Question

1. Richards Inc. stock currently trades for $40, but you believe the company's earnings will decrease dramatically in the next six months which in turn will cause the company's stock to depreciate. Six-month European call options on the stock have an exercise price of $45 and a premium of .75. The annual risk free rate is 3%. You want to create a portfolio that mimics the payoff of owning a 6-month European put on on the stock. Which of the following steps must you do in order to achieve this payoff?

a. Buy the call option, sell the stock, and borrow the present value of $4500 discounted at the risk-free rate.

b. Sell the call option, buy the stock, and invest the present value $4500 discounted at the risk-free rate.

c. Buy the call option, sell the stock, and invest the present value of $4500 discounted at the risk-free rate.

d. Sell the call option, sell the stock, and invest the present value $4500 discounted at the risk-free rate.

2. What should be the price of a six-month European put option with an exercise price of $45 according to put-call parity? Round intermediate steps to four decimals and your final answer to two decimals. Do not use currency symbols or words when entering your response.

$5.08

3. Find your portfolio's profit/loss if Richards stock sells for $32 at the end of six-months. Round intermediate steps to four decimals.

a. 508

b. 792

c. -792

d. -508

e. 658

4. DEF stock currently trades at $112.

	Call Premiums		Put Premiums
Strike	Jan.	Feb.	Jan.	Feb.
105	7.50	7.75	.50	.60
110	6.25	6.50	.65	.75
115	1.15	1.20	3.25	3.62
120	.75	.95	8.10	8.85

What is the time value of the 120 Feb. put option?

a. 0

b. 0.85

c. 0.62

d. none of the above.

I've bolded the answers I believe are right after doing the work. I would just like to double check my work and if I'm wrong please provide an explanation. Thanks!

Answer 1

Your answers to Q - 1, 2 & 3 are correct. Your answer to Q - 4 is wrong. Please rectify it as per solution below.

Q - 1

Use Call Put Parity equation:

P = C - S + PV (K)

Buy a put = Buy a call, Short the stock and invest the PV(K)

Hence, your choice of option c. Buy the call option, sell the stock, and invest the present value of $4500 discounted at the risk-free rate is perfectly correct.

Q - 2

P = C - S + PV (K) = 0.75 - 40 + 45 / (1 + 3%)^0.5 = $ 5.09

Your answer is correct, just rounding off differences.

Q - 3

Payoff from one put option = max (K - S, 0) - P = max (45 - 32, 0) - 5.09 = 13 - 5.09 = 7.91

Hence, payoff from the portfolio containing 100 put option = 7.91 x 100 = 791

Hence, your answer is correct here as well.

Q - 4

Price of Feb 120 put option = Intrinsic value + time value

Hence, 8.85 = K - S + time value = 120 - 112 + time value = 8 + time value

Hence, time value = 8.85 - 8 = 0.85

Hence, the correct answer is option b. Your are wrong here.