 # Delta vs. Hedge Ratio

I’m confused by these two concepts. See Notes5, Page 259, it saild hedge ratio = 1/delta; See Notes5, page 256, say delta = (c1-c0) / (s1-s0); See notes5, page 230, say hedge ratio = (C1+ - C1-) / (S1+ - S1-); So i concluded that delta = hedge ratio, am i right ? Thanks

Yes, you’re right!! I cannot explain this contradictory issue!! Is somebody else able to clarify??

And then a little algebra says hedge ratio = delta = 1 always. Hmm… That can’t be right. These hedge ratiosare for different things. Delta is unambiguously the amount by which the option changes when the underlier changes by 1. The hedge ratio depends on what you are hedging with what. Thus, the hedge ratio for hedging a delta =0.6 call with a stock = 0.6. The hedge ratio for hedging a stock with a delta = 0.6 call is 1/0.6 = 1.67.

Delta is essentially first derivative of the call price with respect to the underlying price. Hence you see the (c’ - c) / (s’ - s). Don’t be confused due to the different notation. While a ratio could be A / B or B / A; it doesn’t matter. So as long as you remember the number of option contracts should be used to hedge the security position = S/Delta you are good to go.

^ that’s right and I should probably fix my sentence above. It’s real problem trying to do option greeks without using calculus since they are all calculus derivatives.

one problem i’ve noticed is that different cfa chapters will have similar subjects and the authors do things some what differently… pretty sure delta ratio and hedge ratio are reciprocals.

JoeyDVivre Wrote: ------------------------------------------------------- > ^ that’s right and I should probably fix my > sentence above. It’s real problem trying to do > option greeks without using calculus since they > are all calculus derivatives. To make matters even worse…they are partial derivatives…

this is how i think about this: Cxhedge ratio=S for example you have 10 options and hedge ratio is 0.5, you’ll have to hedge 50 stocks. if you have 100 stocks, and hedge ratio is 0.5, you’ll need 100 options(C=S/hedge ratio) and thus hedge ratio=delta

wyantjs Wrote: ------------------------------------------------------- > JoeyDVivre Wrote: > -------------------------------------------------- > ----- > > ^ that’s right and I should probably fix my > > sentence above. It’s real problem trying to do > > option greeks without using calculus since they > > are all calculus derivatives. > > To make matters even worse…they are partial > derivatives… Yes, would it really be too difficult to expect a little calculus from finance professionals? Honestly, my kids all take calculus in high school. I help them with their homework and then wonder how come CFAI expects that CFA charterholders can’t do high school work in something they call a post-college graduate certification. A little calc goes a long way with derivatives and fixed income.

I wish I would have paid attention in high school now. 