Risk-Adjusted Spreads Not all trading that removes directional risk is mean reverting. There are times when two related markets move steadily apart, with one product more desirable than another or one company doing better than another. There are many examples in the stock market. One cla.s.sic case was Dell and Compaq. Compaq was the early success story in personal computers and the first company to use MS-DOS (the first product of Microsoft) in the early 1980s. In a sign of the evolution of small computers, Compaq acquired Digital Equipment Corporation in 1998, the most prestigious minicomputer company. In another turn of the tables, Dell's new business model, selling computers with no retail outlets, rapidly overwhelmed other manufacturers, and by 2002 Compaq was forced to merge with Hewlett-Packard. Even the Compaq name didn't survive for long.

DELL AND HEWLETT-PACKARD.

For the past 10 years, Dell and Hewlett-Packard share prices have flip-flopped, with Dell leading for the first five years and HP overtaking Dell in 2006, as shown in Figure 5.1. An investor normally takes advantage of these broad moves by studying the fundamentals of both companies. If they are clever enough to realize that Dell's business model worked brilliantly when profit margins were high but would suffer as price compet.i.tion became more intense, they could have sold Dell short and bought Hewlett-Packard, netting a hefty gain. But our focus is on systematic, algorithmic trading.

FIGURE 5.1 Dell and Hewlett-Packard share prices from 2000.

A basic way to track these markets is to use the standard 200-day moving average. The only thing special about the 200-day moving average is that many traders watch it and it has taken on the role of a significant indication of market trend. We might have expected a 250-day, a 125-day, or a 63-day average to be more interesting because they are multiples of calendar quarters (in business days), and stocks report earnings quarterly. However, it's never a good idea to fight the market, so we'll stay with 200 days. Figure 5.2 shows the 200-day averages for Dell and HP from 2000. The trends are very clear and remain intact for months and years at a time. Simply buying when the trend turns up and selling short when the trend turns down would have been a successful strategy.

FIGURE 5.2 The 200-day moving averages applied to Dell and Hewlett-Packard.

However, following the trend of these two stocks independently means that from 2003 through mid-2005, you would have been long both companies and, during 2001 and from 2008 through mid-2009, you would have been short both. During those periods, amounting to about half the data, you would be exposed to directional risk. The purpose of this book is to avoid directional risk; therefore, we'll only look at positions where we are short one stock and long the other.

If we're patient, we could trade only when the two trends are going in opposite directions. That would actually give us hedged positions, some of which would be held for a long time. It also would create a lot of small trades, many of which will be losses. Even though the moving averages look smooth, and we take our positions from the direction of the moving average, the eye can deceive us. During the sideways period in 2002, the Dell trend wiggled up and down, causing false signals. Figure 5.3 shows the spread trades by posting a +1 when we are buying Dell and selling short HP, a 1 when we are selling Dell short and buying HP, and a 0 when we have no position (both trends are moving in the same direction). We want the chart to have continuous horizontal lines at +1 or 1, which means that we held the trade for a long time, as we did from about September 2005 through April 2007. Unfortunately, that is the only sustained position. From mid-2001 through April 2005, the lines going up and down indicate positions that have been closed out and reset. When more positions are reset, there are more losses.

FIGURE 5.3 Dell-HP trades when their trends are going in the opposite direction.

The better way to look at the Dell-HP trade is by using the ratio of their prices, in this case Dell divided by HP. Some a.n.a.lysts use the difference in prices, but that creates a very different picture. For example, when Dell and HP were both $25, the ratio would be 1.0 and the difference would be zero. If Dell moved to $50 while HP remained at $25 then the ratio would be 2.0 and the difference $25. The ratio indicates that Dell is twice the price of HP, even if Dell was $100 and HP was $50. At that point, the difference would be $50. We would need to remember the starting value of $25 to know that we had doubled the difference. As prices got higher, the differences would also get larger, reflecting higher volatility. But the ratio remains a percentage measurement and offers more consistency.

FIGURE 5.4 The Dell/HP ratio with a 200-day moving average.

FIGURE 5.5 The Dell-HP difference with a 200-day moving average.

Figures 5.4 and 5.5 show the ratio and difference, each with a 200-day moving average. Both of the trends are smoother than the trends of the two stocks separately, as seen in Figure 5.2. The ratio shows a few sustained, smooth trends, while the trend of the differences has two periods where it reversed direction numerous times, during 2003 and 2004 and then again in 2008 and 2009. Strictly from a practical view, the ratio performs better. To show this clearly, we calculated the number of trades for each method, where a trade is based only on the direction of the moving average line and not triggered by the price penetrating the moving average. The trend of the ratio had only 6 trades based on the changing direction of the 200-day trend line, while the trend of the differences had 60 trades over the same period, of which 17 were reversed after only one day. Without calculating the performance of the differences, the net returns using differences are likely to be a large loss.

To trade the ratio, we buy Dell and sell HP short when the trend of the ratio is up, and sell Dell short and buy HP when the trend of the ratio is down. As we did for pairs trading in the previous two chapters, the positions must be balanced according to their volatility. This maximizes diversification and reduces risk. In this case, the volatility was calculated using the average true range over the past 120 days, and the size of the positions were not changed during the length of the trade. Table 5.1 shows the six individual trades for the Dell/HP ratio. In 2001, HP was more volatile than Dell; consequently, it has only 79 shares compared with Dell's 100. During the next few years, as Dell showed more success than HP, it shows more volatility and smaller positions than HP. Overall, the percentage returns over less than nine years were greater than 11% per annum. More important, the big picture satisfies our general concept of when we would go long and short these two stocks, given a strategic approach to trading. And, of course, there is no directional risk.

TABLE 5.1 Trades for Dell and HP using the 200-day moving average of the Dell/HPQ ratio.

TRADING BOTH LONG-TERM (HEDGED) TRENDS AND SHORT-TERM MEAN REVERSION.

The trades in this chapter focus on the long-term divergence of two stocks or futures markets. This divergence can occur even while there are short-term opportunities for statistical arbitrage. The reason for this can be found in Chapter 2. If we look at prices over a very short time interval, we see more noise, but over the longer period, the trend is dominant. We can then be arbitraging Dell and HP over 3-day intervals but be long HP and short Dell for the longer-term trade.

In general, any calculation period under 10 days is targeting market noise, and those over 30 days are looking for the trend. Macrotrend strategies typically use trends in the range of 60 to 80 days, but those periods could be longer rather than shorter. In the previous example we used a 200-day average to base our technical version of a fundamental, or value, trade in order to emphasize the trend and minimize noise.

Balancing Fundamentals and Technicals There is constant debate over which is better, fundamental (or value) trading or technical a.n.a.lysis. The reality is that both can be good or bad. With fundamental a.n.a.lysis, you take a long position because the stock is undervalued, and if it goes down but there is no new information to say that fundamentals have changed, you simply own the stock at an even better price. Then the risk of a value trade can be very large, and there is no way to put a limit on it by using the same fundamental data.

Technical traders have a different problem. Because they may be following a long-term trend, they could go long Eurodollar interest rates when the price is 99.75 (a yield of 0.25%). The return is severely limited because prices can only go to 100, but the risk can be much greater (understanding that there can also be carry profits). The trend calculation does not know that yields are at historic lows and that the risk/reward of the trade is very unattractive. Some traders would call going long simply stupid and following every system trade naive.

Why not use the best of both methods? If you have an opinion on the direction of a stock or futures market, then use the technicals for timing. For example, if you have decided that the U.S. dollar is going to decline because of debt and relative Asian economic strength, then you would want to buy the EURUSD or sell the dollar against the Korean won, USDKRW. But you would do this only when the trend of USDKRW signaled a turn down. Then, if you're wrong, the trend will turn up, and you can exit. As long as you believe the dollar will weaken, you don't go long but wait for another short signal. This way, you've put a risk management plan on top of a calculated decision to sell the dollar and buy Asia.

GOLD, PLATINUM, AND SILVER.

The relationships between gold, platinum, and silver have been studied for many decades. The gold/silver ratio was traditionally considered normal at 35:1, but then gold was fixed at $35 per ounce and silver was $1 per ounce. It was also said that you could buy a pound of meat for an ounce of silver, but times change. With gold at more than $1,200 per ounce and silver at reaching new highs of $20 per ounce, the relationship seems to have broken down and now sits at 64:1. Is it simply adjusting to a new level, or is it a false concept?

These next comments should be prefaced by saying that everything is clear after the fact. If you don't like this explanation, you can subst.i.tute your own. You'll find that the financial news commentators, who are indeed very smart, always sound brilliant when discussing the issues that made the market go up or down yesterday. But these reasons are only clear afterward and never seem to be the same. Our problem is to decide on a profitable position in advance.

Many things have changed, perhaps evolved, during the past 50 years. With regard to gold and silver, some countries still hold a store of gold to back their currency, but it is not as formal or as common as in the past. The value of a currency floats based on the perception of the country's economic strength, with only a slight help from an above-average holding of gold reserves. Yet most people still value gold as an internationally recognized store of value. In addition, the consumption of gold has increased with new electronic uses. Gold turns out to be very good for conducting electricity and has been used as a contact point on high-end circuit boards. Reclaiming that gold is a difficult and highly regulated process, so much of it is lost.

Some history of gold trading is also necessary to understand the changes. Gold was fixed at $35 per ounce until the decision at Bretton Woods on August 15, 1971, to allow gold to float and allow Americans to own gold. The impact of that decision was that the value of a country's currency would be determined by its economic strength and not by its store of precious metals that served to back the currency. Following that decision, gold moved steadily higher, settling near $150 an ounce.

In 1970, the Hunt brothers decided to corner the market in silver, and by 1979, they had effectively accomplished that goal. From 1979 to 1980, silver moved from $11 per ounce to $50, peaking in January 1980 before starting one of the greatest collapses in history. Because of the gold-silver relationship, gold paralleled the silver move, peaking at about $800 per ounce and then plunging along with silver. At the peak, the gold:silver ratio was 16:1, indicating that silver was the driving force.

In the same way investors joined the great tech rally in the 1990s, they also kept buying gold and silver during the run-up to 1980. The general public always seems to have the largest position at the worst time. A large number of companies offered to help investors acquire gold to diversify and improve their personal portfolios. Even now, with gold above $1,200, there are firms saying the same thing. When gold and silver collapsed in 1980, investors were badly hurt-not quite as badly as the tech collapse, because gold and silver have an intrinsic value, but still losses that exceeded 75%.

Silver, which for investment purposes is considered the poor man's gold, never recovered. Those investors had long memories. Even gold prices remained low and very quiet for 20 years, until September 2000. Along with the decline in the economy that paralleled the tech bubble, people started buying gold. It is not surprising that investors would choose hard a.s.sets after losing badly in the stock market. But they did not go back to buying silver. Once seems to have been enough.

For those still considering trading the gold/silver ratio, Figure 5.6 shows the wide fluctuations and occasional volatile shifts. This is not what we would consider a tight relationship. There seem to be large intervals where the ratio trends up or down, making it difficult to put rules in place. Some traders may think of this as a challenge, but we will look for markets that are less risky.

FIGURE 5.6 Gold/silver ratio using nearest futures, from August 1983 through August 2009.

THE PLATINUM/GOLD RATIO.

Unlike silver, platinum is a precious metal, so the relationship between gold and platinum should be more stable. However, the uses for platinum have also changed over the years, with platinum, or platinum group metals, now the key component in catalytic converters. That increases the similarity between gold and platinum because both have industrial uses and both are still a very desirable store of value, but gold remains more popular as an investment. Figure 5.7 shows gold and platinum continuous futures prices from 2000. We use continuous futures because we will be trading futures. There are significant differences in the delivery months, with gold trading in February, April, June, August, October, and December, and platinum trading in January, April, July, and October. Even with these differences, we have no choice but to use the ratio of the nearest delivery. The main difference will be the carry, or interest rate cost as well as storage, both based on the number of days until delivery of the contract. That makes the carry different for both metals except when we trade October.

FIGURE 5.7 Platinum and gold prices from January 2000 (from continuous futures). Movement is similar except for the drop in platinum in 2001 and again in 2008. Gold has been more stable in its rise.

As you can see, prices moved in a very similar pattern most of the time, with notable exceptions in mid-2001 and the relative collapse of platinum in mid-2008. Nearly all commodities dropped precipitously in reaction to the U.S. bailout program and expectations of bad times to come. Because gold only dropped a much smaller amount in 2008, while platinum reflected an antic.i.p.ated drop in consumer spending for jewelry and automobiles, the platinum/gold ratio collapsed to par.

FIGURE 5.8 The traditional platinum/gold ratio, as well as the gold/platinum ratio.

Is the platinum/gold ratio any better than the gold/silver ratio? We think so. Figure 5.8 shows both the platinum/gold ratio and the gold/platinum ratio. Traditionally, the higher-priced market is divided by the lower-priced one because values over 1.0 have better resolution and are not limited as when the ratio approaches zero. The chart shows that the variation in the platinum/gold ratio is greater. We prefer the gold/platinum ratio because gold is the primary market, and the difference in the ratios, when used for systematic trading, will be minimal. Nevertheless, we will include the results of both gold/platinum and platinum/gold to show that computers don't really care as long as the numbers have enough decimal places.

The ratios show that, while there are periods where one market gains over the other, there are also three years when the ratio went sideways. The highly volatile period beginning in November 2007 will be our biggest concern. Will spread trading survive the disaster during August and September of 2008?

Trading the Platinum/Gold Ratio The platinum/gold ratio is easier to trade than stock pairs because there only two components: the trend of the ratio and the position sizes. A simple 60-day moving average of the ratio is calculated; then the spread is bought (long platinum, short gold) when the ratio turns up and sold when it turns down.

As with pairs trading, the volatility of the two legs must be equalized to create a position that is not biased toward one of the two legs. Table 5.2 shows a sample of three trades during the second part of 2009. In this example, platinum is always traded with 10 contracts, and gold is adjusted higher or lower based on its volatility relative to platinum. The position sizes are nearly the same for the three trades because the volatility of the two metals is similar. There are no costs reflected in the profits and losses, but you could subtract $35 per round turn for each leg to be conservative.

TABLE 5.2 Same platinum/gold trades.

The bigger performance picture is more interesting, as shown in Figure 5.9. During the past 10 years, trading the ratio would have yielded losses from 2002 through 2006, then extremely good profits. The NAVs for trading both the platinum/gold ratio and gold/platinum ratio are shown to point out that, while there are differences along the way, the long-term results are nearly the same. The statistics show that the profits per contract were slightly higher using the gold/platinum ratio ($212 versus $194), but the information ratio was slightly higher using the platinum/gold ratio (0.387 versus 0.383).

FIGURE 5.9 Performance of trading the platinum/gold ratio and the gold/platinum ratio from 2000.

Using Volatility It's unrealistic to think that anyone would start trading this ratio in 2000 and still be trading it at the end of 2006 when the losing streak ended. The solution to that problem is the same as the one we looked at in Chapter 4 when we found that inflation scares created volatility that improved performance. There are windows of opportunities that surface during critical economic times, and those opportunities are best recognized by watching the volatility. An abnormal increase in volatility generally signals a stronger correlation between many markets and a potentially profitable trading period.

The opposite of this, a period of low volatility, is often a.s.sociated with listless price movement. The risk may be very low because price movement is quiet, but that doesn't help if wandering prices do not generate profits and make it more difficult to offset transaction costs.

In the same way we looked at volatility in the previous chapters, we will review both the annualized standard deviation and the average true range as the choices for measuring volatility. Because the annualized standard deviation uses only the change in closing prices, while the average true range uses the highs and lows, we have advocated the average true range as more robust. Figure 5.10 supports that claim.

FIGURE 5.10 Volatility measured using (a) the annualized standard deviation method and (b) the average true range method.

The annualized volatility shows that platinum is much more volatile than gold most of the time. From 2000 through 2004, gold remains reasonably consistent at 10% while platinum bounces from 10% to 40%. We expect platinum to have a higher volatility when prices are higher than gold, but this variation does not parallel the ratio between the two metals. To show that clearly, we divide the annualized volatility by the price and compare the results in Figure 5.11. The volatilities of the two markets are very close in the past two years but still varied much more than the volatility measure using the average true range, shown in Figure 15.10b. It is also interesting that gold and platinum had the same dollar-value fluctuations throughout the 10 years using the average true range, but not using the annualized standard deviation. This seems to be another strong argument for using the average true range.

FIGURE 5.11 Comparison of gold and platinum annualized volatility as a percentage of price.

If we focus on Figure 5.10b, we see a clear move to higher volatility at the beginning of 2006, when the average true range reached about $850. If we isolate only those trades from the beginning of 2006, we show a return of 10% per annum at 12% volatility. Because trading these metals using the ratio should be uncorrelated to any other trading, the 10% volatility will be leveraged higher when this performance is mixed with others in a portfolio, a benefit of diversification. The final results of trading the platinum/gold ratio can be seen in Figure 5.12.

FIGURE 5.12 Performance of platinum/gold from 2006. Even after two years of sideways returns, a NAV of 170 is equivalent to an annualized return of 10% at 12% volatility.

Trading the platinum/gold ratio becomes another special situation rather than an ongoing process. But with markets becoming more complicated and compet.i.tion keener, waiting for the right time is more the rule than the exception.

IMPLIED YIELD.

Some commodities are pure carry markets because the forward prices always reflect the cost of holding that product. That cost is mostly the interest on the money needed to buy the product, but it may also include insurance, storage, inspection fees, and additional minor costs. The easiest case to understand is gold. Each forward month of gold reflects the basic costs of carry. It always increases, never decreases. This is not the case with most commodities. Copper is known to trade in backwardation, where the deferred contracts sell for less than the nearby. This is generally caused by a combination of falling demand and purchasers (manufacturers and fabricators) who will wait for the last minute to buy, thereby avoiding the carrying charges and holding unnecessary inventory. Crude oil is similar to copper, sometimes going for years in backwardation. We will not address whether there is any manipulation in these markets because we're not able to use that information for making trading decisions.

Because forward gold prices always reflect the cost of carry, traders can keep the term structure in line by arbitraging the various delivery months. For example, if the current price of gold was $1,000 and the price 12 months forward was $1,050, that would reflect a simple carrying charge of 5%. All things being equal, we would expect the price of the 6-month forward contract to be $1,025, reflecting a return of 2.5% for half the period. However, if the 6-month forward was $1,035, then it is too high, given the 12-month forward. It would imply an annualized yield of 7%, much higher than the 12-month contract shows. We could buy physical gold, sell twice as many of the 6-month delivery and buy the 12-month delivery, a trade called a b.u.t.terfly (with one foot in the cash market). At some point, the 6-month and 12-month annualized yields will need to line up. If not, gold will go to backwardation, which is unheard of. However, the term structure does not get out of line by enough to produce a profitable trade because professional arbitrageurs are hovering like vultures for that opportunity.

Table 5.3 shows the forward prices for the electronic Globex and open outcry sessions for CME gold (previously NYMEX and COMEX exchanges) and the corresponding forward prices for CME Eurodollar interest rates. Prices were posted on the CME web site as of March 16, 2010. Some of the calendar months do not have a futures contract; therefore, for the purpose of this example, the missing yields were interpolated from the surrounding prices.

TABLE 5.3 Forward delivery prices and implied yields for Eurodollar interest rates, Globex gold, and open outcry gold.

To the right of Eurodollar prices in Table 5.3 is the annualized yield implied from the discounted price, which is simply 100 minus the price. As you would expect, yields increase with time, beginning with the current, very low yield of 0.31% and increasing to 2.22% if held until December 2011, about 18 months.

Alternatively, you could buy physical gold and sell Dec 11 futures of an equivalent quant.i.ty (each contract is 100 ounces). Then you would be buying at the spot price of $1,122.50 and hedging by selling short the Dec 11 contract at $1,145.0 for an implied interest rate return of 2.00%. Figure 5.13 shows that the implied yield from both Globex gold futures and open outcry sessions parallel Eurodollar yields, although somewhat lower.

FIGURE 5.13 Comparison of implied yields from Eurodollars and gold (Globex and open outcry) as of April 2010.

Why would someone take 2.00% interest out of gold (or less after costs) rather than the equivalent return in government debt? When you buy U.S. debt, you are subject to variations in the U.S. dollar because when you buy U.S. interest rates you also buy the U.S. dollar. If you are a European investor and the EURUSD rises from 1.400 to 1.428, a relatively small amount in terms of forex fluctuations, you have effectively lost your 2% return when the money is repatriated back into euros.

Counterparty Risk Although bank CDs (certificates of deposit) always pay more than government treasuries, the risk of bank failure became a reality for many investors in 2008. Although they had considered Lehman Brothers bonds a AAA investment, their money was backed only by the strength of the company, which disappeared before anyone could withdraw their funds. Since then, advertis.e.m.e.nts for corporate bonds and CDs are followed by the disclosure "backed by the strength of the inst.i.tution."

ETFs have enjoyed tremendous acceptance and liquidity by the public, but they have various risks that are not well publicized, although probably appear somewhere in the fine print. Some of these risks include: Counterparty risk. ETFs are similar to mutual funds in that you have some direct ownership in the stocks or bonds held in the ETF. But in many cases, the agency has short-sale repurchase agreements with other companies who might not be able to fulfill their end of the arrangement under a worst-case scenario, such as Lehman Brothers.

Label risk. The shares or futures held in the ETF may not be the ones that you expect.

Tracking risk. The agency will try to use fewer stocks to duplicate an index or sector. This might not always work.

Spread risk. Stocks and futures are changed and rebalanced. These transactions are subject to the cost represented by the bid-asked spread and tend to be larger when the ETF is larger.

Fees. Although ETFs can be very efficient, there is a fee paid to the agency that reduces the ETF price, most often applied daily.

If you buy an ETF directly from an agency rather than through the exchange, then you rely entirely on the integrity and financial strength of the issuing company. When you trade through an exchange, you are guaranteed delivery of what you buy-that is, the shares are delivered to you-but the exchange does not guarantee the solvency of the company, nor does it review its financial statements for potential risk that could threaten the shareholders. The exchange is simply a vehicle for share transfer.

A sector ETF is a collection of shares held by the agency issuing the ETF. For a gold ETF, we have a more complicated problem. If the position is created using exchange-traded futures, then it is guaranteed, and there is little risk. If it uses forward contracts (which might be issued by a gold dealer), then there is no guarantee. For example, if you buy physical gold (a bar of gold), then you have no risk; however, if you buy a gold certificate from a bank, you do not own gold, you own the bank's debt, denominated in gold. This is similar to a bank CD in which you own the bank's debt denominated in some currency, such as U.S. dollars or euros. A gold ETF may claim to have physical gold inventoried, but there are no audit procedures that a.s.sure how much gold is held. In addition, if the company issuing the ETF goes under, it is not clear that the investors in the ETF have first claim on the gold, if any. This should not be surprising. Even for stocks listed on the New York Stock Exchange, the exchange itself has no responsibility for financial misrepresentation, as we saw with Enron.

Exchange-traded futures are guaranteed by an independent clearing house with enough funds to cover most losses. Excessive losses, which have never happened, are guaranteed by the members and the value of their memberships. The exchanges make sure that all traders holding positions have adequate funds to cover losses, based on a fiscally conservative expectation of volatility. If there are insufficient funds to cover these antic.i.p.ated losses, the trader must deposit additional money within hours of a margin call, or his or her positions will be liquidated at the market by the exchange. Extracting implied yields from futures contracts has less risk than other forms of interest income and has been used more actively during the past two years by large hedge funds and high-net-worth investors.

The same distinction needs to be made between exchange-traded derivatives and over-the-counter derivatives. One is guaranteed, and the other is not. Most notable are credit default swaps, a vehicle that has been very actively traded but is attributed with the collapse of the mortgage market and the Greek economy. Of course, taking a position to profit if something goes wrong does not cause the collapse, but the publicity of someone (especially a large hedge fund) profiting from someone else's misery can bring about countless Senate hearings and threatened regulation. The biggest issuer of credit default swaps was AIG, and had the government not bailed it out, it would have defaulted on all of them; those inst.i.tutions holding large profits would have lost all their gains, as well as any money on deposit with AIG.

The lesson to be learned is to be aware of counterparty risk. Don't a.s.sume that everything is fine. In the history of financial risk, other than the sovereign debt of the major industrialized countries (which is now not quite as secure as we thought), exchange-traded futures have been the most secure.

THE YIELD CURVE.

Interest rates are the target of many strategies used by investment banks and hedge funds, so there may not be much room for the armchair trader. Normally, the areas that are still open for exploitation require longer holding periods and greater risk. That turns out to be the case with yield-curve trades, with the added restriction that there are fewer opportunities.