Value Line Publishing, Inc. has the oldest continuous ranking service, initiated in 1965. They rank stocks by three qualities: timeliness, safety, and technicals. They boast that the returns on their timeliness ranking are in excess of 26,000% since 1965, compared with the return on the DJIA of 826%. Their web site posts a list of charges for their services.

Starmine (a Thomson Reuters company) is considered one of the high-end providers of a.n.a.lytic tools, as well as stock ranking. They offer newsletters with "earning surprise forecasts" and those companies expected to have material or structural changes in earnings. They target a mostly professional clientele at a fee.

Other services, such as www.TheStreet.com, Cramer's Mad Money, Reuters, and The Motley Fool (www.fool.com) provide both premium and free stock ratings. Examples of the free services are shown in the next section. It is worth repeating that claims of success are a normal part of marketing a product, but whether you are buying a service or doing your own ranking, you must prove that it works.

TABLE 9.1 a.n.a.lyst recommendations provided on the MSN Money web site.

Not Quite a Rating Service.

If you can't afford to pay for a proprietary rating service, there are other options. Many web sites allow you to sort stocks by one characteristic, such as price/earnings ratio (P/E), but MSN Money offers a summary of a.n.a.lyst recommendations. Table 9.1 shows 27 recommendations for Microsoft on May 25, 2010, grouped from strongest to weakest, plus the 3-month history of recommendations. The bottom line gives the mean recommendation, which is interpreted as 1.0 = strong buy, >1.0 to 2.0 = moderate buy, >2.0 to 3.0 = hold, >3.0 to 4.0 = moderate sell, and >4.0 = strong sell.

This seems to be exactly what we would want. The only inconveniences are that: You must enter each stock individually and record its recommendation in a spreadsheet.

You will need to develop a history of performance relative to the recommendations to be sure that the best recommendations bear some relationship to successful performance, or at least fall in the upper 50% of performance of the candidates.

On the other hand, the price is right. MSN Money also has its StockScouter Ratings, which have features similar to other services we are discussing.

TABLE 9.2 From www.TheStreet.com rankings for airlines.

Symbol Equity Rating ALGT ALLEGIANT TRAVEL CO B+.

CPA COPA HOLDINGS SA B.

HA HAWAIIAN HOLDINGS INC B.

LFL LAN AIRLINES SA C+.

LUV SOUTHWEST AIRLINES C+.

TAM TAM SA C.

GOL GOL LINHAS AEREAS INTELIGENT C.

RJET REPUBLIC AIRWAYS HLDGS INC C.

PNCL PINNACLE AIRLINES CORP C.

JBLU JETBLUE AIRWAYS CORP C.

Source: www.TheStreet.com.

TABLE 9.3 Jim Cramer's Mad Money daily stock calls (May 24, 2010).

In addition to access to the Jim Cramer Mad Money daily recommendations, www.TheStreet.com provides both premium and free ranking services. It provides individual stock rankings by sector, shown for airlines in Table 9.2, and Cramer's stock calls are shown in Table 9.3. As with many other services, how the rankings are arrived at is not disclosed.

TheStreet.com Ratings stock model compiles and examines all available financial data on a daily basis to gauge stocks' probabilities of moving up or down. The model scores stocks on various factors-including growth, financial solvency, stock price performance and volatility-which, when taken together, have shown strong correlation with future stock performance. The aim is to deliver investors with stock ideas that we feel have the best chance at delivering top risk-adjusted returns.

Investor's Business Daily also ranks stocks. In an academic paper, "A Test of the Investor's Daily Stock Ranking System" (Financial Review 33, no. 22, March 9, 2005), Olsen, Nelson, Witt, and Mossman conclude that "the best system provides market adjusted abnormal returns of 1.8% per month." While not free, the cost is not excessive.

Do-It-Yourself Ranking The Morningstar Stock Quickrank offers a fully technical ranking approach applied to the major equity sectors, stock funds, ETFs, and some other investment vehicles. You can choose to rank by market cap, sales, year-to-date total return, dividend yield, return on equity, earnings growth, price/earnings ratio, relative strength, and other features. Once selected, you get a list of stocks as shown in Table 9.4.

TABLE 9.4 Sample of Morningstar's Stock Quickrank for all stocks, return on equity.

Ticker Symbol Name Return on Equity % NEGI National Energy Group, Inc. 244.19 FXEN FX Energy, Inc. 240.06 MRIB Marani Brands, Inc. 231.92 MARPS Marine Petroleum Trust 231.11 SPNG Spongetech Delivery Systems Inc. 230.45 TIRTZ Tidelands Royalty Trust 227.77 PAY VeriFone Systems Inc. 223.74 ARB Arbitron Corporation 216.63 IHG Intercontinental Hotels Group PLC 212.39 AH Accretive Health, Inc. 199.92 BJGL Beijing Logistic Inc. 198.76 AJGH American Jianye Greentech Holdings Inc. 196.74 LGBS Legends Business Group, Incorporated 196.36 SNSTA Sonesta International Hotels Corporation 195.48 SWKH SWK Holdings Corporation 194.00 PNGXQ PNG Ventures, Inc. 192.56 ESI ITT Educational Services, Inc. 184.17 IMMU Immunomedics, Inc. 183.92.

WLSA Wireless Age Communications, Inc. 183.35.

MILL Miller Petroleum, Inc. 181.59.

Return on equity (ROE) measures a firm's return on shareholder investment (the shareholders' equity or the net worth of the company). ROE is a useful gauge in determining how efficiently a company is using shareholders' investment. Unlike return on a.s.sets, it considers the amount and cost of the firm's debt.

Source: Morningstar.

The Morningstar ranking is similar to many others available on the Internet. You can rank only one feature at a time, so you'll need to copy the table and move it to a spreadsheet, which is allowed. Then you can give each stock a ranking value, probably just a sequence number where 1 is the best, 2 is next, and so on, and combine the rankings from various attributes to get a composite score. Once that is done, you need to keep a record of whether your ranking reflects the relative success of performance.

MSN Money offers a similar service called StockScouter Ratings on its web site. Enter a stock symbol, and you get a ranking from 1 to 10, with 10 being the best. You can rank sectors, but there are only a few factors to choose from: fundamental, ownership, technical, and valuation. You can also qualify the choices by various levels of capitalization. The actual method of ranking is not disclosed, but then a.n.a.lyst rankings are also not explained.

Rules for Using Ranking Systems To summarize the use of ranking services: Research the services that are available. Those that provide a record of the success of past recommendations may be the best place to start, but you will need to confirm those results yourself or find a review from some other source with no conflict of interest.

If you prefer to try to rank stocks yourself, then choose any of the free services available on the Internet. Decide the sector(s) and the criteria, and then rank the stocks daily. Transfer the rankings to a spreadsheet for tracking.

Record the performance of those stocks in the ranking zone that you've decided to track. That could be the top and bottom 10%, or those in the 7080 percentile range versus the 2030 percentile range. The goal is that those stocks in the upper range remain in the upper range and those in the lower range remain lower.

Choose the stocks to be bought and sold. Calculate how many shares of each stock are needed to have the same risk. This is done by measuring the annualized volatility and then finding the multiplication factor for each stock that brings the position size to a common target volatility or risk.

Enter your positions.

Monitor the ranking and either hold the stocks for a predetermined period based on your ranking success or remove those stocks that fall out of your ranking zone, replacing them with the new stocks that are now in that zone. Positions must be volatility adjusted. To avoid switching too often, if you are using a zone of 7080, then switch when the stock falls below 65 or 60. If it moves above 80, then all the better. Similarly, stocks in the 2030 zone are held below 20 but are switched if they move above 35 or 40.

NEW HIGHS AND NEW LOWS.

An interesting variation on a ranking arbitrage is to trade all stock prices making new highs and new lows, buying the new highs and selling the new lows short. At the extreme, this could be limited to historic (life of the stock) highs and lows or modified to recognize 5-year or 2-year extremes. The longer, the better. The idea is that stocks making all-time highs or lows have something structurally good or bad happening, and this method would profit from that trend continuing.

Once a position is set, you'll need an exit criteria. A reversal from the high or low by 20% could work well. Each time you add or remove a stock, you'll need to rebalance both sides of the trade. It may be important to monitor the stocks making new lows to be sure they are moving; otherwise, you will be leveraging them up in large numbers to offset the obvious price movement in those stocks at the top. That presents two risks: The first is event risk, where a low-priced stock reverses on high volatility. The second is that you effectively trade only the longs, and the shorts offer no risk protection.

MERGER ARB.

Merger arb is an interesting area of trading that some traders consider to be an arbitrage, but it's really not. We'll describe it here to remove any confusion.

Merger arb is an arbitrage between the purchasing company (the acquirer) and a to-be-acquired company (the target). This can be traded a number of different ways.

The most successful arbitrageurs try to antic.i.p.ate the acquisition. On the one side, they know a company is not profitable because of debt, overhead, some crisis (such as loss of crops or a tainted product), or a temporary drop in demand that puts pressure on their cash flow. On the other side, there might be companies such as IBM, Intel, or Berkshire Hathaway that are looking to either complement their portfolios or add a missing piece of technology to their services. The traders may buy an option on what they perceive as the target candidate that pays off with either higher prices or higher volatility, both of which happen when a buyout or acquisition is announced. The trader who is correct about the acquired company even one in five times gets a very big payout because the price of that stock jumps to near the level of the acquisition price. At that point, they may take their profits or join the second group of arbitrageurs.

The second group is more conservative. They wait until the acquisition is announced and the board of directors has approved the deal. If the acquirer is paying a 100% premium for the stock, say, $30 for a company currently trading at $15, then the price jumps immediately to $28. The $2 difference is the uncertainty factor. If the market thinks the deal has a high probability of closing, then the difference between the stock price shortly after announcement and the target price is very small. If the market doesn't like the deal, then the difference is large.

Some traders buy the target company and sell the acquiring company, under the theory that the purchase adds to debt and uncertainty, thereby lowering the price of the acquiring company. Although that may appear to be a market-neutral trade, the movements of the two stocks are not very predictable; therefore, there is no a.s.surance that one move will offset the other and reduce risk.

The greatest risk in a merger arb trade is that the deal falls through. This most often happens when an audit of the company books produces unacceptable surprises. More recently, it happened because tight money made it impossible for some acquiring firms to borrow enough to close the deal. At that point, the stock of the nearly acquired company collapses, normally back to the preoffer price but many times much lower. The company no longer has its antic.i.p.ated support and, if it was losing money, it might spiral into bankruptcy. A trader who has sold the acquiring company may or may not benefit, but in the best of cases, the benefit would never offset the loss of buying the target company near the target price and then seeing the share price decline by half.

Although a merger arb program can have large risk, it is considered to have a short options profile. That means there are many small profits from successful deals closing and a few large losses. A merger arb program typically generates a return of about 8% annually for investment houses and offers a special type of diversification. Most deals close, so that the large losses are rare and can be absorbed by the higher frequency of small gains.

CREATING YOUR OWN INDEX ARBITRAGE.

If you can create your own stock ranking, can you also create your own index and use it for an arbitrage? In the previous chapters, we've used individual stocks and individual futures markets to create pairs. We've looked at using ETFs as well with some success. An ETF is convenient because there are no restrictions on short selling and it allows leverage. If you subst.i.tute an ETF for the short sales in stocks, you reduce the returns because the distortion in one stock is not reflected in the average of all stocks. Instead of capturing the entry points where two stocks or futures markets diverge, you are only capturing the point where one stock moves away from the index. That may be only half the potential profit. During a high-volatility period, that can still generate profits.

Selecting the two markets to use in the arbitrage can be done in a number of different ways. Many traders test their strategy on a wide choice of stocks and then pick the best performers. That's generally not a good method because you may have overfit the data and squeezed profits out of a few stocks by fine-tuning the parameter choices, which in turn identifies entry and exit points. As we saw in the previous chapters, parameters that are fine-tuned may work beautifully on one period of data but have too many or too few trades during other time intervals, usually because of changing volatility. If we are going to have confidence in a method, then it should produce profits using an arbitrary set of related markets and a wide range of parameters.

Another entirely statistical way of selecting the pairs is to find the correlation in price movement of the two legs. Correlations that are over 0.90 reflect markets that are too similar and have little chance of a profit that exceeds the cost of trading. Correlations below about 0.35 diverge for extended time periods, thereby introducing a very large risk each time you trade. Those markets with correlations of about 0.60 would be ideal, provided it's not just a short-term effect. We've looked at cases where the EURUSD and gold would be highly correlated for short periods due to immediate concerns about inflation. Those are excellent trading opportunities, but they can disappear quickly.

In the next section, we'll look at what happens if we create our own index and use it as one leg of a pair. It's similar to trading one stock against an ETF of that sector, when there is no ETF.

Mining Shares and the PMI Index We were very successful trading pairs of gold, platinum, and copper against the physical commodity in Chapter 6, but not everyone wants to trade futures.

Gold is already familiar to us, and the precious metals sector has a relatively small number of active stocks; therefore, it will be our starting point. By looking at the Yahoo! web site, we can find the precious metals (mining) stocks that are most active. They are shown in Table 9.5, in order of volume.

TABLE 9.5 Six most active precious metals mining stocks.

Symbol Name Current Price CDE Coeur d'Alene Mines Corp $0.63 ABX Barrick Gold Corp $28.76 NEM Newmont Mining Corp $38.90 AUY Yamana Gold Inc $8.70 GG Gold Corp $29.70 NG NovaGold Resources, Ltd $2.70 All other stocks traded fewer than 2 million shares per day. The individual stocks' price histories are shown in Figure 9.1. We create an index that we call the PMI (Precious Metals Index) by equally weighting the prices of the six stocks. That index is shown in Figure 9.2. It is easy to see that the index tracks the rise and fall of precious metals prices in a way that is even more exaggerated than the pattern of gold prices themselves. Besides supply and demand, profitability of mining companies is sensitive to operating margins, labor issues, and corporate management. At the time this index was created, gold was above $900/ounce after touching $1,000 (and on its way higher), and the PMI index is about 17 after topping 35, a drop of 50%.

FIGURE 9.1 Six precious metals mining stocks with the highest daily volume.

FIGURE 9.2 Precious Metals Index (PMI), an equal weighting of six mining stocks.

None of the six companies in the index was chosen based on suitability. You might observe that Coeur d'Alene, CDE, shown as the bottom price line in Figure 9.1, is far different from the other five stocks. It is also trading at the lowest price and might be delisted from the NYSE. It has a large business in silver, which might be reflected in the somewhat different price pattern. Perhaps a better index could be created by paying more attention to fundamentals, but our intention is to show that an arbitrage strategy works on an arbitrary set of stocks and a simple index.

One way to see if the components are reasonable choices is to calculate the cross-correlations, as shown in Table 9.6. Low correlations give us an idea that some of these companies are not affected by the same factors. For example, CDE has a low correlation against all other companies and only 0.163 against the index, while ABX, NEM, and GG are all very highly correlated. Correlations that are this low can occur randomly, but we expect that, being in the same sector, there is some fundamental relationship between CDE and the other stocks. For that reason, we'll leave it in this study because it may offer valuable diversification.

TABLE 9.6 Cross-correlations of six mining stocks and the Precious Metals Index, July 19, 2002, through March 6, 2009.

The Rules As with the other steps that we've followed in previous chapters to identify a trade, we'll follow a standard set of calculations and rules: Standardizing the data so both the stock prices and the index are in the same terms. That should be done by indexing.

Identifying the size of the entry distortion needed to capture sufficient profits to overcome costs.

Trading different quant.i.ties of each in order to equalize the risk.

Deciding at what point to exit the trade.

Because the PMI is an average price, it can be treated in the same way as each of the stocks in the index. We'll need to get the daily returns, based on the prices, using The return, rt, can then be used to calculate the annualized volatility (AVOL) of the two series over the past 10 days, and the ratio of the two volatilities gives the volatility factor, VAF, used to equalize the two series.

The 10-day calculation period is chosen because it is short enough to reflect changes in volatility but long enough to have enough data to be stable. Reducing the period to five days is tempting but would cause the volatility to jump around. Many traders might find that using a 20-day period is more in line with standards such as implied volatility or value at risk. With a much longer period, such as 250 days, the volatility will change very slowly and won't be responsive to some of the exceptionally volatile periods we've seen during 2008 and 2009.

The volatility adjustment factor, VAF, will be used for determining the number of shares to trade for every 100 units of the index. The position size for one side of the arbitrage must be fixed, and the other is then determined from the ratio.

Entry Points Finding good entry points will be the most important step. For this, we again use VAF to equalize the relationship between the index and stock price. The basic way of finding distortions is by using the standard deviation of the differences or, in our case, the returns. These will be called the volatility-adjusted differences (VAD). We will also need the average of the VAD values. This is different from previous methods that used a momentum oscillator to identify extremes.

Both of these calculations, the standard deviation of VAD and the average VAD, are based on only the past 10 days in order to be responsive to changes in volatility. It is now time to choose a key parameter, the standard deviation factor that determines how close or how far away the entry points will be placed. We know from statistics that using 1 standard deviation will capture 16% of these distortions (the part remaining on the outside of the distribution curve to the right). If we choose 2 standard deviations, we will only capture 2.5%, although those distortions will be much larger. We're going to choose a value that is smaller, 0.5 standard deviations, with the intention of having many more trades but enough profit to cover costs. Traders may decide to make this number bigger or smaller depending on their own preference for trading frequency and cost. If the standard deviation factor, F, is 0.5, the entry points are then calculated as follows.

Buy the index and sell the stock if VAD falls below the previous value of the average VAD minus the factor F times the previous value of the standard deviation of VAD.

If then buy the index and sell the stock.

If then sell the index and buy the stock.

In both cases, buying and selling, the exit occurs when the current VAD returns to the average VAD over the past 10 days. If the VAD values drift during the time a position is held, results may be better or worse than expected. There are no stop-losses and no maximum holding period. Risk is reduced primarily by diversification and is naturally minimized because there is no directional exposure.

Implementation and Liquidity The size of the positions is determined by the volatility adjustment factor, VAF. If we always trade 100 units of the index, then the number of shares of the stock is 100 VAF. Because we are using the PMI index that we created ourselves, we would buy or sell 1/6 of 100 (16.67) shares in each of the six companies in the index.

Selling short is always an issue, and not all stocks are available, so we need to know in advance which companies can be readily sold. If they cannot, they should not be part of the index. In this stat-arb example, we haven't checked on the status of any of the companies. It is best that we create the index, or trade the strategy, using the most liquid stocks, and those stocks are most likely to allow short selling. They will also have smaller execution slippage because they have a narrower bid-asked spread.

Precious Metals Results When we test the strategy on the six stocks for the 10 years ending March 2009, we get the results shown in Table 9.7. All results are adjusted to 12% annualized volatility, meaning that one standard deviation of the stock returns calculated over the entire 10-year period, times the square root of 252, will be 12%.

TABLE 9.7 Results of stat-arb using PMI and six mining companies, about seven years.

Of the six stocks, four were profitable, with the average result showing a return ratio of 0.284. There were nearly 100 trades per stock per year. The two companies that posted losses, AUY and NG, did not trade during the first half of the test period. The three stocks with the highest volume all posted profitable returns. Remember that there are no costs taken out of the results, and the stock trades posted a net loss of $0.0278 offset by the index gains of $0.027 on higher volume. These are marginal returns even for professional traders. Electronic trading can be done at very low cost, but profits this small are a concern. The performance pattern of each company can be seen in Figure 9.3. However, there is better news.

FIGURE 9.3 Performance of components and portfolio for the PMI arbitrage.

First, there is the advantage of diversification. In Figure 9.3, two of the stocks, ABX and NEM, continue higher during the last year while the other four swing lower before beginning a recovery. If we combine the six NAV streams into an equally weighted portfolio, the individual NAV volatility of 12% is reduced to 5.8%, less than half. This shows a significant amount of diversification, considering these stocks all belong to the same narrow industrial group. The final portfolio can then be leveraged back up to 12% using a factor of 2.05, yielding an annualized return of 8.18% from July 2002, shown in Figure 9.4.

FIGURE 9.4 Combined performance NAVs of six mining companies traded against the PMI.

Volatility is an important factor in arbitrage. It makes the distortions larger and reduces the impact of costs. It should be no surprise that the volatility of nearly all markets increased dramatically during the past two years, and this is reflected in the performance. During that period, the annualized return of the portfolio of six markets was 22.4%. The trading profiles from January 1, 2006, are shown in Table 9.8. We again see that volatility is an ally of the trader.

TABLE 9.8 Performance of each mining company traded against PMI for the period from January 1, 2006, through March 2009.