# Delta

I’m confused with how schweser book explained delta. In schewser book 5, page 64, study session 17, in the example it says:

delta= (10 - 0) / (40 - 22.5) = .5714 SHARES PER OPTION

however book 5, page 79, it stays the definition of delta is: Delta is the price change of AN OPTION for A ONE-UNIT change in the price of the underlying security.

So my question is:

Is delta the change in option price per 1 unit of stock price?

or delta is the price change for stock in per option price?

delta is the change in price of the asset per change in price of the underlying. So the the delta of a call option will be anywhere between 0 and 1 (i…e if the underlying goes up by \$1, the option will change price by \$0.76) and the delta of the underlying is 1 (if the underlying goes up by \$1, then value of the underlying goes up by \$1, sounds stupid but the point is the the underlying also has delta, it just happens to be 1).

Isn’t asset is your underlying?

I amended my post. The option and the underlying both have delta.

It’s really incongruent to think that the underlying has delta. BSM and its underpinnings are really drivers of options valuation, not the underlying. Just saying.

Is delta also your hedge ratio? What is this concept of hedge ratio?

-1/delta is the hedge ratio.

If you’re long 100 shares, and the delta of a call option is 0.25, then you would need -1/0.25 × 100 = -400 calls; you would sell 400 call options for a delta hedge.

Wow thanks… I don’t think the formula you gave just now is in the schweser book

Aether, using S2000s example:

100 shares = 100 deltas

-400 call options = -100 deltas

Total Delta = 100 deltas - 100 deltas = 0 deltas. You are delta hedged.

Just because you don’t need BSM to calculate delta of the underlying doesn’t mean the underlying doesn’t have delta.

U guys r pros

My point is, you can’t utilize the BSM derivations to infer conclusions similar to yours. It’s akin to saying the volatility of the option increases with the option price, when it’s the other way around. Sure, the formula supports it, but when you think about it in terms of the real world, the relation is inappropriate. Outside of options valuation theory, where else have you seen “delta of a stock?” Especially with regards to hedging?

In the real world one equity option represents 100 shares of stock, so 4 calls with .25 delta would hedge 100 shares of stock.

Go online and download any options portfolio management software. Buy 100 shares of MSFT and look at the column that shows you your delta position. It will say 100. If MSFT goes up \$1, you make \$100. That is the definition of delta.

I don’t understand what conclusions you think I’m trying to make.

Not if you’re dealing with mini options :).

cleverCFA: Your posts imply stocks have delta. Stock do not have delta, options do. Delta is the rate of change of the option price with respect to the underlying. In calculus terms, delta is the first derivative (while gamma is the second): dc/dS. “c” is the price of the option. CFAI’s definition - The delta defines the sensitivity of the option price to a change in the price of the underlying. When you say stock has delta, you seem to imply that the stock price is dependent on the option price; this is untrue since the relationship is not associative.

Yes. But CFA Institute will want you to answer that 4 calls represents calls on 400 shares. “Sell 4 calls” won’t be an answer choice.

Aether: I never said that the underlying has a delta (first derivative) with respect to the option price. I said that the “delta of the underlying is 1 (if the underlying goes up by \$1, then value of the underlying goes up by \$1”. This is the first derivative of the underlying price with respect the underlying (i.e. itself). In calculus terms this d S / dS which as you know is 1.

You don’t have to be an option to have delta. Stocks, forwards, swaps, ETFs, futures to name a few all have delta. These are all either equal to or very close to 1 (Delta One instruments).

Understanding that non-option products can be broken down into the “greeks” is fundamental to understanding how to manage risk on a derivatives portfolio. It allows you to understand your risks by comparing apples with apples (i.e. Delta/Gamma/Vega/Theta/Rho). Breaking down every position in your porfolio into these risks allows you to understand your porfolio risk in aggregate (what is my delta exposure, stock delta + option delta + swap delta,etc, what is my vega exposure: option vega + swap vega, etc, etc)

What clever is saying is the stock price depends on . . . wait for it . . . the stock price: dS/dS = 1.

I never said it was rocket science

When it comes to derivatives sometimes you just need to complify the simplicated.

For ten years I was a warhead designer (mostly single and multiple explosively-formed penetrator (EFP) warheads); when I write “it’s not rocket science”, I’m not offering a platitude or being flippant: it’s a professional opinion.

Maybe I’m just seeing things :).

Again, all derivatives (mathematically, pun intended) have delta, gamma (second derivative), etc. Any decent S&T desk would probably laugh at the notion of the underlying being expressed in terms of greeks. You don’t get into greeks until you breach the barrier of first or second derivatives. In Layman’s terms, it’s not the underlying that is dependent on the option, but the option that is dependent on the underlying.

The derivative of a constant is actually zero. So this statement doesn’t really make any sense. I’m not challenging anyone’s intelligence here… so please don’t take this personally. I still can’t digest the claims of lumping analysis of the underlying into the same category as the analysis of attributes of the BSM.