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An investor wants to construct a bear spread using two put options with the same expiration...

An investor wants to construct a bear spread using two put options with the same expiration T. One put has the strike price of $20 and currently sells for $2. The other put has the strike price of $30 and currently sells for $7. Find the range of stock price on T that results in a positive profit for the investor.

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Answer #1

Bear spread is achieved by going long on the put option with higher strike option and selling the one with lower strike option.

We have assumed the following data points and calculated the Payoff and the profit:

  • In long option, till the time the spot price is greater than the strike price, the option is not exercised and therefore the payoff is 0 and loss is = amount of premium paid = -7
  • In long option, when the spot price is equal to or lower than the strike price, the option is exercised and therefore the payoff is strike price - spot price and profit = strike-spot-premium
  • In short option, till the time the spot price is greater than the strike price, the option is not exercised and therefore the payoff is 0 and profit is = amount of premium received = 2
  • In short option, when the spot price is equal to or lower than the strike price, the option is exercised and therefore the payoff is -(strike price - spot price) and profit = -strike+spot+premium
  • Total profit = sum of the profits of both the options
Long Put Short Put
Spot price Exercise price Premium Spot price Exercise price Premium
30 7 20 2
Payoff Profit Payoff Profit Total Profit
14 30 9 14 -20 -4 5
15 30 8 15 -20 -3 5
16 30 7 16 -20 -2 5
17 30 6 17 -20 -1 5
18 30 5 18 -20 0 5
19 30 4 19 -20 1 5
20 30 3 20 0 2 5
21 30 2 21 0 2 4
22 30 1 22 0 2 3
23 30 0 23 0 2 2
24 30 -1 24 0 2 1
25 30 -2 25 0 2 0
26 30 -3 26 0 2 -1
27 30 -4 27 0 2 -2
28 30 -5 28 0 2 -3
29 30 -6 29 0 2 -4
30 30 -7 30 0 2 -5
31 0 -7 31 0 2 -5
32 0 -7 32 0 2 -5
33 0 -7 33 0 2 -5
34 0 -7 34 0 2 -5
35 0 -7 35 0 2 -5

So for the price 0-25 the profit will be positive, as profit after the price of 20 will remain constant at 5

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