Even during this ideal time, NovaGold (NG) posted a loss. Remember that it is currently trading at a very low price, which may make the absolute size of the price moves small. We should understand that, given enough time and hindsight, we can explain why one market lost and another gained and convince ourselves that we should remove the worst performers and keep the best ones. But we really don't know what will happen in the future. As long as these companies qualify according to their fundamentals or by their correlations, they should be included.

One caveat discussed in an earlier chapter concerned distortions in positions. When one market trades at a high price with normal volatility and another at a very low price with corresponding low volatility, the size of the position taken in the low-priced stock would need to be much larger to equalize the risk. This presents a real leverage risk, the possibility that any surprising news involving the low-price stock could cause a very large loss in those pairs using that stock. Our earlier conclusion (see the distortion ratio) was that no pair should be traded if one stock has more than twice the shares of the other stock.

Subst.i.tuting a Mutual Fund for the PMI There are some practical issues concerning the construction of our own index. The strategy has been set up to trade 100 shares of the index and the volatility-adjusted equivalent of each stock. If we are buying the index and there are six companies, we then buy 16.6 shares of each. We need to be able to sell short the other side of the trade. Because we chose companies with the highest volume, we should have less trouble. If volatility is high, as it's been during the past two years, there may be a choice of using options; otherwise, the overhead might be too high.

One way to simplify the problem is to find an ETF or mutual fund for precious metals. Either will track the cash price of the stocks. They have the advantage of allowing long and short positions without penalty and without size limitation. In the case of ProFunds, which offers a broad selection of tradable mutual funds, the precious metals fund PMPIX is twice leveraged and has compet.i.tive costs built into the transaction. PMPIX is only a bull fund-that is, you can only go long-but there is a large number of listings by SPDR, ProShares, Rydex, PowerShares, and iShares that offer various combinations of long, short, and long-short funds. We'll use PMPIX because ProFunds allows downloading historical data easily; therefore, anyone can test strategies.

TABLE 9.9 Correlations of PMI and PMPIX with each of the six mining stocks and with each other.

First we need to see how PMPIX correlates to our six mining stocks. Table 9.9 shows that our six stocks are nearly identical, giving an overall correlation of 0.981 with the mutual fund and showing only small variations in the individual stocks. We can then test the six pairs of mining stocks with PMPIX and get the results shown in Table 9.10.

TABLE 9.10 Results of six mining pairs using PMPIX, June 19, 2002, through March 5, 2009.

Compared with Table 9.7, these results are all better, and they should also improve during the past three years. The net return was a positive $0.03 per share, and the ratio improved from 0.284 to 0.301, which includes the administration mutual fund fees, which are reflected in the daily price. Overall, using a mutual fund, when it is available, is a better choice and simplifies trading.

ARBING THE DOW.

A natural next step might be to try this stat-arb process on the components of the Dow Jones Industrial Average (DJIA) against that average. Those companies are certainly more liquid and are all available for short selling. In addition, the Dow trades as a number of ETFs, including the Diamonds (DIA) on NASDAQ.

Without going through the tedious process of showing results, the conclusion is that stat-arb does not work for the Dow and its components. Consider that we need to find distortions in one stock with respect to the index, and those distortions must correct quickly back to the average value of the index. If all the stocks are part of the same industrial group, as we tried to construct with precious metals, then the same fundamental factors affect all of them. We have reason to believe that any news affecting one company within the group will often have a corresponding, but not equal, effect on the other stocks in the same group. In addition, when one company has good news, it leads the index; then others follow as investors buy the laggards in the belief that they will benefit from the same news.

The result of arbing all 30 Dow components against the index was slightly worse than zero, a small net loss, even before costs were subtracted. With the aid of hindsight, we can say that the Dow components are a diverse group, and one component can keep going up, such as Wal-Mart, while another is going down, as with Bank of America, particularly during the financial crisis of 20082009. Buying Bank of America and selling the DJIA would have resulted in a huge loss, only to be repeated by other huge losses. In reality, half of the stocks generated a profit, and half a loss, which indicates diverse fundamentals.

While arbing one stock against the index doesn't work, a very large business exists in program trading, the process of keeping the cash stock index in line with the futures market or other index markets that track, primarily the S&P, and producing some trading profits along the way.

ARBING THE S&P 500- INDEX ARBITRAGE.

Index arbitrage is a subset of program trading and is an essential part of market pricing. Professional traders track the cash S&P 500 index (SPX) and the nearby S&P futures contract and wait for these two markets to diverge. That often happens when a large pension fund or hedge fund sets an outright position in S&P futures, driving the price up or down without regard to the cash price. This may be an outright trade intended to be profitable or insurance against existing positions. In addition, recommendations by brokers or investment houses can cause the general public to move back into the stock market, pushing up the actual stock prices but not directly affecting futures.

Program trading is a pure arbitrage-a market-neutral program. If the futures markets move up faster than the cash market, then traders will sell futures and (theoretically) buy all of the stocks in the S&P in proportion to the cap-weighted holdings in the S&P cash index. This brings the two markets into equilibrium. If the cash market moves first, then they buy the S&P futures and sell the stocks. Selling short all the stocks in the S&P requires planning and adds considerable risk, so it is not nearly as desirable as trading in the other direction. When a trigger point is. .h.i.t, program traders use computers to automatically generate and execute orders to buy or sell all stocks in the S&P. Some traders try to use a smaller set of stocks to represent the whole index, which, on one hand, can save money and speed up execution but also introduces tracking risk.

It is estimated that all program trading, which includes index arbitrage and algorithmic trading, accounts for nearly 50% of all volume trading on the New York Stock Exchange. The exchange defines program trading as a trade involving 15 or more stocks with an aggregate value in excess of $1 million.

Trigger Points The key to index arbitrage is finding the trigger point at which to activate the trades and generate a profit. This is where the fair value of forward price of the S&P component stocks differs from the futures price, or ETF, or options price, by some minimum threshold. The fair value at time t is calculated as where FVt is the fair value at some future date, t days ahead, SPX0 is the current value of the cash S&P index, RFt is the risk-free rate of return for the calculation period, and Dt is the acc.u.mulated dividends of the S&P components between now and t days ahead. Normally, t is chosen to correspond to the delivery date of the futures markets, around mid-month in March, June, September, and December. As the date gets closer, the acc.u.mulated dividends get smaller, and the fair value approaches the cash value of SPX. It is essential that futures and cash prices converge on the delivery date because the futures delivery is in cash, and hedgers must be sure that any shorts taken in futures to insure against cash stock market losses do indeed perform as expected.

Traders typically look for the difference in the futures price and fair value to exceed $5 or fall below $5 to trigger a trade, but compet.i.tion may cause some traders to jump ahead of that threshold. Once a program trade has been set, stocks and futures should converge within a short time, but the worst-case scenario is that they converge at delivery. The sooner they converge, the sooner traders have their investment back and can use those funds for another trade. If stocks and futures take a long time to converge back to equilibrium, the traders are effectively losing money.

Volatility plays an important role in triggering index arbitrage opportunities. Volatility causes all markets to move quickly, often independent of one another. At the same time, volatility attracts volume. The combination a.s.sures that index arbitrage will come into play.

The S&P is traded in many ways, and all of them are subject to a similar arbitrage to keep prices in equilibrium. There is also a large selection of ETFs that mimic the S&P cash price. The best known of these is SPY ("Spyders"), traded on NASDAQ, but a wide range of leveraged funds are offered by ProShares, ProFunds, Rydex, iShares, and other financial companies.

There are many variations on index arbitrage. It might be possible to sell S&P futures and buy the SPY ETF, or buy S&P futures and sell SPY, avoiding all the short-sale issues. Program trading is a big business, and professionals hold a so-called book of positions in such a way that short-selling can be done instantly. The elimination of the uptick rule and the move to trading pennies instead of eighths have facilitated program trading. The negatives are that, if the S&P drops more than a fixed percentage in one day, all program trading is halted, an awkward situation if you're in the middle of a trade. Also, compet.i.tion has caused some traders to select a smaller set of stocks to represent the S&P futures in order to reduce costs and expedite the process. They might set the arbitrage with marginal profit expectations just to enter sooner than other traders waiting for bigger opportunities. It is a clear case of compet.i.tion improving the spread and liquidity of the market.

How Can We Partic.i.p.ate?

If we're going to partic.i.p.ate in this arbitrage, then the practical answer is to choose a smaller set of markets that has an index that can be traded. Of the futures markets, that would be the DJIA, which has 30 components. Tracking the fair value of the Dow futures would be a straightforward process on a spreadsheet. Each day you would change the number of days to delivery and get a number that can be used all day to monitor differences in the cash and futures prices.

On even a smaller level, you can calculate the fair value of single stock futures and find a trigger point that makes that a profitable trade. While others are out there looking at the same opportunities, taking a slightly smaller profit and a slightly bigger risk may give you an edge.

About the Companion Web Site.

This book includes a companion web site, which can be found at www.wiley.com/go/alphatrading (pa.s.sword: alpha). There you will find a series of six Excel spreadsheets: 1. An Excel spreadsheet showing the calculations needed for creating a pairs trade made with two stocks plus trading signals. You can enter your own signal threshold levels and costs to test the results.

2. An Excel spreadsheet showing the calculations needed for creating a pairs trade using two futures markets plus the trading signals. You can enter your own signal threshold levels and costs to test the results.

3. An Excel spreadsheet showing the calculation of the stress indicator.

4. Two more Excel spreadsheets similar to (1) and (2) showing pairs calculations using the stress indicator.

5. An Excel spreadsheet showing the calculations needed for a crossover pairs trade, one stock and one futures market.

6. An Excel spreadsheet showing a simple portfolio of pairs (or any a.s.sets), including volatility-adjusting.

About the Author.

Perry Kaufman has 40 years of experience in financial engineering and hedge funds, and is well known for his role in algorithmic trading. Beginning as a rocket scientist in the aeros.p.a.ce industry, he worked on the navigation and control systems for the Gemini project. Since 1971, Mr. Kaufman has specialized in the development of fully systematic trading programs in derivatives and equities, as well as risk management and leverage overlays. During his career, Mr. Kaufman headed trading operations for large firms and has partnered three successful hedge funds. He is the author of New Trading Systems and Methods, Fourth Edition (John Wiley & Sons, 2005), A Short Course in Technical Trading (John Wiley & Sons, 2003), and other books and articles that have gained worldwide acclaim.