From The Baseline Scenario:
This guest post is contributed by Ricardo Fernholz, a professor
of economics at Claremont McKenna College. Some of his other work was
profiled on this blog here.
The rise of high-frequency trading (HFT) in the U.S. and around the
world has been rapid and well-documented in the media. According to a
report by the Bank of England,
by 2010 HFT accounted for 70% of all trading volume in US equities and
30-40% of all trading volume in European equities. This rapid rise in
volume has been accompanied by extraordinary performance among some
prominent hedge funds that use these trading techniques. A 2010 report
from Barron’s,
for example, estimates that Renaissance Technology’s Medallion hedge
fund – a quantitative HFT fund – achieved a 62.8% annual compound return
in the three years prior to the report.
Despite the growing presence of HFT, little is known about how such
trading strategies work and why some appear to consistently achieve high
returns. The purpose of this post is to shed some light on these
questions and discuss some of the possible implications of the rapid
spread of HFT. Although much attention has been given to the potentially
destabilizing effects of HFT, the focus here instead is on the basic
theory behind such strategies and their implications for the efficiency
of markets. How are some HFT funds such as Medallion apparently able to
consistently achieve high returns? It is natural to suspect that such
excellent performance is perhaps an anomaly or simply the result of
taking significant risks that are somehow hidden or obscured. Indeed,
this is surely the case sometimes. However, it turns out that there are
good reasons to believe that many HFT strategies are in fact able to
consistently earn these high returns without being exposed to major
risks.
To understand how this works, let’s
consider the S&P 500 U.S. stock index. Suppose that we wish to
invest some money in S&P 500 stocks for one year. Currently, Apple
has a total market capitalization of roughly $500 billion, making it the
largest stock in the S&P 500 and equal to approximately 4% of the
total capitalization of the entire index. Suppose that we believe it is
very unlikely or impossible that either Apple or any other corporation’s
capitalization will be equal to more than 99% of the total S&P 500
capitalization for this entire year during which we plan to invest. As
long as this turns out to be true, then it is actually pretty simple to
construct a portfolio containing S&P 500 stocks that is guaranteed
to outperform the S&P 500 index over the course of the year and that
has a limited downside relative to this index. In essence, we can
construct a portfolio that will never fall below the value of the
S&P 500 index by more than, say, 5% and that is guaranteed to
achieve a higher value than the S&P 500 index by the end of the
year.[1]
This is not a trivial proposition. If we combine a long position in
this outperforming portfolio together with a short position in the
S&P 500 index, then we have a trading strategy that requires no
initial investment, has a limited downside, and is guaranteed to produce
positive wealth by the end of the year. According to standard financial
theory, this should not be possible.[2] Furthermore, the assumptions
that guarantee that our portfolio will outperform the S&P 500 index
appear entirely reasonable...MUCH MORE
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