Thursday, May 7, 2009

Gamma Facts

Gamma, the third letter of the Greek alphabet, is one of the more esoteric Greeks which measures the rate of change of Delta. Delta has been covered in depth in two prior posts. If you missed those posts you can review them here & here.

Delta ranges between 0 and 100 based on whether the option is ITM, ATM, OTM. Thus, as the underlying price fluctuates, delta changes as well. This is where Gamma comes into play.

Gamma measures the rate of change of Delta for a $1 change in the price of the underlying.

Gamma Essentials:

1. Gamma is usually expressed in deltas gained or lost per $1 change in the underlying. Suppose I own the following option on XYZ which is trading at $40:

July Call Delta = 50 Gamma = 5
If XYZ stock rises (falls) $1, my delta will change to 55 (45).
If XYZ rises (falls) another $1, my delta will change to 60 (40).

2. Whereas Delta is positive for calls, and negative for puts, Gamma is positive for both. Consider the following scenario:

ABC trading at $50
○Long 50 call, delta = 50, Gamma = 5
○Long 50 put, delta = -50, Gamma = 5
If ABC increased to $51, the calls will move ITM and puts will move OTM. Because the Gamma is +5, the new delta of both call and put can be calculated by adding 5 to their respective deltas:
○Long 50 call, delta = 55
○Long 50 put, delta = -45

3. Gamma is highest for short term options and lower for long term options.

The May options have a gamma around 5, June options are around 2, October options have gamma around 1, and Jan 2011 option's gamma is sitting at a measly .5.

4. Gamma is highest for ATM options and lowest for ITM or OTM options. In other words, the delta of ATM options changes much quicker than the delta of ITM or OTM options.

AAPL is currently trading around $132.50. As a result the May 135 calls (considered ATM) have a Gamma of 5. May 125 call's gamma = 3. May 145 call's gamma = 1

5. Gamma can be considered the ally of option buyers and enemy of option sellers.

ALLY of Buyers:

When owning positive gamma positions (think straddles/strangles), gamma serves to make you longer as the market rises, and shorter as it falls. Let's analyze 2 examples:

Long call trade on MNO, currently trading at $50.

Long Jul 50 call, Delta = +50
MNO moves to $55, Call delta moves to +70
○As the stock price moves in my favor, I get longer and longer (more delta), which makes me profit more quickly

MNO moves to $45, Call delta moves to +30
○As the stock price decreases I get less long (lower delta) which makes me lose money at a slower rate.

For a long call trade, Gamma is the characteristic of options that causes your position to get longer (profits accelerate) as the stock rises, and less long (losses decelerate) as the stock falls.

Straddle on MNO, currently trading @ $50
Long Jul 50 call, Delta = +50, Gamma = 5
Long Jul 50 put, Delta = -50, Gamma = 5
Net Delta = 0

MNO rises to $51
Long Call Delta = +55
Long Put Delta = -45
Net Delta = +10

MNO falls to $49
Long Call Delta = +45
Long Put Delta=-55
Net Delta = -10

For a straddle trade, Gamma is the characteristic of options that causes you to get longer as the market rises, and shorter as the market falls.

ENEMY of Sellers:

Gamma can be considered the enemy of option sellers. When owning negative gamma positions (think iron condors), gamma serves to make you shorter or more bearish as the market rises, and longer or more bullish as it falls. This is not a recipe for profits when the market is undergoing significant moves, such as the recent rally. Let's analyze 2 examples:

Naked Put on XYZ, currently trading at $50

Short Jul 45 put, Delta = +20 (I make $20 per $1 increase)
—XYZ moves to $55, Short Put delta moves to +10
○As the stock price moves in my favor, I get less long (lower delta) which results in making money at a slower rate.
—XYZ moves to $45, Short Put delta moves to +40
○As the stock price moves adversely (decreases) I get longer and longer (higher delta) which results in losing money at a quicker rate

6. Typically in positive Gamma trades we seek (realized) volatility, as the more the underlying moves the better your chances for raking in profits.

Examples of positive gamma trades are long calls/puts, straddles and strangles, and ratio backspreads. In each of these we're usually better off if the stock undergoes a large move in price.

7. On the other hand with negative Gamma trades we shun (realized) volatility, as the more the underlying moves the worse your chances for raking in profits.

Examples of negative gamma trades are short calls/puts, short straddles and strangles, Iron Condors and Butterflies. In each of these we're usually better off if the stock doesn't undergo a large move in price.

In our next installment on Gamma we'll review the relationship between Gamma & Theta, as well as review how Gamma plays out on a risk graph.

2 comments:

QUALITY STOCKS UNDER 5 DOLLARS said...

Interesting facts

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