The Greeks. Are they Greek to you? Part II

This is an important, basic two-part post for rookies and anyone who wants to learn about using 'the Greeks' to manage the risk of an option position.  Part I.

Each Greek does its own thing

In your example, the position delta is -59, and that translates into an expected loss when the stock moves higher by one point.  I mentioned that the delta is not a constant number, but changes as the stock price changes.  It's gamma that measures the rate at which delta changes.

Your position has -3 gamma.  In terms you an apply to managing the position, that means:

  • If the stock moves lower by one point, you gain 3 delta.  Negative gamma works against you.  Thus, you get shorter on rallies and longer on dips.  Positive gamma works in your favor

  •  If the stock price moves one point lower, the position delta becomes -56.  If the stock moves one point higher the position delta becomes -62

  • Even that is an approximation because gamma is not constant.  It's rate of change is measured by a different Greek.  For the vast majority of trades made by individual investors, it not necessary to be concerned with such details.  Professional traders, who seek every possible penny in edge and take extraordinary caution to trade as 'Greek neutral' as possible, pay careful attention to these Greeks

  • More sophisticated traders also measure the rate at which change in volatility affects gamma.  To learn more about the less frequently used Greeks, this Wikipedia article is a good place to start.  But it's not necessary for us to delve that deeply into how options are valued


You begin the day short 59 delta.  When the stock rallies by one point, the -3 gamma tells you that the new delta should be -62.  Be careful with this next sentence; it's not tricky:  Thus, on average, you were short 60.5 delta over that one point move (59 at the beginning and 62 at the end).  A better estimate of the real world loss is $60.50, rather than $59.


Time decay

Your position theta is 14.  That should translate into a one-day profit of approximately $14 as a result of time decay.   As you probably already know, theta is not constant.  It accelerates as time to expiration decreases.

So, if you lose money ($60.50) on a one point rally, you can anticipate that the real lose may be $14 less, or $46.50 due to the effect of positive theta.

Vega

If the implied volatility changes, the vega component of your position results in a change in the daily profit and loss. 

Bottom line:  The Greeks provide a
reasonable estimate of risk – or how much to expect to make or lose when
the market moves.  Many Greeks interact, so the final result cannot be
exactly predicted. 

Even if you were able to be that accurate, the real world pricing of options (the option price (called the 'mark') that represents the value of the options in your account) can vary from day to day for random reasons.

Don't drive yourself crazy trying to get an exact handle on profit and loss possibilities.  Look at the bigger picture.  If a certain event (stock moves by 7%, for example) results in a predicted loss of $100, it does not matter if the loss is $105.  What must concern you is being aware when a loss that's too big to handle may occur (perhaps when stock is up 12%) – and taking action to reduce the effect of such an event.  That's referred to as adjusting a position.

Clarification:  If that 12% move is dangerous, you may decide not to do anything right this moment to reduce your exposure to loss.  But, if the stock creeps higher, at some point you cannot continue to close your eyes to a dangerous possibility.  Making a small change to your position can be a good way to reduce your potential loss.

There are no hard and fast rules.  The purpose of this two-part post is to be certain you are aware of how useful the Greeks can be in helping you manage portfolio risk.

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4 Responses to The Greeks. Are they Greek to you? Part II

  1. 5teve 04/05/2010 at 8:47 AM #

    Hi, Mark
    Thanks a lot, it is very helpful to me. It gives me a sense of importance of Greeks and connection to the real world trading.
    For Position Vega of -7.49, does it mean I lose $7.49 at the day when IV changed? If Pos.Vega is positive, then I earn a profit at the day.
    Thanks again, Steve

  2. Mark Wolfinger 04/05/2010 at 9:26 AM #

    Puts and call for the same strike and expiration have the same vega.
    If you own an option, you have positive vega. If you sell an option, you have negative vega.
    If the implied volatility moves higher by one point, the value of the option increases by that vega.
    Same for portfolio: With -7.49 position vega, when the imlied volatility moves higher by one point, you should expect to lose $7.49.
    This has nothing to do with the passage of time.
    When IV changes, the price of the option changes immediately (This is the chicken/egg problem: the higher option prices means IV has increased. On the other hand, the higher IV means that the option price increased).
    At the end of the day, it’s difficult to determine exactly which risk factors contributed to the daily profit and loss – because each Greek is a factor in the P/L. But more importantly, the closing price of the option is somewhat random – based on the last trade or the last bid/ask market displayed. Often that’s more than enough to more than compensate for a small factor such as -7.49 vega.

  3. 5teve 04/05/2010 at 9:46 AM #

    Hi, Mark
    Thanks for your helpful response. Can’t wait to learn more from your book “The Rookie’s Guide to Options”. I think I will ask more questions while I reading it.^^

  4. Mark Wolfinger 04/05/2010 at 10:05 AM #

    Thanks,
    Questions welcome
    Regards