# Hedge ratio

In page 239 of book 5, there is a formula of hedge ratio. THey did an example but I have no idea where the numbers are coming from, I am much confused. The forumla is hedge ratio = (C+ - C- )/ (S+ - S-) Any insights are apperciated.

not to confuse myself but hedge ratio also appears in page 259… but this time hedge ratio = 1 / delta i work with delta gamma vega epsilon everyday these days but i dont know what hedge ratio is

The hedge ratio formula in the opening post I believe is the formula for delta. Change in value of the call over change in value of the underlying. The hedge ratio times the number of shares you are trying to hedge creates a delta nuetral position. That is, you are indifferent to price movement of the underlying because you are hedged. Keep in mind that a delta-nuetral portfolio needs to be continuously rebalanced to maintain the hedge, though.

C+ is the value of the call option for a small +ve perturbation in the stock. C- the same only negative.

I am with the guys above. The first formula is for calculating delta. It kind of looks like a duration formula if you look at it. Since delta is the change in the price of the option for a small change (again like duration won’t work for large changes) it is used to calculate the number of options need to make a stock (portfolio) delta neutral. I guess you could also look at gamma like convexity in a way too.

Hedge ratio is the number of underlying units you would have to buy in combination with a short call option so that the portfolio value remains the same when the stock goes up or down. So if H is the portfolio value, H = nS-c where n is the hedge ratio, S is the stock price and c is the call price. If the stock goes up H+ = nS+ - c+ if it goes down, H- = nS- - c- If the portfolio value should remain the same, H+ = H- nS+ - c+ = nS- - c- Solving for n gives the hedge ratio as c+ - c-/S+ - S-

ok, really silly question: delta neutral means delta =0 or delta =constant?. please confirm. i am inclined towards delta =0

Dsylexic Wrote: ------------------------------------------------------- > ok, really silly question: delta neutral means > delta =0 or delta =constant?. please confirm. > i am inclined towards delta =0 Ideally…constantly 0.