

1. (a) Investing all his money in the stock

2. (b) Doubling the amount to invest by taking a loan of $9,000 at an interest rate of 2% for three months, investing the resulting $18,000 in the stock and then repaying $9,180 on the loan

3. (c) Investing all his money in the call options

Determine the return of the investor (defined as change in wealth / initial wealth) under each of the three strategies for the following two scenarios: 1) stock price falls to $60 after three months, 2) stock price rises to $90 after three months. Compare the risks and returns of the three strategies.

Answer 1

a]

change in wealth = change in stock price * number of shares bought

number of shares bought = $9,000 / $72 = 125

b]

change in wealth = (change in stock price * number of shares bought) - interest on loan

number of shares bought = $18,000 / $72 = 250

interest on loan = $9,180 - $9,000 = $180

c]

If the stock price falls to $60, the call options expire worthless as the stock price is lower than the strike price. The entire premium of $10 per option is lost.

Loss = premium paid = $9,000

If the stock price rises to $90, profit = (stock price - strike price - premium paid) = ($90 - $75 - $10) = $5

total profit = profit per option * number of options bought

total profit = $5 * ($9,000 / $10) = $4,500

1 2 за 4 ь 5 с в с Return to investor $60 | $90 | -16.67% 25.00% -35.33% 48.00% -100.00% 50.00%

Return to investor 60 =(125*(B2-72))/9000 =(125*(C2-72))/9000 =(250*(B2-72)-180)/9000 = (250*(C2-72)-180)/9000 =-9000/9000 -4500/9000

With strategy (a), the potential loss and potential profit are moderate as the investor is investing in the cash market.

With strategy (b), the losses and profits are magnified, as the investor uses leverage. Hence, the profits and losses are higher than strategy (a).

With strategy (c), the leverage is even higher than strategy (c) as call options are used. Hence, the profits and losses are higher than strategy (b).