Risk and Reward in High Frequency Trading

By Rajiv Sethi, professor of economics at Barnard College, Columbia University. Cross posted from his blog

A paper on the profitability of high frequency traders has been attracting a fair amount of media attention lately. Among the authors is Andrei Kirilenko of the CFTC, whose earlier study of the flash crash used similar data and methods to illuminate the ecology of trading strategies in the S&P 500 E-mini futures market. While the earlier work examined transaction level data for four days in May 2010, the present study looks at the entire month of August 2010. Some of the new findings are startling, but need to be interpreted with greater care than is taken in the paper.

High frequency traders are characterized by large volume, short holding periods, and limited overnight and intraday directional exposure:

For each day there are three categories a potential trader must satisfy to be considered a HFT: (1) Trade more than 10,000 contracts; (2) have an end-of-day inventory position of no more than 2% of the total contracts the firm traded that day; (3) have a maximum variation in inventory scaled by total contracts traded of less than 15%. A firm must meet all three criteria on a given day to be considered engaging in HFT for that day. Furthermore, to be labeled an HFT firm for the purposes of this study, a firm must be labeled as engaging in HFT activity in at least 50% of the days it trades and must trade at least 50% of possible trading days.

Of more than 30,000 accounts in the data, only 31 fit this description. But these firms dominate the market, accounting for 47% of total trading volume and appearing on one or both sides of almost 75% of traded contracts. And they do this with minimal directional exposure: average intraday inventory amounts to just 2% of trading volume, and the overnight inventory of the median HFT firm is precisely zero.

This small set of firms is then further subdivided into categories based on the extent to which they are providers of liquidity. For any given trade, the liquidity taker is the firm that initiates the transaction, by submitting an order that is marketable against one that is resting in the order book. The counterparty to the trade (who previously submitted the resting limit order) is the liquidity provider. Based on this criterion, the authors partition the set of high frequency traders into three subcategories: aggressive, mixed, and passive:

To be considered an Aggressive HFT, a firm must… initiate at least 40% of the trades it enters into, and must do so for at least 50% of the trading days in which it is active. To be considered a Passive HFT a firm must initiate fewer than 20% of the trades it enters into, and must do so for at least 50% of the trading days during which it is active. Those HFTs that meet neither… definition are labeled as Mixed HFTs. There are 10 Aggressive, 11 Mixed, and 10 Passive HFTs.

This heterogeneity among high frequency traders conflicts with the common claim that such firms are generally net providers of liquidity. In fact, the authors find that “some HFTs are almost 100% liquidity takers, and these firms trade the most and are the most profitable.”

Given the richness of their data, the authors are able to compute profitability, risk-exposure, and measures of risk-adjusted performance for all firms. Gross profits are significant on average but show considerable variability across firms and over time. The average HFT makes over $46,000 a day; aggressive firms make more than twice this amount. The standard deviation of profits is five times the mean, and the authors find that “there are a number of trader-days in which they lose money… several HFTs even lose over a million dollars in a single day.”

Despite the volatility in daily profits, the risk-adjusted performance of high frequency traders is found to be spectacular:

HFTs earn above-average gross rates of return for the amount of risk they take. This is true overall and for each type… Overall, the average annualized Sharpe ratio for an HFT is 9.2. Among the subcategories, Aggressive HFTs (8.46) exhibit the lowest risk-return tradeoff, while Passive HFTs do slightly better (8.56) and Mixed HFTs achieve the best performance (10.46)… The distribution is wide, with an inter-quartile range of 2.23 to 13.89 for all HFTs. Nonetheless, even the low end of HFT risk-adjusted performance is seven times higher than the Sharpe ratio of the S&P 500 (0.31).

These are interesting findings, but there is a serious problem with this interpretation of risk-adjusted performance. The authors are observing only a partial portfolio for each firm, and cannot therefore determine the firm’s overall risk exposure. It is extremely likely that these firms are trading simultaneously in many markets, in which case their exposure to risk in one market may be amplified or offset by their exposures elsewhere. The Sharpe ratio is meaningful only when applied to a firm’s entire portfolio, not to any of its individual components. For instance, it is possible to construct a low risk portfolio with a high Sharpe ratio that is composed of several high risk components, each of which has a low Sharpe ratio.

To take an extreme example, if aggressive firms are attempting to exploit arbitrage opportunities between the futures price and the spot price of a fund that tracks the index, then the authors would have significantly overestimated the firm’s risk exposure by looking only at its position in the futures market. Over short intervals, such a strategy would result in losses in one market, offset and exceeded by gains in another. Within each market the firm would appear to have significant risk exposure, even while its aggregate exposure was minimal. Over longer periods, net gains will be more evenly distributed across markets, so the profitability of the strategy can be revealed by looking at just one market. But doing so would provide a very misleading picture of the firms risk exposure, since day-to-day variations in profitability within a single market can be substantial.

The problem is compounded by the fact that there are likely to by systematic differences across firms in the degree to which they are trading in other markets. I suspect that the most aggressive firms are in fact trading across multiple markets in a manner that lowers rather than amplifies their exposure in the market under study. Under such circumstances, the claim that aggressive firms “exhibit the lowest risk-return tradeoff” is without firm foundation.

Despite these problems of interpretation, the paper is extremely valuable because it provides a framework for thinking about the aggregate costs and benefits of high frequency trading. Since contracts in this market are in zero net supply, any profits accruing to one set of traders must come at the expense of others:

From whom do these profits come? In addition to HFTs, we divide the remaining universe of traders in the E-mini market into four categories of traders: Fundamental traders (likely institutional), Non-HFT Market Makers, Small traders (likely retail), and Opportunistic traders… HFTs earn most of their profits from Opportunistic traders, but also earn profits from Fundamental traders, Small traders, and Non-HFT Market Makers. Small traders in particular suffer the highest loss to HFTs on a per contract basis.

Within the class of high frequency traders is another hierarchy: mixed firms lose to aggressive ones, and passive firms lose to both of the other types.

The operational costs incurred by such firms include payments for data feeds, computer systems, co-located servers, exchange fees, and highly specialized personnel. Most of these costs do not scale up in proportion to trading volume. Since the least active firms must have positive net profitability in order to survive, the net returns of the most aggressive traders must therefore be substantial.

In thinking about the aggregate costs and benefits of all this activity, it’s worth bringing to mind Bogle’s law:

It is the iron law of the markets, the undefiable rules of arithmetic: Gross return in the market, less the costs of financial intermediation, equals the net return actually delivered to market participants.

The costs to other market participants of high frequency trading correspond roughly to the gross profitability of this small set of firms. What about the benefits? The two most commonly cited are price discovery and liquidity provision. It appears that the net effect on liquidity of the most aggressive traders is negative even under routine market conditions. Furthermore, even normally passive firms can become liquidity takers under stressed conditions when liquidity is most needed but in vanishing supply.

As far as price discovery is concerned, high frequency trading is based on a strategy of information extraction from market data. This can speed up the response to changes in fundamental information, and maintain price consistency across related assets. But the heavy lifting as far as price discovery is concerned is done by those who feed information to the market about the earnings potential of publicly traded companies. This kind of research cannot (yet) be done algorithmically.

A great deal of trading activity in financial markets is privately profitable but wasteful in the aggregate, since it involves a shuffling of net returns with no discernible effect on production or economic growth. Jack Hirschleifer made this point way back in 1971, when the financial sector was a fraction of its current size. James Tobin reiterated these concerns a decade or so later. David Glasner, who was fortunate enough to have studied with Hirshlefier, has recently described our predicament thus:

Our current overblown financial sector is largely built on people hunting, scrounging, doing whatever they possibly can, to obtain any scrap of useful information — useful, that is for anticipating a price movement that can be traded on. But the net value to society from all the resources expended on that feverish, obsessive, compulsive, all-consuming search for information is close to zero (not exactly zero, but close to zero), because the gains from obtaining slightly better information are mainly obtained at some other trader’s expense. There is a net gain to society from faster adjustment of prices to their equilibrium levels, and there is a gain from the increased market liquidity resulting from increased trading generated by the acquisition of new information. But those gains are second-order compared to gains that merely reflect someone else’s losses. That’s why there is clearly overinvestment — perhaps massive overinvestment — in the mad quest for information.

To this I would add the following: too great a proliferation of information extracting strategies is not only wasteful in the aggregate, it can also result in market instability. Any change in incentives that substantially lengthens holding periods and shifts the composition of trading strategies towards those that transmit rather than extract information could therefore be both stabilizing and growth enhancing.