Why the answer is short sell a stock? & does short a stock meaning selling a stock? How does this help if the price goes down. We will sell the stock at one particular price.
Short a stock means borrowing the stock from someone who owns it and sell it in the market.
As a long put option has negative delta, so a short put option has positive delta.
To make the position delta hedged, you will need to short sell the stock (negative delta) to offset the positive delta from the short put option.
Look at the payoff diagrams:
- Long call: _/
- Short call: ¯\
- Long put: \_
- Short put: /¯
- Long stock: /
- Short stock: \
So:
- The payoffs on a long call and a short put are similar to the payoffs on a long stock (sloping up to the right); you hedge them with short-stock-type payoffs (sloping down to the right)
- The payoffs on a long put and a short call are similar to the payoffs on a short stock (sloping down to the right); you hedge them with long-stock-type payoffs (sloping up to the right)
Pardom my asking, but wouldn’t it be better to hold a long position on OTM puts instead of shorting stock?
Long put has negative delta and could therefore be used to delta-hedge the short put position, and would also result in limited downside risk. Because long put has positive gamma, which partially offsets the negative gamma from the short put, the resulting portfolio would have a lower gamma in absolute value, which means delta changes less with the underlying.
option C:
Delta hedging is the process of neutralizing exposure to the underlying.
Shorting a put and shorting a stock is equivalent (in terms of profit diagram) to a naked written call, which has unlimited loss potential. Because you can potentially lose an unlimited amount by delta-hedging a short put by shorting stocks, option C seems incorrect, or at least very misleading to me. Thoughts on this? Thanks.
There are two obvious disadvantages to buying OTM puts instead of shorting the stock (to achieve a delta hedge):
- OTM puts have an extremely low delta, so you would have to buy several times as many puts as you would have to short shares of stock to achieve the same delta hedge.
- Buying puts costs money; shorting stock generates money.
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True if the ratio of short puts to short shares is 1:1.
In the delta hedge, it won’t be 1:1, because the delta of the short put is less than 1. Furthermore, as the price of the underlying stock rises, the delta of the put approaches zero, so the number of shares you are short will approach zero.
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you’re right, i forgot to take into accont that the ratio is not 1 to 1.
one major issue with delta-hedging with shares is the potential to lose an unlimited amount if the stock appreciates. my textbook says that for this reason, a short put combined with a short stock (a written covered put) is rarely used in practice.
edit: then again, the textbook was referring to the case with 1:1 ratio, which isnt the case when delta-hedging.
thanks for the explanation, makes perfect sense.
My pleasure.
As I’m capable of making perfect sense only once a week, it appears that I peaked too soon this week.