Reader Q&A: Delta Hedging
With No Math
As promised, here is the simplified explanation of Delta Hedging that readers asked for in a previous post.
Imagine a stock is moving smoothly up and down, with no big moves in either direction. There is a bit of noise in the motion, but nothing extreme. Pretend that the stock is trading at 100- to start. What algorithm could you design to make money from this situation?
Start with a naive model that sells short every time the stock moves up a dollar above the target strike. If it moves down, buy back the stock for a one dollar profit. If the stock falls below the strike, buy it at fixed increments and sell it as it goes up. If all goes well, you will have something like this:
The stock price is listed at the top, the buy/sell action is listed below.
Here is the breakdown of the first six trades:
Sell short 100 shares with the stock at 100-. Position Size = -100 Profit = 0.0
Sell short 100 shares with the stock at 101-. Position Size = -200 Profit = -100.00
Sell short 100 shares with the stock at 102-. Position Size = -300 Profit = -300.00
Buy back 100 shares at 101. Position Size = -200 Profit = -100
Buy back 100 shares at 100. Position Size = -100 Profit = 200.00
Buy back 100 shares at 99 Position Size = 0 Profit = 300
So far the model generated 300- in profit and the position is flat. As the stock continues to gyrate, the model then makes money from the long side, as it buys when the stock moves down, and sells for a profit as the stock moves up.
If everything stays the same, this model is a real money machine.
The problem with this simple model is when one of two things happen:
The stock trends up or down, and you never get to close out your opening positions.
The stock gaps up or down, and erases all of the profits you collected so far, and then some.
What can you do to minimize risk? One easy thing to do would be to buy a cheap 100 strike straddle (long one put/long one call) and trade the stock just like in the example. If the straddle costs less than the profit generated by the stock trades, it captures some (but not all) of the stock profit, and makes even more money if the stock trends or gaps. Of course, if the straddle costs more than the stock trades, you lose money on the difference. Back in the early 2000s there was a famous financial TV commentator named Jim Cramer whose wild and sometimes questionable commentary created big gaps in the market at unexpected times. In the trading room I used to work in, you would often hear traders scream:
GOD DAMN CRAMER JUST BUSTED MY HEDGE!!!!!
But that is less frequent these days, since Delta hedging is not very profitable if you have less than a couple of hundred million dollars in your account.
How many shares of stock do you need to trade to break even, on any given straddle?
This is easy. The Delta parameter (calculated in an online calculators or in your brokerage platform) offers the exact number of shares to buy or sell for a single straddle, assuming that the volatility of the stock remains constant and that there is no trend or gap in either direction. If the stock stays in a tight range, the volatility does not budge, and there are no commissions/bid-ask spreads, this hedge will break even. If you thing the stock will move out of a narrow range, you can use the Gamma parameter to estimate the change in Delta as the stock moves.
Keep this conceptual framework in mind when you read more complicated explanations of the Delta parameter in quantitative finance textbooks.
DISCLAIMER: All content on he Nuclear Option Substack is for Education and Information Purposes Only. It is not a recommendation or solicitation to buy or sell any security. Before trading, consult your Professional Financial Advisor and read the booklet Characteristics and Risks of Standardized Options Contracts, published by the Options Clearing Corporation.