Previously in this column, we compared time decay between the near-week and the next-week Nifty options. Time decays faster for the near-week compared to the next-week options. In contrast, next-week options have higher time value than near-week, which means more potential gains from time decay for short positions. This week, we discuss why theta is not the primary reason for long positions to earn lower or negative returns.    

Delta matters

The gain or loss in options position can be best understood using in-the-money (ITM) options, as ITM options have both intrinsic value and time value. Consider the next-week 17400 call on the Nifty Index that trades at 201 points. With the spot index at 17523, the 17400 strike has 123 points of intrinsic value and 78 points of time value. To isolate the effect of time decay, suppose volatility, spot price and interest rate do not change and one day passes by. The option could decline to 193 points the next day. The effect of time decay is, therefore, eight points. But what if the index were to decline by 50 points the next day? The option could decline to 159 points, 34 points more than if time decay were the only reason for the decline. If the decline in the index were 100 points instead, the option could drop to 128 points, shedding another 31 points.

The above discussion shows that delta matters. Delta is the change in the option price for a one-point change in the underlying asset price. Call options have positive deltas, whereas put options have negative deltas as puts move in the opposite direction to the underlying. ITM calls have delta greater than 0.50, tending towards one. If the underlying price declines, a call’s delta will decline too. For instance, if the Nifty index were to decline 100 points the day after you buy the 17400 call, the option’s delta will likely decline from 0.70 to 0.57. This decline means that call options will earn lower positive return or generate losses as the underlying falls.

Therefore, the returns you earn on options is a function of the directional movement in the underlying. Of course, time decay matters for long positions. But delta is typically a dominant factor. Consider the 17550 next-week call which has a delta of 0.50. This option could lose 50 points, from 109 to 59, if the index were to decline 100 points in one day. Approximately eight points of this decline can be attributed to time decay.

Know your return
The returns you earn on options is a function of the directional movement in the underlying
Optional reading

This discussion was meant to show that directional traders must be more worried more about the option’s delta than time decay for two reasons. One, delta is a dominant factor that drives option returns. And two, delta is a risk whereas time decay is a known loss because time value of options must become zero at expiry. The exception to this argument is delta-neutral trades that are frequently rebalanced.

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