The goal of equity market neutral managers is precisely to avoid any net market exposure in their portfolio. Selling and buying are no longer sequential independent activities; they become related and in some cases even concurrent. In addition, long and short positions are regularly balanced to remain market neutral at all times, so that all of the portfolio’s return is derived purely from stock selection and no longer from market conditions. This explains why many investors perceive equity market neutral as the quintessential hedge fund strategy. Indeed, when correctly implemented, it offers the promise of true absolute returns (the alpha) without having to bear the market sensitivity (the beta). But beware! “Market neutral” has become a catch-all marketing term which embeds several different investment approaches with varying degrees of risk and neutrality.

Dollar neutrality is extremely appealing because of its simplicity. It has the great benefit of being directly verifiable, as the initial value of the investments is observable, at least to the hedge fund manager. But is it sufficient to make a portfolio market neutral? The answer requires closer examination of some of the unobservable risk characteristics of the long and short parts of our portfolio.

To create such a beta neutral fund, it is necessary to go back to the basics of Model Portfolio Theory (MPT). According to MPT, the volatility of a stock (or a portfolio of stocks) can be decomposed into a market risk component and a specific risk component. The market risk component depends on the volatility of equity markets as well as on the market risk exposure, which is measured by the beta coefficient.¹⁰² The specific risk component is independent from the market and it normally gets diversified away at the portfolio level (Figure 9.1).

The beta of a portfolio is a weighted average of the betas of its component stocks. Consequently, being dollar neutral does not necessarily guarantee that the portfolio will be insensitive to the market return, i.e. will have a beta equal to zero. It all depends on the beta of the long and the short positions. For instance, if the beta of the long position is 1.4 and the beta of the short position is 0.7, an equal dollar allocation between the two will have a net beta of 0.35 = (50%) × (1.4) − (50%) × (0.7). This positive beta implies that the market risk of our dollar neutral portfolio is not nil and that its correlation to equity markets is actually positive.

To make our portfolio really beta neutral, we need to size the long and short positions adequately. In our example, given the ratio of the two betas (1.4 versus 0.7), we would need to double the size of the short position relative to the long position. That is, for any dollar in the long position, we would need to have two dollars in the short position. In this case, the beta will be exactly zero, which means that the systematic risk of the portfolio has been neutralized. Going forward, if our long position appreciates in value and our short positions decreases in value, we would still need to adjust the size of our positions on a regular basis to avoid the drift towards a positive beta.

At this stage, the reader may wonder why a hedge fund manager might want to have a beta neutral portfolio. The answer is simple: to take risks only where he has skills. Many hedge fund managers prefer to focus on stock selection where they think they have a competitive advantage, rather than on forecasting the returns of the market or of some of its sub-sectors. Consequently, they prefer to run a portfolio of carefully selected stocks but with no net beta exposure, as this makes them completely independent from the behaviour of equity markets (Box 9.1).¹⁰³

To avoid that risk, it is necessary to go one step further and balance the long and short positions in the same sector or industry. This preserves the beta neutrality at the aggregate level, but also adds sector neutrality. Similarly, practitioners may also consider the market capitalization of the stocks in their portfolio to ensure that it is capitalization neutral, or the value/growth attributes of their longs and their shorts to ensure that it contains no biases.¹⁰⁵

To create a factor neutral portfolio, it is necessary to have beforehand identified a series of factors that influence the returns of individual stocks. The simplest model is obviously the market model, where only one factor, the market, is common to all stocks and explains their correlation. However, empirical observation and academic research suggest that there are other factors beyond the market influence. Some of these common fluctuations are explained by fundamental characteristics of the portfolio: stocks in the same industry tend to move together, value stocks tend to move together, growth stocks tend to move together, small caps tend to move together, and so on. Some of these common fluctuations are also explained by more general economic factors such as oil price, the level of interest rates, inflation, etc. Since the market risk is obviously not responsible for these common behaviours, specific risk must therefore be the place to investigate.

Multi-factor models simply decompose the “old” specific risk of Figure 9.1 into additional sources of risk, namely common factor risks and residual specific risk (Figure 9.3). Common factor risks represent forces that are not linked to the market risk, but still have a common influence on subgroups of stocks. Examples of such forces include their sector (biotechnology, energy, etc.), but also some macro factor risks (oil prices, the level of interest rates, etc.) as well as some micro factor risks such as the market capitalization of the company, its price to book value (P/B) ratio, its price to earning (P/E) ratio, etc. Residual specific risk then captures a refined source of risk derived from forces that uniquely influence an individual company.

A factor model allows quantitative portfolio managers to statistically construct a portfolio having the highest expected excess return while being neutral to a selected series of underlying factors. How does this work? As an illustration, let us consider the Barra Integrated model for the US stock market. This is a commercial factor model with 55 sector factors (each firm may participate in up to 6 sectors) and 13 common risk factors (variability in markets, success, size, trading activity, growth, earnings/price, book/price, earnings variation, financial leverage, foreign income, labour intensity, dividend yield, and low capitalization). Each month, Barra supplies the evolution of these 68 factors as well as the sensitivities (the betas) of all the US stocks to each of these factors.

The betas of a given portfolio to the respective factors are easily obtained by a weighted average of the component stocks’ betas. If some of the portfolio betas are not equal to zero, then the portfolio is not neutral to the corresponding factors. For a long/short equity portfolio to be truly market neutral, the manager must therefore extend his risk controls beyond market risk to include all the common factor sources of risk (Table 9.1).

Of course, there is always a limit to market neutrality. As more risk factors are being hedged away, the opportunity set to add value is reduced. Ultimately, if all risk factors are perfectly hedged, the portfolio becomes risk free and should theoretically yield the risk-free rate, minus transaction costs. Market neutrality is therefore a trade-off between eliminating some undesirable risk sources and reducing the set of return generating opportunities. For skilled quantitative managers, market neutral is a comfortable space to operate into, because it allows them to avoid taking risk in areas where they do not have skills while simultaneously maintaining some risk exposure where they have a competitive advantage.

The success of pairs trading depends heavily on the approach chosen to identify potential profitable trading pairs, i.e. model and forecast the time series of the spread between two related stocks. There is a variety of approaches, and the choice of one of them often depends on the background of the fund manager. For instance, the first equity market neutral funds were run by managers with a pure stock-picking background. Not surprisingly, they chose to approach stocks using a fundamental valuation perspective. For instance, they analysed each company in a given sector against all its competitors, and established a long/short position by purchasing the most undervalued company and selling short the most overvalued one. The process was then repeated across sectors, and each position was held until the spread between the associated companies had sufficiently reverted, or a stop loss level had been reached. More recently, numerous statisticians have entered the equity market neutral space. Since their competitive advantage is in time series analysis rather than in fundamental valuation, they often use purely statistical models to identify pairs whose two components deviate sufficiently. Using statistics and being systematic in the application of a model allows them to cover a large investment universe without being exposed to incorrect discretionary judgements, but it also implies that the strategy no longer has the flexibility of incorporating prior economic or financial knowledge in representing the relationship between the two time series.

Most of these models use some sort of distance function to measure the co-movements within pairs of securities. The simplest distance between two stocks is the tracking variance, which is calculated as the sum of squared differences between the two normalized price series.¹⁰⁷ The position in a pair is initiated when the distance reaches a certain threshold, as determined during a formation period. For instance, this threshold distance could be two historical standard deviations away from its mean, as estimated during the formation period, or be specified as a certain percentile of the empirical distribution. The pair is closed when the distance reaches another threshold, either with a gain (the mean reversion occurred) or with a loss (a stop loss level was hit).

As an illustration, consider the example of Figure 9.5. The upper graph shows the normalized price series of two related stocks. A normalized price series starts at 1000 and increases or decreases by the stock’s gross return compounded daily. Most of the time, the two normalized price series tend to move together. However, the normalized prices of the two stocks differ from each other by more than the trigger value (two historical standard deviations of historical price divergence) on several occasions. On each of these occasions, a position is open, where the most expensive stock is sold and the least expensive is purchased. The bottom graph shows when, and for how long, a position remains open. It also shows the cumulative return to this pairs-trading strategy. Note that there are flat (no profit) periods when the pair’s position is not open, but this is usually not a concern at the portfolio level because other pairs will be open during this period.

Of course, more complex distance functions can also be used. Let us mention the co-integration approach, which allows for co-integration between the stocks,¹⁰⁸ or the stochastic spread approach, in which the evolution of the spread between two stocks is explicitly modelled as a continuous time stochastic process exhibiting some form of mean reversion.¹⁰⁹ This latter approach is extremely convenient for forecasting purposes as well as for calculating information such as the expected holding period and the expected return of each pair. Alternatively, some pairs traders also like to use the orthogonal regression approach (Box 9.2) to measure the distance between two stocks.

Data snooping is obviously an important issue when forming such pairs-trading rules. This is why the entry and exit rules for any pair should be based on sensible assumptions, and not just be the result of any back-tests or simulations. Remember that an in-sample optimal trading rule may not remain optimal out-of-sample. Moreover, one of the main risks involved with pairs trading based only on statistical analysis is that a fundamental change in the relationship between the two stocks can get masked and the trader can enter positions when the prices are not expected to revert to historical means. This can happen when, for example, there is a fundamental change in the strategy of one of the companies as a result of which the price level changes permanently.

Surprisingly, the profitability of pairs trading seems now to be well established – see Box 9.3. This goes in complete contradiction with the weakest form of market efficiency, as a relatively simple rule purely based on the behaviour historical prices and their expected mean reversion seems sufficient to make money. More puzzling is the fact that this profitability is not only arising just because of mean reversion – a systematic contrarian strategy, e.g. buying past losers and selling short past winners, should then be highly profitable, but it is not the case, at least not over some considered periods. So far, the most convincing explanation is qualitative: pairs-trading profits would indirectly be related to some sort of “systematic dormant factor” due to the agency costs of professional arbitrage, i.e. the compensation for keeping prices in line. However, the level of that compensation still seems high.

The criteria selected to slice and dice the universe are the most critical elements in the strategy. In reality, what arbitrageurs are trying to do is use factors that explain well historical equity price movements and also have some sort of predictability. The challenge is to avoid factors with little explanatory power, or factors that just have a temporary impact, and rely only on intuitive and significant factors, whose empirical performance can easily be documented. Examples of such factors are valuation indicators, growth estimates, leverage, dividend yield, earnings revision, momentum, etc. Once a factor is selected, the arbitrageur scores the universe of stocks according to it and goes long the top scorers and short the lowest scorers. The resulting portfolio is factor neutral by construction,¹¹⁰ and its performance depends on the factor’s future ability to separate top from bottom performers. Most of the time, this ability is linked to specific market reactions that can be classified as short-term, medium-term and long-term momentum and reversal patterns. In a momentum pattern, past winners/losers are expected to be future winners/losers, while in a reversal, past losers/winners are expected to be future winners/ losers.

Such patterns are well known in empirical finance. For instance, over the short run (3 to 12 months), markets seem to favour momentum.¹¹¹ That is, stocks that have performed relatively poorly in the past continue to lag, and stocks that have performed relatively well in the past continue to perform well. This apparent inefficiency can somehow be justified by some momentum in earnings announcements, but it also comes from investor overconfidence and other well-documented behavioural finance biases. In any case, it can easily be exploited by a statistical arbitrage strategy. For instance, an arbitrageur could take again the S&P 500 companies, sort them according to their past three-month performance and create 50 groups of 10 companies. The first group contains the stocks that have realized the highest return (referred to as “winners”), while the last group contains those that have realized the lowest return (referred to as “losers”). The arbitrage portfolio will go long the first group and short the last group. If momentum persists, the arbitrage portfolio will be profitable.

Mean reversion or contrarian trading is, in a sense, the opposite of momentum trading. It is based on the empirical evidence that price reversals tend to take place two or three years after the formation of a momentum portfolio. Some researchers have argued that mean reversion is in fact the long-term consequence of the price momentum effect – investors overreact in the short term, but realize later that they were wrong and prices will therefore adjust. If this is true, then an interesting arbitrage consists in going long past losers and short past winners, where losers and winners are measured over a longer time horizon (say three years).

Another popular trade of statistical arbitrageurs is the value versus growth bias. Growth companies may temporarily outperform value companies, but over the long run (two to five years), value companies display higher average returns.¹¹² A statistical arbitrageur that would expect this situation to persist in the future and had a sufficient time horizon should immediately attempt to profit by going long value and short growth stocks. For instance, he could take the S&P 500 companies, sort them according to their price/earning (P/E) ratio or their dividend yield and create 50 groups of 10 companies. The first group will contain the stocks that have the highest value attributes, while the last group will contain the stocks that have the highest growth attributes. Our arbitrageur could then go long the first group and short the last group. If value continues outperforming growth over the long run, his portfolio will be profitable.

Of course, these strategies seem relatively simple, but the devil is in the details. The generic idea might be straightforward to understand, but the implementation is not. In particular, each of these trades relies on selection rules that should be carefully calibrated to market data in order to identify the optimal length of the observation period, the optimal number of groups to create and the most efficient way to structure and rebalance the portfolio. Most statistical arbitrageurs spend a lot of time on fine-tuning and back-testing their selection rules. Note that they do not have to limit themselves to using only one rule. As soon as their time horizons are different, momentum and contrarian strategies can actually coexist in a portfolio, very similarly to commodity advisers using several trading rules. Indeed, momentum trading functions very well in trending markets (pro-cyclical strategy) while contrarian trading comes into action when prices revert back to more sustainable levels (anti-cyclical strategy). Mixing them may actually smoothen out the performance of the portfolio. For instance, Figure 9.7 shows the back-test of a strategy that aims at systematically exploiting over-and under reactions in the market by arbitraging short run momentum and a medium run reversal in the S&P 500 stocks. The strategy has worked perfectly from 1986 to 2002.

The next question, of course, is whether it will continue to perform as well in the future.

However, being successful in very high frequency trading requires four elements: brainpower (to design the trading rules or the learning algorithms), high-frequency historical data (to test the trading rules), computing power (to apply the selected trading rules in real time) and best execution (to limit as much as possible trading costs and slippage). In our opinion, very few firms have been successful at combining these four elements. One of them, of course, is Renaissance Technologies – see Box 9.4.

The track record of equity market neutral hedge funds is remarkably consistent over the years, although returns have been slightly declining since 2001. As a result, the excess skewness and kurtosis are very small, and the return distribution can be approximated by a normal distribution (see Figure 9.10 and Table 9.3).

The maximum drawdown of the strategy is also extremely small (−3.55%) and does not seem related to equity market drawdowns. Lastly, the 12-month rolling return evidences the relative attractiveness of the track record. (see Figures 9.11 and 9.12).