THERE’S A HELPER LURKING
But delta has an accomplice. An evil enabler
that should, in a fair world, get its share of
blame for the “l” half of “p/l.” Gamma, we’re
looking at you.
First, the textbook definition of gamma:
It’s the second derivative of the option’s price
with respect to the stock’s price. It’s how
much an option’s delta changes when the
stock price changes $1. Some traders leave it
at that—potentially, to their peril.
Let’s say you’re bullish on a $100 stock,
and you short a $95 put for a $1 credit with 45
days to expiration. The put has a delta of 0.23,
giving it risk equivalent to about 23 shares of
long stock. You’re cool with that. Two weeks
pass, the stock is still at $100, and your short
put’s price has dropped to
$0.65—time decay in action!
The put’s delta has dropped
to 0.19, which means you now
have less delta risk than you
did two weeks ago. What’s
not to love?
You’re still bullish as the
stock moves up and down a
little for the next 28 days, but with three days
to expiration, the stock has dropped to $97.
The put’s now worth about $0.13—still profitable—and its delta is only about 0.14. You
figure you can handle the risk of 14 shares
of stock. So, you keep the short put on until
expiration, confident the stock won’t drop
below $95 in the next three days.
But it does. Ouch.
While you were watching the stock’s price
and the put’s delta, the gamma of that short
put went from a tame - 4 when it had 45 days
to expiration and the stock was at $100, to
a wild - 12 with three days to expiration and
the stock at $97. So for every point the stock
moved down, the short put would be manu-
facturing three times as many long deltas as
when you first put the trade on. Your delta
risk now fluctuates much more as the stock
With one day to expiration, the stock is
at $95, the put’s delta is 0.50 (which may be
more risk than you’re comfortable with), and
the put’s gamma has grown to -0.38. As the
stock drops from $95 to $94, the put’s delta
grows to 0.83. As the stock moves back to
$96, the put’s delta drops to 0.16. Your risk is
fluctuating dramatically with every point the
stock changes. Yes, your p/l is being driven by
the put’s delta. But it’s really the put’s short
gamma that’s making the trade’s risk tough
Negative gamma manufactures negative
deltas when the stock rises, and positive
deltas when the stock drops. Positive gamma manufactures positive deltas when the
stock rises, and negative deltas when the
Gamma is what makes your delta go from
mild to ferocious, from small to large. If you
trade options, you’ll have gamma. If gamma
didn’t exist and the option’s delta stayed
constant, an option would act a lot more
like shares of stock (which have delta, but
no gamma). Then you’d only have to worry
about the price of the stock going up or down.
But an option’s delta doesn’t stay constant.
And the instability of that delta depends on
the option’s gamma.
Likewise, gamma itself isn’t constant. All
things being equal, gamma is highest for the
at-the-money (ATM) options and is lower the
further an option is out of the money (OTM).
Gamma is also higher the closer an option is
to expiration. In other words, the ATM op-
tion at expiration has the highest gamma.
This is often why traders get excited
about expirations. Expirations are busy
times—rolling positions, adjusting hedges,
getting ready to exercise or be assigned
on in-the-money (ITM) positions. Those
activities become more urgent around ex-
piration, partly because deltas can fluctuate
from big to small with relatively minor price
changes for stocks and indices. And that’s
caused by large gamma.
If gamma’s so important, where can you
find it? On the thinkorswim® platform from
TD Ameritrade, you can see each option’s
gamma on the Option Chain on the Trade
page. Load gamma as one of the columns to
see that gamma is higher for ATM options,
for example, and how gamma changes from
one expiration to another.
You can see the gamma of your positions
on the Position Statement section of the
Monitor page (Figure 1).
Here you see how much gamma you have
relative to your deltas. The position can
also be beta-weighted to show how much
beta-weighted gamma could affect beta-weighted deltas.
Say the beta-weighted gamma is -1.34, and
the beta-weighted SPX delta is -77. If the SPX
moves up a point, your delta would theoretically go from -77 to -78.34, and if the SPX
moves down a point, the delta would theoretically go from -77 to -75.66.
Yet, as time passes, that gamma could
grow, even if the deltas don’t. Which is why
you need to monitor your portfolio’s gamma
as much as its delta.
FIGURE 1: Delta vs. gamma. On the Monitor page of thinkorswim, bring up the position statement and beta-weight an entire portfolio to an index to see gamma relative to deltas.
POOR OLD DELTA ALWAYS GETS THE BLAME WHEN A STOCK GOES AGAINST AN
OPTION POSITION. IF YOU SHORT A PUT AND THE STOCK DROPS, THE PUT’S LONG DELTA
IS CAUSING THE PAIN. IF YOU SHORT A CALL VERTICAL AND THE STOCK RALLIES, THE
VERTICAL’S SHORT DELTA IS COSTING YOU EVERY POINT THE STOCK GOES UP.
delta and gamma