Delta is probably the first greek an option trader learns and is focused on. In fact it can be a critical starting point when learning to trade options. Simply said, delta measures how much the theoretical value of an option will change if the stock moves up or down by $1. A positive delta means the position will rise in value if the stock rises and drop in value of the stock declines. A negative delta means the opposite. The value of the position will rise if the stock declines and drop in value if the stock rises in price. Some traders use delta as an estimate of the likelihood of an option expiring in-the-money (ITM). Though this is common practice, it is not a mathematically accurate representation.

The delta of a single call can range anywhere from 0 to 1.00 and the delta of a single put can range from 0 to -1.00. Generally at-the-money (ATM) options have a delta close to 0.50 for a long call and -0.50 for a long put. If a long call has a delta of 0.50 and the underlying stock moves higher by a dollar, the option premium should increase by $0.50. As you might have derived, long calls have a positive delta and long puts have a negative delta. Just the opposite is true with short options—a short call has a negative delta and a short put has a positive delta. The closer the option’s delta is to 1.00 or -1.00 the more it responds closer to the movement of the stock. Stock has a delta of 1.00 for a long position and -1.00 for a short position.

Taking the above paragraph into context, one may be able to derive that the delta of an option depends a great deal on the price of the stock relative to the strike price of the option. All other factors being held constant, when the stock price changes, the delta changes too.

What many traders fail to understand is that delta is cumulative. A trader can add, subtract and multiply deltas to calculate the delta of the overall position including stock. The overall position delta is a great way to determine the risk/reward of the position. Let’s take a look at a couple of examples.

Let’s say a trader has a bullish outlook on Apple (AAPL) when the stock is trading at $128 and purchases 3 March 130 call options. Each call contract has a delta of +0.40. The total delta of the position would then be +1.20 (3 X 0.40) and not just 0.40. For every dollar AAPL rises all factors being held constant again, the position should profit $120 (100 X 1 X 1.20). If AAPL falls $2, the position should lose $240 (100 X -2 X 1.20) based on the delta alone.

Using AAPL once again as the example, lets say a trader decides to purchase a March 130/135 bull call spread instead of the long calls. The delta of the long $130 call is once again 0.40 and the delta of the short $135 call is -0.22. The overall delta of the position is 0.18 (0.40 – 0.22). If AAPL moves higher by $3, the position will now gain $54 (100 X 3 X 0.18) with all factors being held constant again. If AAPL falls a dollar, the position will suffer a $18 (100 X -1 X 0.18) loss based on the delta alone.

Calculating the position delta is critical for understanding the potential risk/reward of a trader’s position and also of his or her total portfolio as well. If a trader’s portfolio delta is large (positive or negative), then the overall market performance will have a strong impact on the traders profit or loss.

John Kmiecik

Senior Options Instructor