EC 362

Fall 1998

Prof. Baum

Problem Set 3 : Answer Key

1. Problem 2.4

1. Are the calls with a strike of 35 in/out of the money? S = 37 3/8 exceeds K = 35, the calls are in the money.
2. Are the 35 puts in/out of the money? Since S > K, the puts are out of the money.
3. What is the intrinsic value of Feb 40 calls? What is their time value? C = 15/16, S = 37 3/8, K = 40. Intrinsic value zero, time value 15/16.
4. What is the intrinsic value of Apr 40 puts? What is their time value? P = 4 1/8, S and K as above; intrinsic value 2 5/8, time value 1 1/2.
5. Buy one Apr 45 call. Polaroid closes at $44.25. What would be P/L, and rate of return? C = 13/16. If S = 44 1/4, C is worth zero; your loss is 13/16 ($81.25), 100% loss of your investment.
6. Write one Apr 35 naked put. Polaroid closes at the same price it did on Jan 11. What would be P/L? When would the owner of the put exercise? P = 1 1/2. If S is 37 3/8 at expiration, this put expires worthless, and you make the premium ($150.00). The put will only be exercised at S < 35.

2. Problem 3.1

You buy a 60 call for 2 5/8. What is the maximum loss? Maximum profit? At what expiration day stock price will you break even? Maximum loss is the premium, no maximum to the potential profit. The profit is S(T)-60 at expiration, when C(T) = max[0,S(T)-K]. For breakeven, C(T) must equal the original premium of 2 5/8, so 62 5/8 is the breakeven stock price.

3. Problem 3.2

You write a naked 40 call, with premium 4 3/4. What is the maximum loss? What is the maximum profit? At what expiration day stock price will you break even? Maximum loss is unbounded; maximum profit is the call premium if the call is out-of-the-money and unexercised. At expiration, the writer breaks even if C(T) = S(T)-K = call premium, so that 44 3/4 is the breakeven stock price.

4. Problem 3.3

Prepare the profit table for buying FedExp Oct 65 put. What is the breakeven expiration day stock price? Premium of 3 5/8, which is the initial cash outflow.

The breakeven stock price is 65 - 3 5/8 = 61 3/8.

5. Problem 3.5

Buy 100 shares of IBM at 159 3/8, sell one July 160 call at 6 3/8, buy one July 145 put for 3/4. Net CF(0) = -154 3/4 per share.

6. Problem 5.5

Suppose S = 40 and r = 10 percent. The stock pays no dividends. An European call with K = 40, T = 6 months sells for 7. An European put with the same K, T sells for 4. What riskless rate of return can you earn by writing the call, buying the put, and buying the stock?

Your cash outflow at time 0 is $37 per share.

If the stock at expiration is below 40, you exercise the put and earn $40 per share.

If the stock at expiration is at or above 40, the call will be exercised, and you earn $40 per share. In all cases you end up with $40, for an initial investment of $37.

This is an 8.108 % return over this 6 month period, less the 5 per cent cost of borrowed funds for six months, so the resulting 3.108 % return can be earned without risk.

7. Problem 6.1

A stock sells for $35 per share. One year from today it will sell for either $36 or $38 per share. The riskless interest rate is 10 percent. How can an arbitrage profit be earned?

The 'd' rate of growth is 2.86%; the 'u' rate of growth is 5.55%. Both are dominated by the 10% rate of return available in Treasury bills. Sell the stock short, receiving $35, and invest in Tbills. They will return $38.50 in a year's time, and covering the short will cost either $36 (for a profit of $2.50 per share) or $38 (for a profit of $0.50 per share).