In the good old days (precisely defined as the years
1989-1994), I worked on the floor of the Chicago Mercantile Exchange. It was a
rowdy, physical, loud, and awesome experience. A normal day had me standing at
my post in the British Pound or Japanese Yen pit by 6:30 in the morning so I
could secure my spot for the 7:20 am opening. You really got to know the people
standing six inches from you all day! What a different world from the moment,
huh? By the time the pits closed at two in the afternoon, I would be sweaty and
exhausted. Every day was like a workout.
One of the most important things I had to master in trading currency
options was hedge management. There are four very basic paired actions for an
options trader when managing his hedge position: when buying calls, sell some
of the underlying; when selling calls, buy some of the underlying; when buying
puts, buy some of the underlying; and when selling puts, sell some of the
underlying.
Let me give you a practical example using stocks, which are
more familiar to most folks. Pretend Coca-Cola (KO) is trading at a price of
$50/share and I sell someone one of the December $60 calls. This call would
give them the right, but not the obligation, to purchase 100 shares of Coke from
me at $60 in December. They would have to pay me a premium for this right, and
I would pocket that money. The only problem for me is that by December, the
price of KO might be higher than $60.
Meaning I would lose money—quite possibly more than the premium I pocketed—to
fulfill the executed call. You can go broke doing that too often! To hedge this
risk, when I sold calls I would also buy some shares of KO to mitigate this
risk. But how many shares will completely hedge my risk? What is the proper
ratio? Should I buy 5, 10, 20, or more shares? This question plagued option
traders for many years, until the development and adoption of the Black-Scholes
model became widespread. Don't worry! We're not going to dig into that detailed
math today—talk about a workout! Instead, I want to focus on two key outputs
from that model.
The first is called Delta. Delta answers the riddle above.
At any given point in time, I can solve for the Delta of my option which is the
amount of hedging I need to do. For our example, let us pretend that when I run
Black-Sholes on the December $60 calls at the current market price for the
underlying stock ($50), I get a Delta of 0.35. This means I would need to buy
35 shares of Coke at $50 to hedge my 100 share sold call option. Delta can be
thought of as the first derivative of price. It actually gives me a
statistically accurate number on the rate of change in the price of my option,
relative to changes in the price of the stock. So, when a 100-share call option
loses a dollar, 35 shares of the underlying gain a dollar, and vice versa.
Hedged!
In theory, once hedged, a professional options trader should
not really care which way Coke moves.Keep in mind the four basic rules above. If I am buying and selling
calls and puts all day, and I calculate my hedges using the Black Scholes model,
I can put my on hedges and go take a nap, right?
Delta is super helpful, but the problem with it is that it's
constantly changing with the change of prices in the underlying. It is calculated
for a given price on the underlying—if that price changes, the proper Delta
also changes. If Coke starts diving, its Delta will decrease and I will have to
sell some of my stock (at a loss) to correctly manage my hedge. If it starts to
skyrocket, I would find myself in the unfortunate situation of being short 100
shares at $60 and so I would need to perversely start buying more stock (Delta
would be increasing). Do you see the conundrum? As the strategies get more and
more complex, managing their hedges gets tougher and tougher. Imagine if you
had call and put positions in multiple different stocks or products and they
are all moving fast at the same time. It can be really hard to keep up, I
promise you. So, this brings me to my title: Gamma Trap. Gamma is the rate of
change of the Delta, and it can (and has) ruined the careers of many
professional option traders.
Ok, great. What does any of this have to do with fixed
income investing?
It turns out that most financial institutions are
professional options trading operations. Yes, it's true. The only functional difference between them and
pit traders of yore is that most financial institutions only SELL options. And for
the most part, they sell CALL options. Think about this. It may take a few
seconds to settle in. A loan that can be paid back early is a sold call. A
mortgage-backed security that can experience prepayments is a sold call or set
of calls. And the most obvious: The purchase of a callable bond is a sold call.
Callable bonds are perennially among the most popular
investments in the fixed income world. Purchasing a callable bond is also
simultaneously selling an imbedded call option, which gives the issuer the
right, but not the obligation, to purchase the bond back at a future time and
price (almost always $100.00) even if the value of the underlying is much
higher. This is similarly true in mortgage pools and securities, in which case
the individual borrowers can independently "call" that part of the pool or
security at par, just when it was much more valuable. Almost all fixed income
portfolios are riddled with short option positions, so I can assume that many
of the readers of this post, by definition, are actively managing their edges
by buying and selling the "underlying"…right? Sure! We are constantly
re-running our Black-Sholes model to find Delta, and then…but we don't do that,
do we?
But most investors do something similar. Duration and Modified
Duration are actually highly analogous to Delta. It is an attempt to calculate
the rate of change in the price of fixed income securities, and it is the first
derivative of price, just as Delta is for options. Unfortunately, it also has
the same perilous flaw as Delta. The problem with duration is that as the price
of the underlying changes, so does the proper value of duration. Remember how
crazy it sounded for an options trader trying to manage his hedges on many
different stocks, all moving quickly at the same time? You are doing the same
thing if you are managing a fixed income portfolio and relying on duration to
manage your hedge—that is, to control your risks.
Think about the past 3-4 months. What has happened to the
price (rates) of the fixed-income underlying? They have soared higher, as rates
screamed lower. What has happened to durations across the country? They have
all gotten shorter, lower, as the call options we have sold in the past have become
more and more "in the money." This can become a vicious cycle, as more and more
people look at their portfolio reports and realize that all of a sudden they
need to "add" duration, and so buy longer and longer bonds. Unfortunately, most
market participants actually compound their problems, because as they buy these
longer durations, they simultaneously again sell (imbedded) call options!
Uh-oh! In the CME pits, we called this cycle a "Gamma Trap."
When something started moving really quickly, some hedgers would
start chasing their short option positions until they were fully committed, and
sometimes it would then turn. The thing is, most professional option traders
lived off the premiums of selling short options and try to avoid ruin through
hedging. Unfortunately, every once in a while someone would get wiped out. I
have seen many an option trader get pulled out of the pit by the margin clerks
because his account had gone upside down.This was almost always the result of falling into a Gamma Trap.
Did I mention most fixed-income investors are also short
tons of options?
Houston—we have a problem.
So, what's the solution? We need to really question and
understand our option positions. We need to stop relying on a single statistic
parameter like duration because it will change! It is a real-life Gamma Trap, and
I fear that it is happening to many investors right before my eyes.
As I have mentioned in earlier posts, it is my belief that our
industry needs to take a more disciplined approach to understanding our
portfolios—over time and across different possible future interest rate
scenarios. Furthermore, we need to do this in the context of institution-wide
modeling; options, as well as potential hedges, lie in many spots across our balance
sheets.
I can't promise this discipline will be easy, but it can be very
rewarding. More on this next time.
Final, final thought: I played golf this weekend and was reminded
that I should probably take up tennis instead.
