Question

Assume it's March 27, 2018. Apple stock (AAPL) is selling for $168.98 per share. Using the option prices provided earlier in this lesson, provide analysis to answer the following four questions:

Calls	Last Sale	Open Interest	Puts	Last Sale	Open Interest
18 Apr 165.00	7.15	13376	18 Apr 165.00	3.10	23436
18 Apr 170.00	4.50	42666	18 Apr 170.00	5.20	44816
18 Apr 175.00	2.20	30085	18 Apr 175.00	7.75	24071
18 May 165.00	10.10	3032	18 May 165.00	6.05	13753
18 May 170.00	7.27	9105	18 May 170.00	8.34	14121
18 May 175.00	5.00	12421	18 May 175.00	10.68	7615
18 Jun 165.00	11.21	11080	18 Jun 165.00	7.10	14599
18 Jun 170.00	8.30	18666	18 Jun 170.00	9.50	13292
18 Jun 175.00	6.20	24639	18 Jun 175.00	11.92	13026
18 Jul 165.00	12.80	2793	18 Jul 165.00	7.95	3565
18 Jul 170.00	9.70	12054	18 Jul 170.00	10.35	8952
18 Jul 175.00	7.60	7937	18 Jul 175.00	13.15	4218
18 Oct 165.00	16.45	241	18 Oct 165.00	9.19	144
18 Oct 170.00	13.55	349	18 Oct 170.00	11.15	289
18 Oct 175.00	11.70	744	18 Oct 175.00	17.55	1613

1.Focus on the October 175 call. Suppose you bought this call at the price indicated. How high must AAPL's price rise at expiration to break even on this option?

2.Now, look at the October 175 put. Provide a table showing the profit at expiration to a put buyer across a range of stock prices.

3a.Assume you own 100 shares of AAPL stock (at $168.98 per share). Use the June 165 put to develop a protective put strategy. How will this strategy protect your position in AAPL if the stock price falls to $140?

3b.What if the price rises to $190?

3c.Calculate the net profit generated by the stock and the put at these prices and assuming they occur at the time of the option's expiration.

4a.Create a strangle by buying the May 175 call and the May 165 put. What's the maximum loss for this position and what range of stock prices will produce it?

4b.Where will you break even? Why would an investor establish a position like this?

Answer 1

1.Focus on the October 175 call. Suppose you bought this call at the price indicated. How high must AAPL's price rise at expiration to break even on this option?

Call premium, C = 11.70; Strike Price, K = 175, Current Share Price, S₀ = $ 168.98.

If S is the price at expiration, then payoff from the call option = max (S - K, 0)

Net gain from the position = Payoff from call option at expiration - Call premium paid = max (S - K, 0) - C

Hence, for break even, max (S - K, 0) - C = 0 Or, max (S - K, 0) = C:

Or, S - K = C; S = K + C = 175 + 11.70 = $ 186.70

Hence, AAPL's price should rise to $ 186.70 at expiration to break even on this option.

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2.Now, look at the October 175 put. Provide a table showing the profit at expiration to a put buyer across a range of stock prices.

October 175 Put Premium, P = 17.55

Strike Price, K = 175

If stock price at expiration is S, then profit at expiration to a put buyer = max (K - S, 0) - P

Hence, the profit table is as shown below:

S ($)	Profit ($) = max(K - S, 0) - P
140.00	17.45
145.00	12.45
150.00	7.45
155.00	2.45
160.00	-2.55
165.00	-7.55
170.00	-12.55
175.00	-17.55
180.00	-17.55
185.00	-17.55

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3a. Assume you own 100 shares of AAPL stock (at $168.98 per share). Use the June 165 put to develop a protective put strategy. How will this strategy protect your position in AAPL if the stock price falls to $140?

Protective Put strategy is: Buy the stock and buy the Put on the same stock with strike price close to stock's purchase price

Since, we own 100 shares of AAPL stock (at $168.98 per share), we will buy 100 nos. of June 165 put to develop a protective put strategy.

S₀ = $ 168.98, K = 165, Put premium, P = 7.10, N = 100

Profit from the protective put strategy = Payoff from long stock position + Payoff from the long put position - Price paid for long put position = N x (S - S₀) + N x max (K - S, 0) - N x P = N x [(S - S₀) + max (K - S, 0) - P]

if the stock price falls to $140, i.e. S = $ 140, then profit from the protective put strategy = 100 x [(140 - 168.98) + max (165 - 140, 0) - 7.10] = - $ 1,108

The payoff on the each of the put option = 165 - 140 = $ 25 has absorbed the majority of the loss on each of the stock = 168.98 - 140 = 28.98. Thus the protective put has saved the investor from losses on decline in stock price and limited it to $ 1,108.

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3b. What if the price rises to $190?

if the stock price rises to $190, i.e. S = $ 190, then profit from the protective put strategy = 100 x [(190 - 168.98) + max (165 - 190, 0) - 7.10] = $ 1,392.00 primarily driven by the long stock position. The Put option will be left unexercized.

3c. Calculate the net profit generated by the stock and the put at these prices and assuming they occur at the time of the option's expiration.

Net profit generated in case of 3(a) = - $ 1,108

Net profit generated in case of 3(b) = $ 1,392

4a. Create a strangle by buying the May 175 call and the May 165 put. What's the maximum loss for this position and what range of stock prices will produce it?

May 175 Call Price, C = 5, Gain or loss from long call = max (S - K, 0) - C = max (S - 175, 0) - 5

May 165 Put Price, P = 6.05, Gain or loss from long put = max (K - S, 0) - P = max (165 - S, 0) - 6.05

Hence, total gain or loss from the strangle = Gain or loss from long call + Gain or loss from long put = max (S - 175, 0) - 5 + max (165 - S, 0) - 6.05 = max (S - 175, 0) + max (165 - S, 0) - 11.05

If S > 175, the long call option will have a positive payoff. If S < 165, the long put will have a positive payoff. Hence, the maximum loss will occur if $ 165 ≤ S ≤ $ 175 and that loss will be = max (S - 175, 0) + max (165 - S, 0) - 11.05 = 0 + 0 - 11.05 = - $ 11.05

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4b. Where will you break even? Why would an investor establish a position like this?

We have plotted the gain / loss matrix at various price points:

S ($)	Gain = max (S - 175, 0) + max (165 - S, 0) - 11.05
140.00	13.95
145.00	8.95
150.00	3.95
153.95	-
158.95	(5.00)
163.95	(10.00)
168.95	(11.05)
173.95	(11.05)
178.95	(7.10)
183.95	(2.10)
186.05	-
191.05	5.00
196.05	10.00

There are two break even price points.

The first break even price is S = $ 153.95. At this price, gain or loss = max (S - 175, 0) + max (165 - S, 0) - 11.05 = 0 +11.05 - 11.05 = 0

The second break even price is S = $ 186.05. At this price, gain or loss = max (S - 175, 0) + max (165 - S, 0) - 11.05 = 11.05 + 0 - 11.05 = 0

An investor establishes a position like this if he believes that stock price may fluctuate significantly on either side of the current price. If there is a large price movement on either side (increase or decrease) the strangle helps the investor make money otherwise his losses are insulated to the premium he pays on both the options.
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