Returns, in USD, based on yesterday's position sizes and today's price moves.

On the far right of part C are the total changes in shares and the total profits or losses for the day.

Performance.

When we test this method using the four calculation periods, we get the results shown in Table 8.14. As with our other tests, these results would be excellent if only the returns per share were higher. Considering that costs have already been taken out, information ratios above 1.0 are very good, and annualized returns are also attractive.

TABLE 8.14 Results of market-neutral trading using the DJIA for varying calculation periods.

TABLE 8.15 Results using a 2 percent low-volatility filter.

FIGURE 8.5 Unfiltered results for market-neutral program.

We again fall back on the need for a volatility filter to increase the profits per share. In this case, we found that a 2% filter was best. Smaller filters improved the per share returns, but not by enough. Results of using the 2% filter are shown in Table 8.15. The slope period of 15 shows the highest per share returns of nearly $0.10, with only a small decline in annualized returns and information ratio. Figures 8.5 and 8.6 show the c.u.mulative profits of both the unfiltered and filtered tests for the four slope periods. Performance is not very different for any of the calculation periods, and using the filter eliminates trading for the four-year period in the middle of the test. Again we see that mean-reverting strategies should not be traded during periods of low volatility.

FIGURE 8.6 Results of the market-neutral program using a low-volatility filter.

TABLE 8.16 Using only 8 stocks in the buy and sell zone, with and without a low volatility filter.

There is still one last option to test, changing the number of stocks in the buy and sell zones. By including 13 in the current test, we are not selecting those stocks that might have moved further apart from the other stocks. By reducing the number of stocks in each zone, we might add some element of timing plus a higher average volatility. Instead of 13, we'll use 8. With 8 in each zone, we have 13 in the neutral area that are not traded. We won't go to 4, 2, or 1 because we lose diversification and increase switching costs, as the few stocks move in and out of the buy and sell zones. Results are shown in Table 8.16. Although using 8 stocks has a slightly lower return per share, it has an impressive improvement in both the annualized returns and the information ratio. If we can produce the better returns trading fewer stocks, then that's a better choice. The trade-off is that fewer stocks present greater risk, regardless of what the numbers show.

THOUGHTS ABOUT MARKET-NEUTRAL TREND FOLLOWING.

The statistics show that mean reverting is a better strategy for stocks in the long term. However, we must all feel that there are times when that's not true and those times could present higher risk. Ideally, if we could identify when these markets are trending, then we might switch to a different trading mode. This concept has been called regime switching.

Most regime switching has been unsuccessful, mainly because of the lag needed to identify one regime from another. In addition, each time we switch from trending to mean reverting, we would need to change all the long positions to short and all the shorts to long. That can be a very large cost unless you hold the positions long enough to make up the cost.

One criterion for making the switching decision would be the slope of the equally weighted average of those stocks in the portfolio. If the slope is nearly flat, then there is no dominant trend in the market, and mean reversion would be the best choice. However, when the entire stock market trends, and even the laggards in the Dow show a rising slope, then a trending regime may be the way to make the most profits. At the same time, to emphasize the trend, you would want to increase the calculation period for the slope to 60 or 80 days. The longer the calculation period, the more likely we'll see a sustainable trend.

Unfortunately, research is a never-ending process, and regime switching won't be covered here. It is, however, an intriguing approach to improving many trading programs.

MARKET NEUTRAL USING FUTURES.

Futures markets would be an ideal venue for a market-neutral program. There is high leverage and the ability to go long or short with no restrictions. We discussed pairs trading for both equity index and interest rate futures in Chapters 4 and 7; now we'll look at using a traditional market-neutral method applied to interest rate futures.

The fixed-income futures markets are among the most liquid trading vehicles in the world. Eurodollar futures alone trade an average of 2 million contracts per day, each contract having a face value of $1 million, for a total notional value of $2 trillion. The 10-year Treasury notes, considered the benchmark interest rate, trade more than 300,000 contracts each day for a notional value of $30 billion. Entering and exiting do not pose a problem, and there is even a modestly active after-hours market.

Unlike stocks, trading futures provides exceptional leverage. To buy one contract of 10-year Treasury notes with a face value of $100,000, an investor needs only $2,700 in margin. Note that margin for futures is not the same as stocks. It is a good faith deposit and is based on the volatility of the market, not the face value. At this time, the 30-year bond margin is $4,860, the 10-year note margin is $2,700, and the 5-year note margin is $1,755. A study of the volatility of these three markets will show that the margin requirements closely parallel relative volatility.

It is important to understand margin because it provides extremely high leverage, but few traders take advantage of the maximum levels. For example, if June 2009 Eurodollars rates (to distinguish it from EURUSD FX) are trading at 99.025, and the face value is $1 million, then every 1.0 move is worth $2,500 (only 25% of the value because it is a 3-month delivery). The margin requirement is only $500. If you were long and the price dropped 20 basis points, all your margin would be gone-a 100% loss. And because margin is a good faith deposit, you are responsible for any additional losses.

Most traders deposit 3 to 4 times the amount of margin, reducing the amount of leverage normally to about 4:1. For our market-neutral program, we will calculate how much money needs to be invested to target returns reflecting 12% volatility. Unlike stocks, we will not find out that our investment wasn't enough to buy all of the contracts that we need.

The contract size of each futures market presents problems for traders with a small amount of capital on hand. In our example, we will track 9 markets and trade 4 long and 4 short. If each market requires a margin of $1,000 per contract, then we need at least $8,000. If we want to deleverage, and have reserves for losses, we should invest about 4 times that amount, or $32,000.

But the strategy also requires that we volatility-adjust each position so that they all have the same risk. From the margins for the 30-year, 10-year, and 5-year rates given earlier, we can see that we would need to trade approximately 3 of the 5-year notes, 2 of the 10-year, and 1 of the 30-year to have any similarity in volatility across markets. That means a lot more margin. And unless we trade a large number of contracts and invest millions of dollars, it will be difficult to fine-tune the size of the positions, unlike the stock market, where you can add one share at a time.

With that in mind, let's look at the market-neutral strategy for fixed-income markets. The process will be similar to arbing the Dow, but perhaps simpler. We'll calculate position sizes differently.

The Rules for Mean-Reversion Trading with Futures When we applied pairs trading to both equity index and interest rate markets, we found that all the profits were made when the pairs consisted of one market from the U.S. and one from Europe. Keeping that in mind, we chose those nine most active interest rates to include Eurodollars, U.S. 30-year bonds, U.S. 10-year notes, U.S. 5-year notes, Euribor, short sterling, Eurobunds, Eurobobls, and the long gilt. Since 2005, these markets close each day at the same time.

The other rules are: An investment of $100,000.

2, 3, or 4 markets in the buy and sell zones.

A $50 cost per round turn for each trade in one futures market.

The gilt presents a problem because it closes one hour earlier than the U.S. markets, but that could be resolved by posting prices for all markets just before the gilt close or eliminating the gilt from the strategy. For now, we'll leave it as part of the mix. Markets are usually very quiet in Europe toward the end of the day. Although there still may be active U.S. markets, the reality is that not as many European traders are interested in staying in front of their screens until 10 P.M. That may change.

The contract size will play an important role in our ability to balance the number of contracts to create equal volatility. It will also be used to calculate the correct daily PL: where signal is +1 for long and 1 for short, and the conversion factor is the value of a 1 big point move in the futures market. For 30-year bonds, the conversion factor is $1,000, representing the value of a move from, for example, 115.00 to 114.00. Conversion factors are Market Conversion Factor.

Eurodollar rates $2,500.

U.S. 30-year bonds $1,000.

U.S. 10-year notes $1,000.

U.S. 5-year notes $1,000.

Euribor 2,500.

Eurobund 1,000.

Eurobobl 1,000.

Long gilt 1,000.

Many of these markets now have mini versions. These minicontracts would have more flexibility for balancing the portfolio; however, commission costs are not reduced in proportion to the contract size, so trading the larger, original contracts whenever possible is more cost effective.

At some point, we will need to deal with the currency conversion. Ideally, we should know the currency rates on each day throughout our test history and repatriate both euros and sterling back to U.S. dollars after the close. We won't do that for these tests, but we can treat all non-U.S. trades as though prices were always at the current rates of EURUSD 1.30 and USDGBP 1.45. That is easily done by changing the Eurobund and Eurobobl conversion factors to $1,300 and the gilt conversion factor to $1,450.

As we did with the Dow, the second day of trading is shown in Table 8.17. All of the rows are the same as in the previous example except that, instead of shares, there are contracts. The number of contracts may seem large, but the correlations between these interest rates are very high, and the risk of being long one and short another is surprisingly small. Because of that, the profits are also small.

TABLE 8.17 Detail of the second trading day for interest rate futures using two markets in each of the buy and sell zones.

Results of Interest Rate Trading Interest rate differences correct very quickly, so the calculation periods need to be short. We found that this was true when we first looked at pairs trading in stocks. We also tried buy and sell zones with 2, 3, and 4 markets. Table 8.18 shows the information ratio (a), profits per contract (b), and annualized rate of return (c) for these combinations. The lower right corner of the table, the 4-day calculation period and only two markets in each zone, is the best combination; however, most combinations were good.

TABLE 8.18 Market-neutral results for interest rate futures showing the (a) information ratio, (b) profits per contract, and (c) annualized rate of return.

The returns per contract, which are net of $50 round-term commissions ($25 for each leg although trading them as spreads will reduce that amount), show a very safe margin of error for trading and make this an attractive method. Given the results we had applying pairs trading to equity index markets in both the U.S. and Europe, we would expect similarly good results with those futures markets.

MARKET-NEUTRAL COMMENTS.

Traditional market-neutral programs applied to stock sectors or industries were the first of the major algorithmic trading methods. They profited mostly during the 1990s, when compet.i.tion was not as keen and markets were less noisy. They took advantage of a new level of computing power that had become more broadly available.

The principles of market-neutral trading, separating the strongest and weakest stocks within a fundamentally related set and then either buying the strongest and selling the weakest or, less often, selling the strongest and buying the weakest, are still sound. Only now, we need to be more selective.

Success in trading a market-neutral program can be in two areas: an above-average interval of volatility in stocks or the cross-regional use of futures. By far the best payout is in using futures. Both equity index and interest rate futures offer profitable opportunities because globalization has caused all of these markets to be linked, even if it might be seen as a dirty link. They don't follow exactly, but they don't drift too far apart without reacting back. That makes mean reversion the strategy of choice. With U.S. and European markets now open at the same time, every investor has an equal chance of profiting.

Chapter 9.

Other Stat-Arb Methods.

Stat-arb is short for statistical arbitrage, a traditional way of identifying and profiting from price distortions in related stocks. We've used the term pairs trading instead. For years, this was a bread-and-b.u.t.ter trade for the inst.i.tutions. They simply watched for companies within a sector to perform differently from one another and then placed a trade that profited from the two stock prices coming back together. It was just short of printing money. Unfortunately for us, compet.i.tion has become keen in every area of trading, with stat-arb being a primary target. Any system that removes directional risk and avoids the brunt of price shocks is in high demand. The big investment houses have migrated their approach to high-frequency trading, where even the proximity to the source of data gives one company milliseconds of an edge against another. Some exchanges have just recently required that users have their computers no closer than 500 feet to the exchange transmission source. It's their attempt to even the playing field. We can't compete in that venue, but there still are selected areas where we can be profitable and have no directional risk. Some of the primary opportunities have been covered in the previous chapters.

This chapter will look at a few different approaches to trades that don't have directional risk. First we'll see what happens when we create our own index and use that for one leg of the pair, or use one of the mutual funds available from a number of different companies. Then we'll see if it makes sense to create pairs from the components of the Dow or the S&P. We'll also look at creating a market-neutral strategy from stock rankings provided by companies that specialize in that service.

TRADE-OFFS.

We can't know which combination of trading frequency, size of returns, and risk that any one trader will choose. Some traders prefer risk avoidance; others are risk seekers. That's a characteristic called investor risk preference. In most of the approaches discussed in this book, we've taken a centrist approach, trying to find the greatest common denominator.

Pairs trading is best when it's short term and mean reverting. All mean-reverting strategies have the same risk and reward trade-offs. If the entry point is set closer, there are more trades with smaller profits. If the entry is further away, there are fewer trades but larger profits per trade. As far as risk is concerned, entering a trade sooner means you must hold the trade with a larger open loss if it moves against you, but you will take smaller profits more often. By entering at a point of greater distortion, you will not suffer an unrealized loss that is as large, but you will need to wait longer for each new trading opportunity. For our purposes we are interested in which trade-off has the best return to risk ratio, which is our ultimate measure of preference. A fast trading method may have smaller losses, but a series of losses can be equally as large as a single, poor trade using a slower system. The final performance for a mean-reverting method has the shape of a short-options profile-many small profits and a few large losses. You can't change this shape, although you can scale the leverage up or down.

SYSTEM BRIEFS.

There are trading methods that are difficult to backtest, although they may be perfectly thought out and fully systematic. For the first method discussed in this section, taking advantage of upgrades, downgrades, and promotion on the television or radio, the computer has not yet reached the level where it can be subst.i.tuted for the human brain. In the second method, the availability of historic data is scarce and sometimes requires a hefty fee to partic.i.p.ate. Both are cla.s.sic stat-arb trading methods, both are systematic, and both can be very profitable.

Taking Advantage of Upgrades and Downgrades We are all familiar with the daily market alerts on the financial news networks that say "Microsoft has been upgraded from neutral to buy" or from "buy to hold" (whatever that means) or occasionally from "neutral to underweight" (rarely do they give an outright "sell," even for Enron). Other shows, such as Mad Money with Jim Cramer, cover a number of companies with less tactful recommendations to buy or sell those shares.

Recommendations by large financial inst.i.tutions, such as Bank of America, influence many investors. Clients of Bank of America, J. P. Morgan, or any other big investment house will have already received those recommendations and acted on them. After all, it doesn't seem right to offer the benefit of their research to the general public, without payment, before or at the same time as their own clients. And Cramer fully discloses that his recommendations may have been disseminated beforehand. None of that is a problem. One web site where you can find upgrades and downgrades posted each day is www.TheStreet.com.

Stat-arb trading triggers an action after the market has moved; therefore, we want the recommendations to cause investors to stampede, buying or liquidating en ma.s.se. While that's unlikely to happen, we would be satisfied with a move in the target company that differed from the market as a whole. It would be difficult to identify whether the buy recommendation had investors rushing to acquire the stock if both the target and the entire S&P index moved up by the same amount. Without the recommendation, perhaps the company would have declined in price while the rest of the market rallied; however, that's more difficult to measure than if the company being recommended rose more than the overall market.

Our stat-arb trade looks for moves in individual stocks that are clearly stronger or weaker than the overall market, but only under three certain conditions: 1. The move must be preceded by a visible recommendation by a service, financial inst.i.tution, or television show with a large following.

2. It cannot be caused by a quarterly earnings report.

3. It cannot be caused by an announcement of a merger, scandal, or major event internal to the company.

Note that we are looking for buying and selling recommendations, not structural changes in the company or in the price of its stock. The impact on the company share value must be temporary and inconsistent with the movement of the market as a whole. A quarterly earnings report is a structural change. If earnings are below expectations, then you can expect that company to underperform the S&P index, but it does not provide an opportunity to buy.

The premise of this traditional arbitrage is that a.n.a.lyst recommendations are badly timed and have no lasting significance on price movement. A buy recommendation pushes prices up as investors buy at the market, without regard to getting a good price. And it always happens after the fact. For example, Merck will announce that a new drug has pa.s.sed the next step in the FDA approval process. Prices rise. A few days later, because prices have risen, an investment house recommends that its clients buy. Of course, the recommendation is intended to take advantage of the longer-term effect of the announcement, not a 2- or 3-day price move. But the market has already moved up to discount the longer-term move as best it can. Our best trade is to sell the rally for a very short-term profit.

But what if we sell and the overall market is rallying due to generally good economic news? That would mean we were right about Merck but lost money anyway.

We can protect against that contingency by selling the S&P when we buy Merck, volatility-adjusting the position sizes to be the same. That effectively hedges the position and isolates the alpha. We make money only if we were correct about the distortion of the Merck price and cannot have either a windfall profit or loss because of moves in the overall market. Alpha means that we make money if we're smarter.

These trades will be more obvious for smaller companies than for members of the Dow. Even if Cramer recommends buying General Electric, it is unlikely that a surge of buying will be seen in the price move. The company is just too big. However, if he recommends a small-cap company making hydrogen batteries, then it is very likely that we would see a market impact. So the size of the company will make a big difference. For larger investors, these smaller companies will have limited liquidity and limited returns; however, results should be better.

The steps to follow for this cla.s.sic stat-arb trade are: Watch for all upgrades, downgrades, and other recommendations to buy or sell given by investment houses, research firms, or television reports.

Wait for the market to open stronger or weaker than the S&P, confirming the direction of the buy or sell recommendation. Normally, these recommendations are disseminated after the close on the previous day.

Be careful to check that there is no news just released by the target company that would cause a structural change in the share price. This could be an earnings release, merger, change of management, or other major announcement.

If the price is up, then sell the individual stock and buy the S&P, being sure that you have correctly volatility-adjusted the position sizes so that they have the same risk.

Take off the position when the stock gives back its gain or loss relative to the S&P, but no longer than three days, perhaps less.

Do not subst.i.tute a sector ETF for the S&P. When one company in a sector is upgraded, it is often the case that other companies benefit. For example, when the first of the microchip manufacturers or computer companies reports its quarterly earnings, the market takes that as an indication of how the rest of that sector will perform. If Dell has an unexpected rise in sales and its price jumps by 3%, it is very likely that Hewlett-Packard will also rise.

Based on this sympathetic movement, it is possible to sell the sector ETF and buy the S&P to capture the temporary move across a broader range of companies. Of course, the move when averaged out will be smaller for the sector than for the target company, but it still may be an attractive trade. And arbing an ETF and S&P futures means that the position can be leveraged and there are no awkward short sales.

Creating a Stat-Arb Trade Using a Rating Service There are quite a few firms offering services that rank stocks in order of expected performance. By searching the Internet, you can find "stock rankings systems" or "stock ranking services" that are computer programs you can buy or services to which you can subscribe. The best ranking systems seem to have proprietary black box algorithms. They won't tell you how they do it, but they will sell the rankings each day. Many other services are free but require much more effort to rank stocks if you have more than one criterion. This discussion is not intended to recommend any of these services or a.s.sess which one is better than another. Part of the process of generating a successful strategy will be to determine that yourself.

The intriguing part of a ranking service, or any ranking method, is that you can find forecasts for both the best and the worst expected performance. The stat-arb trade is created using the most actively traded stocks and then buying the highest ranking stocks and selling short the lowest ranking. This gives you a cla.s.sic market-neutral portfolio. The only calculation you must make yourself is to size the positions according to volatility, so that the risk of all the long positions equals the risk of all the shorts.

The hard part of this process is determining if the forecasts are credible. That is, the minimum requirement is that those stocks that ranked in the upper 10% should perform above average and those in the lower 10% should perform below average. That doesn't seem to be a particularly demanding requirement, but you cannot a.s.sume that it will happen. It may be more reasonable to look at those stocks ranked in the top 8090% range, or even 7080%, under the theory that the highest-ranking stocks are experiencing an abnormal, short-lived period in the spotlight, while the ones in a more modest position are the slow but steady performers. Whatever you decide, you must prove that the rankings have forecasting power before they can be used.

The problem of forecasting ability is particularly true if you are creating your own ranking. Do you rank by the P/E ratio? By the size of the dividends? By the recent or long-term performance? It may be interesting to know that the U.S. government's Leading Economic Index (LEI) includes many components, but the most important and most reliable is the previous move of the stock market, for example, the S&P. If the S&P has risen recently, then the LEI is likely to be positive. It may seem as though it's a dog chasing its tail, but the point is that a rising stock price can be a strong indicator of continued success.

Ranking for Hire.