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Guy Cohen

Time Decay with Options

by Guy Cohen 18. November 2007 18:05

Theta T The characteristic of option prices to change purely as a result of the passage of time is known as time decay. Theta is a measure of how time decay affects the option premium. As such, theta is nearly always negative for bought options (although it can be positive for deep in the money puts in certain circumstances). This makes sense because time decay erodes the option value as time to expiration diminishes.Theta T The characteristic of option prices to change purely as a result of the passage of time is known as time decay. Theta is a measure of how time decay affects the option premium. As such, theta is nearly always negative for bought options (although it can be positive for deep in the money puts in certain circumstances). This makes sense because time decay erodes the option value as time to expiration diminishes.

Theta is arguably the most important sensitivityof the Greeks, and is certainly on a par with delta (see UniversitySection in the Illuminati Trader website members area for more details about the Greeks). 
Theta starts with a T and stands for Time
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 timevalue (please note this is just an illustration.  In practice timedecay 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 30days left to expiration.  Time decay accelerates at its fastest duringthe last 30 days to expiration.  Remember that OTM and ATM options haveno Intrinsic Value, so they must be made up purely of Time Value. Since we know that time value decreases exponentially during the finalmonth before expiration, it makes sense not to hold onto these options.
  • Sell options you don’t already own as anadjustment to existing trades – we’re not talking about creating nakedpositions here, the sold option would be complementary to your existingplay (for example, Bull and Bear spreads).
  • Buy short-term deep ITM options, e.g. a deep ITMput or deep ITM call will have lots of Intrinsic Value and virtually noTime Value.  If there is no Time Value, then it can't decay anyfurther, can it?  Remember about Time Value and Intrinsic Value.  Well,here we’re talking about there being so little Time Value as aproportion 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 illustrationof how theta decay works with options.  Notice how the slope falls offat its steepest during the last 30 days.

Diagram: Time Decay

Time Decay.jpg

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

Note that here we’re not advocating sellingoptions naked and exposing yourself to an unlimited risk profile. Manypeople successfully sell OTM options every month and collect a decentpremium. However, if the market suddenly jolts against them and theyget exercised, then an entire year or more can be wiped out (or more)in literally one day. The fact remains that selling options naked isnot a businessperson’s way to trade. Although there are somehigh-probability mathematical techniques of naked options selling, ifyour capital can be wiped out that fast when you’re not looking, thenthat’s simply not a sensible way to go about your business. It’s farbetter to be able to sleep at night, that way you’ll pass the test oflongevity and be able to consistently trade and invest for many yearseven well into your retirement.

 

Buy short-term Deep ITM options


You can mitigate the effects of time decay by buying Deep inthe Money (DITM) options, the reason being because Intrinsic Value isvastly outweighing Time Value. If there is little to no Time Value inthe option (as compared with Intrinsic Value) then your risk exposureto time decay is, by definition, little to none!

Diagram: Time value for deep ITM options

Time Value for DITM.jpg

Example:

Let's say a stock is priced at $42.10. There areonly 18 days left to the May expiration and just over six weeks lefttill 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                      27.80        
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 theentire option premium which is taken up by Intrinsic or Time Value asthe option gets Nearer the Money)

Call option           Last ($)        Intrinsic Value        Time Value        
May 12.5                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 heavilyweighted by Intrinsic Value and minimally weighted by Time Value, thusreducing the exposure to time decay? And how Time Value tends todominate the short-term ATM options?


Say we have a simple call option, the stock price is $69 and the 70strike January call option is priced at $9.80. Let’s look at the thetaas at 20 April and compare it with the position of theta with only onemonth left to expiration:

Notice how both theta lines are negative butespecially notice how much more theta decay is harming our long callposition when there is only one month left to expiration. Also noticehow theta is at its lowest at the $70 level, i.e. At the Money (ATM).


Chart: Long Call theta profile

 
Long Call Theta.jpg

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

Chart: Long Put theta profile

Long Put Theta.jpg

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

Chart: Short call theta profile

Short Call Theta.jpg


Chart: Short put theta profile

 
Short Put Theta.jpg
Generally, when theta is positive, time decay is helping the position. When theta is negative, time decay is hurting the position.  When webuy options, we have a negative theta, indicating that time decay hurtsour long option position.  This makes sense as an option is a wastingasset.  When we write options, we would expect the opposite to be thecase, which of course it is.  When we write an option, its value willdecline as we approach expiration.  If we write a $1.00 OTM option with10 days left to expiration, assuming that time decay reduces the optionby $0.10 per day, then by day 5, we’d only have to pay $0.50 to buy itback, 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 optionfrom us with only 10 days to expiration has lost 50% within the first 5days assuming there is no movement in the stock price.  

If time decay is unhelpful to your long optionpositions, then it stands to reason that it will be helpful to yourshort option positions. You can see this by way of simple graphicalrepresentation in that now the theta lines are positive, showing thattheta decay is helpful to a short option position.

Diagram: Theta Summary

Theta Summary.jpg