Recall that a straddle is a combination of a long put and a long call, both of the same strike and expiry.

$($a$)$ Explain how the payoff diagram for the straddle would need to be adjusted to become a profit diagram. Then state the conditions under which a profit is made.

$($b$)$ Suppose now that the strikes are not equal, in particular that the strike of the put is lower than the call. This combination$/$strategy is known as a strangle.

i$.$ Explain why strangles cost less than straddles.

ii$.$ Plot the payoff of a strangle.

iii. Comment on why the higher cost of the straddle might be justified for the investor