# Hedge Ratio Formula Question

Are there two ways to compute the hedge ratio? 1) 1/delta 2) C+ - C- / S+ - S- is that correct?

i believe 2 is calculating delta to use for 1

Delta is the number of shares to hold for each short option so 1/delta is the number of options per share. The formula is simply delta in the binomial model i.e.change in option value over change in underlying.

Hold on a sec, without taking into account the positive/negative convention, isn’t the hedge ratio simply delta? e.g. If I own 100 calls (1 share per call) and the delta is .85, I would need to short 85 shares in order to hedge my position.

Yea, delta and the hedge ratio are the same thing.

That’s how I understand it. And if you own 100 puts and delta was the same (negative obviously) then you’d need to buy 85 shares to hedge your position.

bpdulog Wrote: ------------------------------------------------------- > Hold on a sec, without taking into account the > positive/negative convention, isn’t the hedge > ratio simply delta? > > e.g. If I own 100 calls (1 share per call) and the > delta is .85, I would need to short 85 shares in > order to hedge my position. A delta of 0.85 means you should short 85 calls to hedge for 100 shares; so you wrote just the opposite.

To put it together. schweser sample exam, book 7 exam 1, #109 which of the following positions will best delta hedge Nolte’s long position? He owns 5,000 shares, the delta for the 1 month calls is .54 we are given the delta, and we have to compute the hedge ratio hedge ratio tells us # of calls (per share) to short hedge ratio = 1/delta = 1.54 = 1.851 answer: sell 9259 calls

revisor - Isn’t the effect the same?

same thing pretty much. Usually you are hedging a stock position (as opposed to hedging an option position), so the hedge ratio is shares/delta. in your examply, stock moves up \$1 you lose 85 on the stock and make 85 on the call if i am short 85 shares in stock, i would need 85/.85 = 100 calls

is revisor correct? I thought the delta shows how many units of the underlying asset you would need to buy/short for every option.

after reading other posts, I am assuming he is wrong.

shares owned/delta = hedge ratio, or so i thought. Represents the # of short calls necessary to eliminate the exposure to change in the asset price…

agreed. thanks.

CFA.Rhythm Wrote: ------------------------------------------------------- > To put it together. > > schweser sample exam, book 7 exam 1, #109 > > which of the following positions will best delta > hedge Nolte’s long position? > > He owns 5,000 shares, the delta for the 1 month > calls is .54 > > we are given the delta, and we have to compute the > hedge ratio > > hedge ratio tells us # of calls (per share) to > short > > hedge ratio = 1/delta = 1.54 = 1.851 > > answer: sell 9259 calls I assume the answer is simply inverse if you are a dealer selling calls looking to hedge? #calls x delta

The way I see it, the # of calls can never exceed the # of shares of stock. At the most, the # of shares will equal the # of calls assuming a delta of 1.

Bpdulgo^^ Isnt it the opposite? I will always need more short calls to hedge a share position, unless delta is 1, in whcih case the numbers are equal. Upper delta limit on calls is 1. so I always need more calls than share to hedge.

bpdulog Wrote: ------------------------------------------------------- > The way I see it, the # of calls can never exceed > the # of shares of stock. At the most, the # of > shares will equal the # of calls assuming a delta > of 1. yeah, i think you’re off on this…hedge ratio is shares/delta. When delta = 1, #calls = # shares. All other times, calls > shares needed

Yeah, you’re right, I meant the opposite: # of shares < # of calls Unless delta = 1 # of shares = # of calls