Question

5. Apple Computer stock recently closed at $324.67. An investor wants to create a put ratio backspread. This consists of writing the AAPL Oct 330 put @$17.73 and buying 2 AAPL Oct 325 puts @$15.65. a) Write the specific profit function for this position b) Find the breakeven price(s) c) What is the maximum potential profit of this position and when will it occur? d) What is the maximum potential loss of this position and when will it occur? e) Draw the profit-loss diagram for this position 1) Under what circumstances would you undertake a put ratio backspread?

Answer 1

a) Specific profit function for this position = Profit from writing the put + Profit from buying the put

= P1 - max (K - S1, 0) + 2 x [max (K2 - S, 0) - P2]

= 17.73 - max (330 - S, 0) + 2 x [max (325 - S, 0) - 15.65]

= 2 x max (325 - S, 0) - max (330 - S, 0) - 13.57

b) For break even: the profit function = 0

Case 1: Let's assume S ≤ 325

2 x (325 - S) - (330 - S) - 13.57 = 0

Hence, 320 - S - 13.57 = 0

Hence, S = 320 - 13.57 = $ 306.43

Hence, the break even price = S = $ 306.43

Case 2: Let's assume 325 < S ≤ 330

(S - 330) - 13.57 = 0

Hence, S = 330 + 13.57 > 330

Hence, the original assumption is not met. Hence there is no solution here.

Case 3: Let's assume S > 330

None of the put options will be exercised. Then there will be a net loss. Hence, again there is no solution here.

Hence, the final answer is: the break even price is $ 306.43

c) Maximum potential profit occurs when the stock price S = 0 and the maximum potential profit = 2 x max (325 - S, 0) - max (330 - S, 0) - 13.57 when S = 0 i.e. = 2 x 325 - 330 - 13.57 = $ 306.43

d) Maximum potential loss = $ 13.57 and it occurs at any price S ≥ 330

e) Profit loss table:

S	Profit
0	306.43
25	281.43
50	256.43
75	231.43
100	206.43
125	181.43
150	156.43
175	131.43
200	106.43
225	81.43
250	56.43
275	31.43
300	6.43
325	-18.57
350	-13.57
375	-13.57
400	-13.57
425	-13.57
450	-13.57

And the diagram is:

Profit 50 100 150 200 250 300 350 400 450 500

f) I will undertake the put ratio back spread, when I have a bearish view on the market. If i believe that market may fall, I will adopt this back spread to gain when stock price falls and my losses will be capped, if the stock price doesn't fall.