Time Decay with Option

Example of Time Decay

You pay me $1.00 for an OTM option with 10 days until expiration.

With each day that passes, let’s say the option loses $0.10 of time value (please note this is just an illustration. In practice time decay is not linear).

So, assuming there is no movement in the underlying stock price, the option value will behave as follows:

Day Option Value Buyer Profit Seller Profit

Day 0 $1.00
Day 1 $0.90 (0.10) + 0.10
Day 2 $0.80 (0.20) + 0.20
Day 3 $0.70 (0.30) + 0.30
Day 4 $0.60 (0.40) + 0.40
Day 5 $0.70 (0.50) + 0.50
Day 10 $0.00 (1.00) +1.00

Do you see how time decay has helped me (the seller) and hurt you (the buyer)?

Lesson: Never buy OTM options with less than 1 month to expiration unless it forms part of a multi-legged spread trade.

The negative value of theta indicates to us that as time gets closer to expiration, time decay increases. With options, time decay increases exponentially during the last month before expiration. Put another way,

time value decreases exponentially

during the last month before expiration.

The big question is how can we mitigate time decay?

• Sell off any owned ATM or OTM options with 30 days left to expiration. Time decay accelerates at its fastest during the last 30 days to expiration. Remember that OTM and ATM options have no Intrinsic Value, so they must be made up purely of Time Value. Since we know that time value decreases exponentially during the final month before expiration, it makes sense not to hold onto these options.
• Sell options you don’t already own as an adjustment to existing trades – we’re not talking about creating naked positions here, the sold option would be complementary to your existing play (for example, Bull and Bear spreads).
• Buy short-term deep ITM options, e.g. a deep ITM put or deep ITM call will have lots of Intrinsic Value and virtually no Time Value. If there is no Time Value, then it can't decay any further, can it? Remember about Time Value and Intrinsic Value. Well, here we’re talking about there being so little Time Value as a proportion of the option premium because the option is so deep ITM.

Let’s take at look at each one of these points in turn:
Sell off OTM or ATM options with less than 30 days to expiration
The diagram below gives us a perfect illustration of how theta decay works with options. Notice how the slope falls off at its steepest during the last 30 days.

Diagram: Time Decay

Sell options you don’t own as an adjustment to existing trades …

Note that here we’re not advocating selling options naked and exposing yourself to an unlimited risk profile. Many people successfully sell OTM options every month and collect a decent premium. However, if the market suddenly jolts against them and they get exercised, then an entire year or more can be wiped out (or more) in literally one day. The fact remains that selling options naked is not a businessperson’s way to trade. Although there are some high-probability mathematical techniques of naked options selling, if your capital can be wiped out that fast when you’re not looking, then that’s simply not a sensible way to go about your business. It’s far better to be able to sleep at night, that way you’ll pass the test of longevity and be able to consistently trade and invest for many years even well into your retirement.

Buy short-term Deep ITM options
You can mitigate the effects of time decay by buying Deep in the Money (DITM) options, the reason being because Intrinsic Value is vastly outweighing Time Value. If there is little to no Time Value in the option (as compared with Intrinsic Value) then your risk exposure to time decay is, by definition, little to none!

Diagram: Time value for deep ITM options

Example:

Let's say a stock is priced at $42.10. There are only 18 days left to the May expiration and just over six weeks left till the June expiration.

Question:

How much Time Value and Intrinsic Value is there for the following options?

Remember:

• Call option Intrinsic Value = stock price – strike price


• Call option Time Value = call option price – Intrinsic Value


• Intrinsic Value minimum = Zero

See if you can fill in the table below:

Call option Last ($) Intrinsic Value Time Value
May 12.5 30.20 42.10 – 12.50 = 29.60 30.20 – 29.60 = 0.60
May 15 27.
May 17.5 25.30
May 20 22.80
May 22.5 20.30
May 25 18.00
May 40 5.50
June 20 23.20
June 22.5 20.90
June 25 18.70
June 40 8.20

Answers: (take note of the percentage of the entire option premium which is taken up by Intrinsic or Time Value as the option gets Nearer the Money)

Call option Last ($) Intrinsic Value Time Value
May 12. 30.20 29.60 98% 0.60 2%
May 15 27.80 27.10 97.5% 0.70 2.5%
May 17.5 25.30 24.60 97% 0.70 3%
May 20 22.80 22.10 97% 0.70 3%
May 22.5 20.30 19.60 96.5% 0.70 3.5%
May 25 18.00 17.10 95% 0.90 5%
May 40 5.50 2.10 38% 3.40 62%
June 20 23.20 22.10 95% 1.10 5%
June 22.5 20.90 19.60 93.8% 1.30 6.2%
June 25 18.70 17.10 91.5% 1.60 8.5%
June 40 8.20 2.10 25.6% 6.10 74.4%

Do you see how DITM options premiums are heavily weighted by Intrinsic Value and minimally weighted by Time Value, thus reducing the exposure to time decay? And how Time Value tends to dominate the short-term ATM options?
Say we have a simple call option, the stock price is $69 and the 70 strike January call option is priced at $9.80. Let’s look at the theta as at 20 April and compare it with the position of theta with only one month left to expiration:
Notice how both theta lines are negative but especially notice how much more theta decay is harming our long call position when there is only one month left to expiration. Also notice how theta is at its lowest at the $70 level, i.e. At the Money (ATM).
Chart: Long Call theta profile

The same applies to puts. Let’s look at the equivalent example with puts:

Chart: Long Put theta profile

Now have a look at theta decay for the Short call and Short put positions. Can you guess what will happen and how they will look?

Chart: Short call theta profile

Chart: Short put theta profile


Generally, when theta is positive, time decay is helping the position. When theta is negative, time decay is hurting the position. When we buy options, we have a negative theta, indicating that time decay hurts our long option position. This makes sense as an option is a wasting asset. When we write options, we would expect the opposite to be the case, which of course it is. When we write an option, its value will decline as we approach expiration. If we write a $1.00 OTM option with 10 days left to expiration, assuming that time decay reduces the option by $0.10 per day, then by day 5, we’d only have to pay $0.50 to buy it back, thereby making a $0.50 profit assuming the stock has not moved. In this scenario time decay has helped us, the writer of the option. On the other hand, the person who (stupidly!) bought the OTM option from us with only 10 days to expiration has lost 50% within the first 5 days assuming there is no movement in the stock price.

If time decay is unhelpful to your long option positions, then it stands to reason that it will be helpful to your short option positions. You can see this by way of simple graphical representation in that now the theta lines are positive, showing that theta decay is helpful to a short option position.
Diagram: Theta Summary