Trading delta: how much an option really moves

The lesson in plain words

The same lesson as the slides above, written out in full.

1. Trading Delta

Welcome. Delta is the first Greek, and honestly the most useful one to master. In our overview lesson we learned its definition, how much an option's price moves for a one dollar move in the underlying. A delta of nought point five means the option gains fifty cents for every dollar the stock rises. But delta is far richer than that single definition. It quietly tells you three things at once. How much your position will move, how much real exposure you are actually carrying, and even a rough probability of your option finishing in the money. Let us go deeper. One note before we begin. This is financial education only, not financial advice.

• Delta measures how much an option moves for a $1 move in the underlying.
• It is the most useful Greek, and the one you will lean on most.
• It tells you your true directional exposure and a rough probability.

A quick note: This is financial education only, not financial advice. Do not buy, sell, or hold anything based on this lesson.

2. Your True Exposure

First, delta as exposure. A single option contract usually controls one hundred shares of the underlying. So a call with a delta of nought point five behaves, in the moment, like owning about fifty shares of the stock. This is your effective exposure. And delta changes with how far in or out of the money the option is. A deep in the money option has a delta approaching one, so it moves almost dollar for dollar with the stock, behaving very much like the shares themselves. A far out of the money option has a delta near zero, so it barely responds to the stock's moves. Knowing your delta means you always know how much you are truly exposed.

• One option contract usually controls 100 shares.
• A 0.50 delta contract behaves like holding about 50 shares.
• Deep in the money, delta approaches 1: it moves almost like the stock itself.
• Far out of the money, delta approaches 0: it barely responds.

3. Delta as a Probability

Here is a wonderful second meaning. Delta doubles as a rough probability of the option finishing in the money at expiry. A nought point five delta option is roughly a coin flip, about a fifty per cent chance. A nought point two delta option is a long shot, roughly a twenty per cent chance. This is an approximation, not an exact statistic, but it is a brilliant gut check. When you see a very cheap, far out of the money option, its low delta reminds you why it is cheap, it is a low probability bet. It stops you mistaking a lottery ticket for a bargain.

• Delta doubles as a rough probability of finishing in the money at expiry.
• A 0.50 delta is roughly a coin flip; a 0.20 delta is about a 20% chance.
• It is an approximation, not an exact figure, but a useful gut check.
• It helps you see when a cheap option is cheap for a reason.

4. Match Delta to Conviction

So how do you use all this to trade? You choose your delta to match your conviction. If you have strong conviction and want your option to behave much like the stock, you buy a higher delta option, say nought point seven to nought point nine. It costs more, but it participates fully in the move. If you want a cheaper, more leveraged, lower probability bet, you buy a lower delta option, around nought point two to nought point three. The middle ground, near nought point five, balances cost and leverage. And here is the reassuring part that runs through everything we do. Whichever delta you choose, because you are buying a long option, your risk stays defined. The most you can ever lose is the premium you paid, known from the very first minute. That defined risk is exactly why we express our directional views this way.

• High-delta options behave more like the stock: costlier, but strong participation.
• Low-delta options are cheap, with lower odds and more leverage.
• Match your delta to your conviction and budget.
• Throughout, your risk stays defined: the most you can lose is the premium paid.