Question

A put option with a strike price of $65 costs $8. A put option with a strike price of $75 costs $15. 1) How can a bull spread be created? 2) With the bull spread created above, what is the profit/loss if the stock price is $70? 3) With the bull spread created above, when would the investor gain a positive profit?

Answer 1

1) How can a bull spread be created?

A bull spread is created by buying the $65 put and selling the $75 put. This strategy gives rise to an initial cash inflow of ($15-$8 =) $7.

2) With the bull spread created above, what is the profit/loss if the stock price is $70?

If Stock Price (ST) = $70

Payoff = higher strike price - stock price = $75 - $70 = -$5

The profit = initial cash inflow from bull spread + Payoff

= $7 - $5 = $2

Therefore profit of $2, if the stock price is $70.

3) With the bull spread created above, when would the investor gain a positive profit?

The payoff table is below -

Stock Price	Pay-off	Profit (initial cash inflow from bull spread + Payoff)
ST ≥75	$0	$7
65≤ ST˂75	ST- $75	ST-$68
ST˂65	-$10	-$3

From above table, we can conclude that the investor gain a positive profit if the stock price is above the (higher strike price - initial cash inflow) or ($75 -$7 = $68)

Therefore if the stock price is more than $68, than the investor gain a positive profit.