Measuring Market Impact: Transaction Cost Analysis Comes to the Futures Market
by Galen Burghardt
One of the main reasons futures have been such successful trading
instruments is that they almost always are cheaper to trade
than their related cash instruments. As a result, we have attracted
a cost sensitive clientele. And with every passing year, our markets
have become more liquid and more efficient to trade.
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Even so, one area in which the futures industry lags behind the
securities industry is in providing clients with estimates of market
impact and transaction costs. In the U.S. equities market, transaction
cost analysis has been an area of real competition among
broker-dealers for some time, and a lot of interesting quantitative
work has been done in that area.
This is now beginning to happen in the futures industry. The rapid
growth and expansion of electronic trading now makes it possible
to study transaction costs in a way that conventional pit trading
did not allow.
In talking about transaction costs, this discussion is not referring
to brokerage commissions or exchange fees. Rather, electronic
trading makes it possible to analyze the cost of market impact
with much greater mathematical precision than ever before. To
put it another way, we can use the vast amount of data generated
by electronic trading to analyze the daily ebb and flow of liquidity
and use that information in trading strategies. This is especially
important for institutional customers, such as money managers or
hedge funds, that want to trade in size and can benefit from quantitative
estimates of the potential cost from moving the market
one way or the other.
We now have several years of electronic
trading in the major interest rate contracts
under our belts, and even longer with the
stock index products. More than 80% of
Eurodollar futures are traded electronically,
and average daily volume in the E-mini stock
index contracts far outstrips their larger
brethren still traded on the floor. In addition,
the falling cost of computing power makes it
more feasible for the large broker-dealers and
the large funds to perform complex calculations
on very large amounts of data.
So it is entirely possible to compile a continuous
series of tick-by-tick market data for a
wide range of futures contracts. Calyon
Financial recently completed just such a project,
and the results have proved to be quite
useful in helping our clients minimize the
market impact of their trades. And we are
well aware that a number of money managers
with experience in these markets are undertaking
similar projects, and in some cases
have already modified their trading strategies.
Having the ability to make precise measurements
of market impact can be useful in
at least three trading applications. These
include optimal trading strategies, that is,
those that are designed to minimize market
impact or produce the best trade-off between
market impact and tracking error. A second
is the design of tactical execution rules for
working orders, such as in determining the
likelihood for being filled at the bid or the
offer. A third is in the analysis of benchmarks,
tracking error, and execution costs.
The remainder of this article provides
some examples of the kind of transaction
cost analysis that is now possible with electronic
trading. The examples are drawn from
a longer paper published by Calyon, which
explains in detail how the various calculations
were made. One interesting aspect of
the analysis is that the results confirm several
theoretical insights into market behavior.
Building the Data Set
Calyon Financial has invested heavily in
gathering a continuous time market depth
database that allows us to observe the limit
order book in nearly continuous time and to
track the flow of actual trades. In the case of
the limit order book, we are tracking the best
five bids and best five offers. This data set is
exceptionally valuable for studying market
liquidity and the impact of trades of various
sizes throughout the course of a trading day.
For example, it allows us to calculate a
sweep-to-fill measure of market impact—the
effect on the price of instantaneously trading
as far into the order book as necessary to fill
an order of a given size. For large orders, it
may be necessary to go well beyond the number
of contracts available at the best bid or
best ask, and the resulting average price is
known as a sweep-to-fill price.
As of this writing, we are gathering data
for 51 markets—16 equity, 12 bond, 6 money
market, 7 currency and 10 energy. We are
also gathering data on calendar spread trading
for 24 of these markets. And we continue
to add to the list as quickly as we can.
We also have learned more than we
thought possible about the peculiarities these
data sets present. For one thing, synchronizing
clock times is a challenge. Filtering out
special trades from actual market trades is
another. Paying attention to the way that
exchanges aggregate data is a third.
Market Impact in Practice
Exhibits 1 and 2 provide two different
perspectives on market impact. Exhibit 1
shows the sweep-to-fill market impact cost at
a particular time of day over the course of an
entire quarter. The reason for picking a particular
time of day is that market impact is a
function of both volume and volatility,
which vary systematically and predictably
with time of day. In this case, the dataset
contains all trades in the E-mini S&P 500 at
8:40 a.m. for every trading day in the first
quarter of 2006. Typically the E-mini market
is very active at that time of day.
While there is considerable variability in
market impact for trades of a given size, the
scatter makes it clear that the impact of a
trade on the market is less than linear—that
is, market impact is not directly proportional
to the size of the trade. And the convex share
of the curve indicates that larger trades—
more than 1,000 lots—are not as expensive in
terms of market impact as one would expect.
Exhibit 2 looks at the same contract, but
this time the dataset covers the entire trading
day. We can see that the market impact of a
trade can vary a lot over the course of a trading
day. In this case, we find that the most
liquid time of day for E-mini S&P futures corresponds
to 3:00 p.m. Chicago time, which is
when the cash market closes. We can also see
that the futures market loses some liquidity
after the cash close but is still more liquid at
the futures close than at other times of the
trading day, including the futures open at
8:30 a.m. Exhibit 2 also confirms the non-linear
nature of market impact, in that the
sweep-to-fill cost for a 2,000 lot order is not
twice the cost for a 1,000 lot order.
Analyses like these can be very useful to
traders. For one thing, traders can identify
the most liquid times of the trading day. For
another, traders can make informed choices
between tracking error and the costs of trading,
rather than relying on subjective impressions
or past experience.
Market Impact in Theory
Our research on liquidity and market
impact suggests that we can explain what we
see in Exhibits 1 and 2 using the simplest
possible theory. In particular, if we assume
that the great pool of traders whose business
it is to provide liquidity can be represented
by a single, risk averse market maker, we can
first get an idea of how risk averse this hypothetical
market maker is by fitting a curve to
the scatter plot in Exhibit 1.
The rest of the theory suggests that the
bid/ask spread that the market maker would
quote is directly related to the volatility of
the price (i.e., its standard deviation) and is
inversely related to the square root of trading
volume. From the same data set that we use
for calculating sweep-to-fill prices and
impacts, we can calculate trading volume
and price volatility profiles by time of day.
Then, armed with our estimate of risk
aversion and our estimates of trading volume
and price volatility, we can produce theoretical
estimates of market impact like those
shown in Exhibit 3. For someone in research,
the beauty of this exercise is that the theoretical
market impact profiles in Exhibit 3 conform
almost perfectly to the empirical market
impact profiles found in Exhibit 2. In other
words, the simple theory works.
Hidden Liquidity
What you see with a limit order book is
not necessarily what you get. First, it shows
phantom liquidity—bids and offers to which
traders are not really committed and that are
withdrawn either for no apparent reason or
because the market begins to move in their
direction. Whether these are available for
sweep-to-fill orders is to some extent a matter
of timing and fast action. Also, the limit
order book does not reveal hidden liquidity—
all of those potential bids and offers
controlled by traders who don’t want to show
their hands.
Of the two, it seems that hidden liquidity
is the more important consideration when
analyzing market impact. As have others, we
find that the apparent impact of trades tends
to be smaller than sweep-to-fill measures of
market impact would suggest.
Using data for the first quarter of 2006,
we first calculated the distributions of sweep
to fill prices at the beginning of each minute
of each trading day. For each of these snapshots,
we calculate five sweep-to-buy prices
(exhausting the number of contracts offered
at each price) and five sweep-to-sell prices
(again, exhausting the contracts bid at each
price). We then calculate the absolute value
of the difference between these sweep-to-fill
prices and the true market price at each
moment. We then proceeded to see how
many contracts actually traded in the interval
immediately following each snapshot
(five seconds in the case of E-mini S&Ps)
and calculated the volume-weighted average
price at which these trades were done.
Comparing the two distributions, we find
that actual trade prices reveal more liquidity
than is apparent in the limit order book. As
shown in Exhibit 4, the effect of hidden liquidity
was worth slightly more than a cent for
small orders and just under two cents for
fairly large trade sizes. For intermediate-sized
trades, though, the presence of hidden liquidity
was worth considerably more. For
trades between 500 and 1,000 contracts, hidden
liquidity was worth 4.4 cents, while for
trades between 2,000 and 3,000 contracts,
hidden liquidity was worth about 3.8 cents
per contract.
Practical Applications
The range of possible applications for
these insights into market liquidity is fairly
broad. We find, for example, that the most
common trade size, at least in the E-mini
S&P 500 futures market, has become a one
lot, that is, a single contract. This suggests
that computerized trading platforms are
being used to minimize transaction costs by
minimizing market impact. The trading volume
profiles also can be used to conduct
what are known as VWAP (volumeweighted
average price) trades, which are
common in the equity world and which are
gaining a foothold in the futures world.
Market liquidity measures are useful in
choosing how to work orders over time and
allow those of our clients who are less time
sensitive than others to be providers rather
than consumers of liquidity. To this end, part
of our research has been devoted to scoping
out what might be called the efficient execution
frontier—those ways of working orders
that offer the greatest possible benefit in
exchange for the least amount of risk.
The same data set that allows us to measure
and monitor market liquidity also allows us
to evaluate the quality of trade execution
against objective benchmarks such as arrival
price, VWAP, or closing price. Our experience
suggests that brokers and their clients have
selective memories that give too much weight
to unusually bad fills and, as result, they tend to
choose execution strategies that give too much
weight to risk and not enough weight to
potential reward. Being able to assess trades
objectively will allow everyone to make more
informed decisions about how to trade.
We find too that this theory in practice
allows us to anticipate the effects of key scheduled
economic announcements. We find, for
example, that FOMC announcements produce
predictable spikes in both volume and
volatility that, in turn, radically change the
shape of the day’s market impact profiles.
Exhibit 1
Sweep to Fill Costs Versus Order Size
E-mini S&P 500 futures trades at 8:40 a.m. during the first quarter of 2006
Source: Calyon Financial |
|
Exhibit 2
Sweep to Fill Cost by Time of Day
E-mini S&P 500 futures during the first quarter of 2006
Source: Calyon Financial |
|
Exhibit 3
Theoretical Market Impact for
E-mini S&P 500 Futures on a Typical Day
(Projected spread to the “true” price)
Source: Calyon Financial |
|
Exhibit 4
Hidden Liquidity Summary for E-mini S&P 500 Futures
((1/3/06 - 3/31/06)
Source: Calyon Financial |
|
Galen Burghardt is senior vice president and director
of research at Calyon Financial Inc. and a member
of the editorial advisory board of Futures Industry. He
is also an adjunct professor of finance at the
University of Chicago's Graduate School of Business,
where he teaches an MBA-level class on derivatives.
He has published several articles and books on interest
rate futures and options and has served in the
research division of the Federal Reserve Board. He
thanks Jerry Hanweck, principal partner at Hanweck
Associates, a consulting firm specializing in investment
and risk management for financial institutions,
and Lauren Lei in the research department at Calyon
Financial for their contributions to the analysis of tick
size and transaction costs.
