Collecting Theta in practice

Discussion in 'Beginner Traders' started by Evgeny, Apr 27, 2017.

  1. Evgeny

    Evgeny New Member

    Hi all! My question may sound strange and naive but this is sth I really can't understand.
    Reading about the Greeks I usually come across phrases like 'collecting theta', 'collecting delta' and so on. But what does that collecting mean practically?
    Say I've bought some credit spread and held it for 10 days. If it's theta was 0.18 - does that mean that I should collect 1.8 of theta altogether? If yes, how and in which moment I'll get this money as profits?
  2. Tim

    Tim Well-Known Member

    Hi. Good Question.

    Theta represents daily time decay and is defined as how much an option's premium declines in a day. Specifically it is the time value that decays but since the total premium is composed of time value and intrinsic value, it is the amount the premium declines in a day.

    If you are long the option, theta decay hurts you. Simply because if you buy it for say, $1.00 and it decays .18 per day, it will be worth $.82 the next day (all other things being equal). Multiplied by the multiplier of 100 for most options, you lose $18 per day to theta. If you are short the option, your position goes up in value $18 per day that you are in it. Again because you sold it for $1.00, and the next day you can buy it back form $82 or $18 profit.

    Theta is reported differently in different platforms. It may show as positive or negative. I think of the decay as the absolute value of whatever number is reported.

    So "collecting theta" is a common term for saying that your short options rise in value by the amount of the theta every day.

    Now there is a distinction: Theta varies as the option is more ITM or OTM. It is greatest when the option is ATM, ;less above or below the money. So if an ATM call option has theta of $.30, but by the next day its premium rises in value because the underlying rose, its theta might now be .20. How much theta would you have "collected" on your short position that day? You would only "collect" .30 if the theta was still at .30 but it isn't. It is now .20 and that would be the amount of decay "built in" at the new price. It is important to know because you might be in a butterfly position and see a theta of $30, but the next day your position theta might only be $15. You didn't gain $30 because of the change.

    I realize that this explanation may not be academically 100% correct but it comes from practical experience.

    This is assuming that delta, and volatility remain the same. They don't. The change in price day to day is affected by all three greeks. As well as market order flow and bid-ask spreads at the time.

    Lastly, I will use an example. Many people think that if they sell options on Friday and buy them on Monday they can automatically get 3 day's worth of theta. That often isn't true. Market makers realize that people will try this and can lower the premium you can sell on Friday and/or raise it on Monday which often eliminates the weekend theta gain. Sooner or later they must price the options in line with their theta greek (if they didn't there would be arbitrage opportunities), but they have the ability to manipulate the prices in the short term. Often weekend theta decay "comes out" Wednesday or Thursday the week before, or Monday or Tuesday after. Sometimes even longer. In option vue we can see this effect if the Graham dot is above or below the t+0 line. It manifests itself as distorted IV.

    Will comment on delta more later I have to run to a meeting for now.
    Evgeny likes this.
  3. Neil

    Neil Active Member

    I hope this isn't too long winded.

    Theta is the time value of an option. As time moves to expiration the value of Theta decays. Assuming the market stays flat and the other Greeks don't change much, if you have sold Theta (your position has positive Theta) you get to keep whatever Theta decay has occurred until you close your position. If you hold your position until expiration, you will get to keep all of the Theta that you sold when you opened the position. That is "collecting" Theta (I'm not sure I've heard the term "collecting Delta"). You can skip the rest of this if you already understand how the rest of the Greeks impact options.

    But the other Greeks also impact the value of your position. If Delta is negative (most of our trades lean negative Delta when they're opened) and the market goes down, you will collect additional income from the Delta change in the position (market goes down - negative change - multiplied by a negative Delta = a positive number). Of course Delta changes as the market moves and if Delta moves into positive territory on a downward move you will start losing money (market goes down - negative change - multiplied by positive Delta = a negative number).

    As the market moves around the value of Delta changes and the amount of the change is defined by Gamma. When the curve of the T+0 PnL line is "humped"* Gamma is negative, when the T+0 PnL line is curved upward* Gamma is positive. Gamma is zero when the slope of Delta changes from being humped to curving upward. You can see this in ONE by watching the value of Gamma as you move across the T+0 PnL graph, pay attention to how Gamma changes as you move back and forth. Our strategies typically start with negative Gamma. When the market moves down the value of Delta increases because of negative Gamma (market goes down - negative change - multiplied by negative Gamma = a positive number). On down moves eventually all of the positive Deltas (caused by Gamma) added to an initially negative Delta position will cause the Delta of the position to turn positive, from then on continued downward market movement will cause the position to lose money.

    Volatility also impacts the value of a position but it also decays until expiration. If the options of your strategy all expire at the same time the impact of Vega on the trade will decay to zero at expiration. So vertical spreads, butterflies, and condors using options that all expire at the same time will eventually be unaffected by Vega. But during the life of a trade Vega can have a big impact on the T+0 PnL of any strategy. Strategies that use options with different expirations (Calendars and Diagonals) may be profitable (or not) solely because of differential changes in volatility of the front month vs. back month options during the life of the trade.

    * Technical terms ;) - "humped" is similar to being on top of a hill, curving up is like the shape of a bowl.
    Evgeny likes this.
  4. Evgeny

    Evgeny New Member

    thanks for all of these marvelous comments, really appreciate!
    may I give an example to be sure if I've got all that right
    say, I'm selling an Iron Condor for overall credit of 2. this is a delta neutral strategy, and let's assume that VI also doesn't change significantly.
    so say, I sold it 60 days to expiration with theta being +0.2
    what (all thing being equal) will be my profit if I close my position in 30 days when the price stays somewhere between my spreads (in the "green" zone)?
    will it be 2+(0.2*30)?
  5. ACS

    ACS Well-Known Member

    Theta, like all the Greeks is dynamic and will change with time, volatility and skew. Even if the price and volatility don't change, the P&L in your scenario will almost surely be different because the Theta will change over the course of those 30 days.
    Evgeny likes this.
  6. Bruno

    Bruno Moderator Staff Member

    Most of us here are market neutral rather deeply negative Vega traders. In terms of modelling, Greeks calculate sensitivity (1st and 2nd order derivatives) to various parameters like underlying price, IV etc. Collecting Theta is a misnomer and I would rather focus on collecting premium. For simplicity's sake, let's say that your highest Greek, most often Vega, will take precedence on others hence collecting premium (all other things being equal) then means collecting Vega.
    Evgeny and Steve S like this.
  7. onyxperidot

    onyxperidot Well-Known Member

    Having sold your condor for a credit of $2, your plan (hope) is that the market will stay in your profit zone, i.e. between your 2 short strikes. If you held on to your condor until expiration, your condor's market value would decline to $0, and you would keep your $2 premium. If you wanted to close your condor position 30 days before expiration while the market was still in the profit zone, you would have to buy your condor back at market value which has to be less than $2 in order to yield a profit. The market price of your condor should be [ $2 - cumulative theta decay since you opened the condor ]. The decay might be somewhere near 0.2*30 with a significant margin of error because theta decay is non-linear. The actual price of your condor would mostly depend on the then prevailing implied volatility and market price of the underlying security.
    As Bruno has pointed out, you are collecting Vega because you sold your condor at a price based on implied volatility such that you are obligated to receive realized volatility of the underlying for the duration of the contract. In essence you are betting that realized volatility will be less than what implied volatility indicated. If you had been wrong, realized volatility would have exceeded implied volatility -- the underlying would have moved so much that it was outside your profit zone (beyond your short strikes in either direction).

    If you want a deeper understanding of trading volatility, I recommend Euan Sinclair's book "Volatility Trading -- 2nd edition".
    In chapter 6, equation (1.12) states that your option position total profit and loss is approximately equal to
    Vega * (Sigma - Sigma_implied) or Vega * (Realized_volatility - Implied_volatility).
    He also commented on forecasting volatility in his blog .
    Last edited: Apr 28, 2017
    Evgeny likes this.
  8. Evgeny

    Evgeny New Member

    thank you very much! it's much clearer now

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