Measuring Risk; Using ‘The Greeks’

Attention option rookies:  It's time to spend some time discussing 'the Greeks.' 

It's difficult to spend much time reading about options without encountering several mentions of specific Greek letters.  If those encounters have been confusing, I hope this simple lesson brings clarity.

One of the advantages of trading options instead of stocks or index funds is that it's far easier to measure and manage risk.  With stocks, the risk is pretty much limited to how much the stock can rise or fall.  When dealing with options, you can track risk associated with stock price movement, implied volatility, the passage of time, varying interest rates, plus others that we will avoid here. [I haven't paid much attention to others for many years.]

It has universally been accepted to use Greek letters (except that one of the letters is not Greek!) to express those risk factors.   

There are five basic Greeks that are used by the majority of investors, but there are others that are used only by those who are more sophisticated and who seek  any tiny edge then can accumulate when trading.

For our purposes, let's talk about delta, gamma, vega, theta, and rho.

The term
'approximately' is used below because there are several risk factors in play simultaneously,
and each affects the price of an option. 
You can estimate the effect of a specific risk factor (Greek), but cannot know with certainly how the option price will be affected in the marketplace because all variables are coming into play at the same time.

EXAMPLE: A stock moves from 40 to 41.


Delta
is an estimate of how much the price of an option changes when the underlying asset moves one point.

Call options have a positive delta.
Put options have negative delta.

In the example, a call option with a delta of .60 should increase in value by approximately $0.60.  Similarly, a put option with a delta of -.25 should decrease in value by approximately $0.25


Gamma
is an estimate of the rate at which delta changes when the underlying asset moves by one point (in either direction).

Gamma is always a positive number. 

If the gamma of an option is five (that means 0.05), then the delta of the call (example above) increases by five when the stock moves one point higher – from .60 to .65.  It decreases by five when the stock moves one point lower, from .60 to .55.

NOTE:  In our example, the call option began with a delta of .60 and ended with a .65 delta.  Thus, over the one point move from 40 to 41, the average delta was 0.625, and the option price is expected to increase by $0.625, not $0.60

If the put has a gamma of two, then the delta moves from -25 to -23 when the stock moves from 40 to 41, and would move from -25 to -27 if the stock declined from 40 to 39.

Theta represents the value of an option that is lost as one day passes.  Options are wasting assets, and theta measures the rate of decay.

Vega is not Greek, but no one seems to mind.  It measures the change in the value of an option when the implied volatility (IV) increases by one point.  Vega is a positive number and is the same for the put and call with the same strike and expiration.  Both options increase in value when IV increases.

Rho represents the change in the price of an option when interest rates increase by one point.  Rho is the least important of these risk parameters and only becomes important when the option has a long lifetime (thinks LEAPS) or interest rates undergo a drastic change.

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4 Responses to Measuring Risk; Using ‘The Greeks’

  1. JCVictory 05/20/2009 at 8:11 AM #

    I have always been a bit confused about theta.
    This might be a strange question, but I’ll ask it . . .
    Let’s say I have an Iron Condor with a theta of 10, so I’m collecting $10 in premium on this position each day. Is this $10.00 gain reflected in changes in bid / ask spreads on the various options on the morning open?
    Of course, I imagine theta gain is “everthing being equal”, and volatility and price changes would reduce or augment any theta gains.

  2. Mark Wolfinger 05/20/2009 at 9:04 AM #

    Good morning James,
    Not strange at all.
    Let’s look at this from the point of view of a market maker – the person who publicly displays bids and offers for all options that trade in his pit on the trading floor.
    He/she uses a computer to calculate the theoretical price of the option. From that theoretical price, coms the bids and offers.
    That computer is fed all appropriate information – including a method for determining which violatility (and skew) to use for each individual option series etc.
    Built into that is the recognition that time is passing and that option values are declining because of theta. The MMs do not set their computers to think: “ok, today is a new day, so we’ll move the clock forward by 24 hours.” Most have a built-in algorithm that recognizes that time passes smothly and the computer takes the current time into consideration when calculating a theoretical value.
    That means the answer is ‘no,’ You will not see the effect of theta each morning. It’s a continuous process. More than that, as you mention, the effect of theta could easily be dwarfed by a change in implied volatility.

  3. JCVictory 05/22/2009 at 11:44 AM #

    Interesting . . .
    I’ve also heard that Market Makers do something (I’m not sure what) to prevent people from selling options on Friday and then collecting two free days of theta. Is this true? If so, do they simply lower the bid / ask prices on Friday?
    James

  4. Mark Wolfinger 05/22/2009 at 12:42 PM #

    JC,
    1)It really bothers me when people try to blame everything on the market makers. To me, those are just people who lost money and must find somone else to blame. You are too smart to fall for that stuff. You will run into a lot of it.
    2) Look at it this way: You enter an electronic order. How is anyone know if it’s a ‘legitimate’ order, or somone trying to steal THREE days of theta? Impossible. There is nothing the market makers can do to prevent you from trading.
    3) It is not three free days of theta. Wars can begin over the weekend. The US government has made significant announcements over the weekend. Remember Bear Stearns and Lehman Brothers? There was no free time decay over those weekends.
    4) Do you believe anyone in his/her right mind would attempt to gain by selling naked options on Friday and buying them back Monday? Slippage is far greater than three days of theta.
    And if you are referring to spreads instead of naked options, then the slippage is even worse.
    This is not something anyone who understand how options works would attempt. That being said, if you plan to sell some options for your position, you are probably better off selling Friday than Monday – but don’t force the trade to gain three days of theta.
    5) I’m sure all market makers use a timing algorithm that moves the clock faster than real time, so that by the time Friday arrives, the clock that calculates the value of an option (and thus, the bids and offers) is already using a time that’s at least Saturday and accelrates as the day progresses. So yes, that’s how they lower bids.

Please share your thoughts.