iffering maturity bonds pay varying interest rates.
Currently, the two-year Treasury note yields 2 percent, while the 10-yearTreasury note yields 4 percent. As an investor, I may prefer to buy the higher yielding 10-year note instead of the lower yielding two-year Note. Relative value players would take the trade one step further by buying the 10-year note and shortingthe two-year note, expecting the yield differentials to return to more normal levels.The difference in yields between maturities can be very volatile. Figure 9.2graphs the difference between the 10-year note and the two-year note between1990 and 2001.Another interest rate play is to value the curvature of the yield curve overtime. Note that in the yield curve graph above, the yield does not follow a straightline compared with maturity. The curve actually bends as time to maturity increases. This degree of this curvature changes over time and can be measured by comparing the yields of three maturities. If we want to measure the bend between thetwo-year note, 10-year note, and 30-year bond, we create the following series:Butterfly = 10-year yield – 0.5 ⭈ two-year yield – 0.5 ⭈ 30-year yieldThe combination of three yields in this manner is often referred to as a butterfly trade, as shown in Figure 9.3. When the butterfly trades high in yield, we willbuy the 10-year note and sell the two-year note and 30-year bond. When the butterfly trades low, we buy the two-year note and 30-year bond while selling the 10year note.For the purpose of trading the yield curve using quantitative trading methods, wecreate four yield curve series using constant maturity yields of U.S. Treasury products:
CHAPTER 9 New Ideas of Markets
253
Ten-Year Yield Minus Two-Year Yield
Difference (bps)
300
200
100
0
1/3/01
1/3/00
1/3/99
1/3/98
1/3/97
1/3/96
1/3/95
1/3/94
1/3/93
1/3/92
1/3/91
1/3/90
1/3/89
–100
DateFIGURE
9.2
10-Year Yield minus Two-Year Yield. By purchasing one bond and shorting another, we can gain exposure to the differencebetween yields of different maturity bonds.
2’s–10’s: Yield of 10-year Treasury note minus yield of two-year Treasury note2’s–5’s: Yield of five-year Treasury note minus yield of five-year Treasury note10’s–30’s: Yield of 30-year Treasury bond minus yield of 10-year Treasury note2–10–30 Fly: Yield of 10-year Treasury note minus 50 percent of two-yearTreasury note and 50 percent of 30-year Treasury bondUsing these yield curve data series, we will test our trading methodologies todetermine if we can predict movement in the U.S. Treasury yield curve. If ourstrategies are profitable, we can trade either futures or the actual governmentbonds to establish positions.Credit SpreadsWhile the debt of the U.S. government is safe (after all, the government can alwaysprint money), debt of individual corporations or municipalities carries no suchguarantee. As a result, nongovernment debt trades at higher yields than corresponding government Treasuries to compensate investors for taking this risk.Credit spreads are the excess yields required by investors to accept the added risksof investing in these non-Treasury investments.
PART 2 Harnessing the Power of Quantitative Techniques to Create a Trading Program
254
Two's-Ten's-Thirty's Butterfly100
50
0
–501/3/89
1/3/91
1/3/93
1/3/95
1/3/97
1/3/99
1/3/01
DateFIGURE
9.3
Two’s-10’s-30’s Butterfly. By purchasing two bonds and shorting another bond, we can gain exposure to the curvature ofthe yield curve.
The recent demise of Enron and WorldCom explain how important it is tomeasure the credit of these securities. Once rated investment grade, the bonds ofEnron and WorldCom (which once traded near 100) now trade for pennies on thedollar after each companies’ problems were brought to light. When a company isnot able to make an interest payment, their bonds are said to be in default.Bondholders, banks, and shareholders then begin to restructure the company inwhatever way possible to return money to each class of owners. Once banks arepaid in full, bondholders begin to receive money. Only after all creditors have beenpaid in full do shareholders receive any remaining value. In many default situations, bondholders may only receive pennies on the dollar if the financial health ofthe company is truly troubled.The risk of default creates a premium in yields of corporate bonds versuscorresponding Treasuries. This difference, or credit spread, tends to narrow during a growing economy as business prospects improve and the likelihood ofbond defaults diminishes. Conversely, credit spreads widen during weakeconomies, as troubling business prospects hurt the potential for repayment ofcorporate debt.
CHAPTER 9 New Ideas of Markets
255
There are two widely watched market measures of credit riskiness: swapspreads and high yield spreads. Swap spreads are vehicles used to trade the yielddifference between the London Interbank Offered Rate (LIBOR) and U.S.Treasuries. LIBOR is the predominant business lending index in the United States.It is an international average of offered rates for dollar deposits based on quotes ateight major banks. Being an overseas deposit, it does not carry FDIC depositorinsurance, and therefore carries the credit risk of the bank that holds the deposit. Asa result, these deposits carry risk and trade at higher yields than U.S. Treasuries.The spread that LIBOR trades over comparable U.S. Treasury yields can betraded by means of a swap spread with maturities between one year and 30 years.(See Figure 9.4 for a history of five-year swap spreads.) The swap spread productwas utilized heavily by Long Term Capital Management. In When Genius Failed,author Roger Lowenstein reported that LTCM lost approximately $1.6 billion byshorting swap spreads.Swap spreads = Five-year swap spread yieldsHigh yield spreads are calculated by taking an average yield-to-maturity ofhigh yield bonds and subtracting the interest rate of a corresponding U.S. Treasury.
Five Year Swap Spreads
Spread Yield (bps)
120
80
40
1/10/01
1/10/00
1/10/99
1/10/98
1/10/97
1/10/96
1/10/95
1/10/94
1/10/93
1/10/92
1/10/91
1/10/90
1/10/89
0
DateFIGURE
9.4
Five-Year Swap Spreads. Swap spreads measure the difference between government debt and highly rated corporate debt.
PART 2 Harnessing the Power of Quantitative Techniques to Create a Trading Program
256
High yield bonds are by definition rated lower than BBB by major debt-ratingagencies. Companies with such low credit ratings have significant risk of discontinuing interest payments on outstanding debt.If a company is forced into bankruptcy due to a default on its interest payments, bondholders face much uncertainty whether they will receive any paymenton their claims to the company’s assets. Due to this uncertainty, investors requirehigher yields to compensate for the added risk. The yield spread between high yieldbonds and Treasury notes signifies the market’s perceived riskiness of this lowerquality corporate credit. Our values of high yield credit spreads are derived fromsubtracting a five-year Treasury note yield from the average yield to maturity on theMerrill Lynch Master II index (see Figure 9.5).High yield = Yield to Maturity on Merrill Lynch Master II Index – five-yearTreasury yieldWe’ll test our trading strategies on these two series to determine if creditspreads are predictable and follow historical patterns. Swap spreads are readilytraded as Over-the-Counter derivatives products, while high yield spreads can be
Corporate High Yield SpreadsPremium over Treasuries (bps)
1200
950
700
450
1/3/01
1/3/00
1/3/99
1/3/98
1/3/97
1/3/96
1/3/95
1/3/94
1/3/93
1/3/92
1/3/91
1/3/90
1/3/89
200
DateFIGURE
9.5
Corporate High Yield Spreads. High yield spreads measure the extra payment that companies with weak balance sheetsmust pay in order to finance their debt.
CHAPTER 9 New Ideas of Markets
257
traded by buying high yield bonds and shorting an equal amount of Treasury notesor futures to remove their exposure to interest rates.Equity VolatilityVolatility is slowly becoming a better understood market phenomenon. Many tradingdesks on Wall Street focus solely on trading and managing the volatility risk associated with stocks, stock indices, and bonds. Some hedge funds that trade volatilityview their exposure to it as an asset class similar to stocks, bonds, or real estate.Investors can trade volatility through options such as calls and puts. A traderwho buys a call option has the right, but not the obligation, to buy a security at afixed price at a specific date in the future. If I buy a one-month $100 strike calloption on IBM, I have the right to buy IBM at $100 per share for the next month.If, at the end of the month, IBM is below $100, I allow my option to expire and Iwalk away. If IBM is above $100, I exercise my right and buy IBM at $100. At thatpoint I can sell the shares or hold on to them in anticipation of further advance. Acall option has a payoff structure similar to a hockey stick (Figure 9.6).A trader who buys a put option has the right, but not the obligation, to sell asecurity. If I buy a one-month $100 strike put option on IBM, I have the right to sellIBM at $100 per share for the next month. If, at the end of the month, IBM is above$100, I allow my option to expire and I walk away. If IBM is below $100, I exercise my right and sell IBM at $100. Similar to the call option, at that point I can buythe shares or hold on to the short in anticipation of further declines. A put optionalso has a payoff structure similar to a hockey stick (Figure 9.7).Here’s where the volatility component gets interesting. If I simultaneouslybuy both a call and put option of the same strike—called a “straddle” in popularterminology—my payoff diagram looks like the graph in Figure 9.8.It becomes clear that when I buy the call and put combination, I am indifferent to whether the stock rises or falls. However, I make more money if the stockis more volatile and moves far away from $100. In essence, this is what volatilitytraders are trying to accomplish. They buy cheap options and sell rich options thatappear to be mispriced by the market. Volatility traders constantly trade stock orfutures on the underlying asset in order to immunize the directional bet embeddedin calls and puts, leaving them with a pure play on volatility.The most popular measure of stock market volatility is derived from optionprices on broad market indices. The Chicago Board Options Exchange has maintained a daily record of the volatility implied by options prices since 1986. TheCBOE’s Volatility Index (VIX) measures at-the-money option volatility on the S&P100 (OEX). The VIX was developed by Robert Whaley to track implied volatility onthe S&P 100. Using four options from the nearest contract month and four optionsfrom the second nearest option month, the VIX interpolates the implied volatility ofa hypothetical at-the-money option with 30 calendar days to expiration.
PART 2 Harnessing the Power of Quantitative Techniques to Create a Trading Program
258
Call Option Payoff Diagram25
Call Option Payoff
20
15
10
5
0
120
115
110
105
100
95
90
85
80
–5
Stock PriceFIGURE
9.6
Call Option Payoff Diagram. Call options give the purchaser the right, but not the obligation, to buy the underlying asset.
Large discrepancies exist between the VIX and actual levels of impliedvolatility. A computational error in the VIX flaws its representation of impliedvolatility. Salomon Smith Barney’s Leon Gross (February 2001) was the first topublish the bias in the VIX calculation methodology. As we see in Figure 9.9, theVIX and actual implied volatility of OEX options track each other very closely. Infact, the ratio of the two measures seems to be constant, with the VIX alwaysroughly 1.20 times the level of actual implied volatility.Whaley, in his attempts to correct for a weekend effect present in options, incorrectly adjusted for the difference between calendar days in a year (365) and tradingdays in a year (roughly 252). As a result, if we multiply the VIX by SQRT (252/365),we arrive at an unbiased estimate of one month implied volatility on the S&P 100.Despite its bias, the VIX does measure the relative value of stock marketimplied volatility. Its most common use is for market-timing the S&P 500—a usethat has received much notoriety over the past couple of years. Increases in theVIX are a result of higher option prices—often a sign of market worry. This worrycan lead to good buying opportunities for stocks. Lower VIX levels are a result offalling option prices—often a sign of market complacency and a good sellingopportunity for stocks. In this chapter, however, we will focus on trading the actu-
CHAPTER 9 New Ideas of Markets
259
Put Option Payoff Diagram25
Put Option Payoff
20
15
10
5
0
120
115
110
105
100
95
90
85
80
–5
Stock PriceFIGURE
9.7
Put Option Payoff Diagram. Put options give the purchaser the right, but not the obligation, to sell the underlying asset.
al levels of the VIX and view it as a bona fide stand-alone market that we can tradewithin our relative value umbrella.The VIX measures implied volatility, which can be traded in the form ofstraddles, strangles, or more esoteric products such as volatility swaps. (For moreinformation and detail on trading volatility, see Demeterfi et al., “More Than YouEver Wanted to Know About Volatility Swaps,” Goldman Sachs QuantitativeStrategy Research Notes, March 1999; and Leon Gross, “Introducing VolatilitySwaps,” Salomon Smith Barney, January 1998.) When our models generate buysignals, we can gain exposure to volatility by purchasing straddles, strangles, andvolatility swaps. When our models generate sell signals on the VIX, we can sellstraddles, strangles, and volatility swaps in order to gain exposure to volatility.VIX = closing VIX priceRelative Performance of Stock IndicesWe will also study the relative performance of U.S. stock indices, utilizing the S&P500, the Nasdaq 100, and the Russell 2000. The S&P 500 is a capitalization-weight-
PART 2 Harnessing the Power of Quantitative Techniques to Create a Trading Program
260
Straddle Payoff Diagram
Straddle Payoff
2520151050
120
115
110
105
100
95
90
85
80
–5
Stock Price
FIGURE
9.8
Straddle Payoff Diagram. By purchasing a call and a put, we create a strategy that gains exposure to anasset’s volatility.
ed index of large cap U.S. equities. The Nasdaq 100 (sometimes referred to as theNDX) is a modified capitalization-weighted index of the largest 100 nonfinancialstocks trading on the Nasdaq marketplace. The Nasdaq 100 is highly weightedtoward information technology, telecommunication service, and biotechnologycompanies. The Frank Russell Company created the Russell 2000 as a benchmarkfor small cap performance. The Russell 2000 is comprised of U.S. stocks whosemarket cap ranks between 1001 and 3000 in the universe of all U.S. equities.Each index has periods of outperformance. In the 1980s, small cap stocks, asmeasured by the Russell 2000, outperformed large caps for many years. In themid-1990s, the nifty-fifty theme of large multinational corporations was veryprominent and the S&P 500 outperformed other indices. In the late 1990s, thetechnology bubble led to stellar returns for technology stocks. As a result, theNasdaq 100 outperformed other stock index benchmarks (Figure 9.10).Our goal will be to trade the relative performance of one stock index versusanother. We will study past data and test models to determine if we can predict periods of outperformance. Positions can be instituted by trading stock index futures listed on the Chicago Mercantile Exchange, or Exchange Traded Funds such as the SPYfor the S&P 500, the QQQ for the Nasdaq 100, and the IWM for the Russell 2000.We create two series to test long/short strategies for trading the S&P 500against the NDX and for trading the S&P 500 against the Russell 2000. Eachseries is calculated by taking the natural log of one index divided by another.Logarithms are mathematical functions used to simplify and manipulate equations
1.4
50
1.2VIX (thick)
1
40
Ratio0.8
300.620
Ratio
Implied Volatility
S&P 100 Implied Volatility, VIX, and Ratio60
0.4Implied volatility (thin)
10
0.2
11/14/01
7/3/01
2/23/01
10/13/00
6/7/00
1/28/00
9/13/99
5/13/99
01/4/99
0
Date
FIGURE
9.9
S&P 100 Implied Volatility, VIX, and Ratio. The VIX constantly gives readings about 1.2 times the value of at-the-moneyimplied volatility of the S&P 100.
Normalized Performance of Stock Indices
Performance (1989=100)
3000
Nasdaq 1002000
S&P 5001000Russell 2000
1/3/01
1/3/00
1/3/99
1/3/98
1/3/97
1/3/96
1/3/95
1/3/94
1/3/93
1/3/92
1/3/91
1/3/90
1/3/89
0
DateFIGURE
9.10
Normalized Performance of Stock Indices. The S&P 500, Nasdaq 100, and Russell 2000 have had periods of outperformance and underperformance.261
PART 2 Harnessing the Power of Quantitative Techniques to Create a Trading Program
262
that involve exponents. One special case, the natural log, is primarily used withinthe physical sciences. The natural log function is included in most software packages, such as Excel and TradeStation:SPX/NDX = ln(SPX/NDX)SPX/RUY = ln(SPX/RUY)Each of the two time series represents the normalized performance of oneindex versus another (Figure 9.11). When the new series increases, the S&P 500is outperforming the other index on a percentage basis. When the new series isfalling, the S&P 500 is underperforming on a percentage basis. We will use thisnatural log method for many of the price relationships we study.By utilizing a natural log of the price ratio, we are indifferent as to the securities chosen in the numerator or denominator of the ratio. These ratios will besymmetrical using the log method, while if only price ratios are used, the marketselected for the numerator or denominator will affect trading results. Figure 9.12also plots two series: the natural log of the S&P 500 divided by the Nasdaq 100,and then the natural log of the Nasdaq 100 divided by the S&P 500.
Natural Log of Price Ratios1.51.0
ln(SPX/RUY)
0.5
ln(SPX/NDX)0.0–0.5
–1.0
1/3/01
1/3/00
1/3/99
1/3/98
1/3/97
1/3/96
1/3/95
1/3/94
1/3/93
1/3/92
1/3/91
1/3/90
1/3/89
–1.5
DateFIGURE
9.11
Natural Log of Price Ratios. In each case, the S&P 500 is outperforming when the series rises and underperforming whenthe series falls.
CHAPTER 9 New Ideas of Markets
263
In Figure 9.12 not only are the two series mirror images of each other, buttheir scales are identical. That is, if one series rises by 0.20, the other series willdecline by 0.20, and vice versa.Single Stock PairsStock pairs will be used frequently in our market-neutral relative value tests. Pairstrading, as it is known on Wall Street, is used extensively by proprietary tradingdesks and hedge funds. Typically, pairs are identified using correlation analysis.Once they are identified, deviations from an expected value generate trading signals. I have arbitrarily picked 15 pairs of stocks from the U.S. market based onsimilarities in businesses. In each case, price series are calculated by taking thenatural log of the ratio of stock prices.Two of the pairs, UN/UL and RD/SC, have a particularly unique relationship(see Figures 9.13 and 9.14). Unilever PLC (UL) and Unilever NV (UN) are holdingcompanies that have a defined economic interest in their parent company, the Dutchand English based Unilever Company. However, both shares trade independently andare not fungible, meaning that one share cannot be exchanged equally for another.
Mirror Images0.800.600.40
Ratio
0.20
ln(NDX/SPX)ln(SPX/NDX)
0.00–0.20–0.40–0.60
12/21/2001
11/30/2001
11/9/2001
10/19/2001
9/28/2001
9/7/2001
8/17/2001
7/27/2001
7/6/2001
6/15/2001
5/25/2001
5/4/2001
4/13/2001
3/23/2001
3/2/2001
2/9/2001
1/19/2001
12/29/2000
–0.80
DateFIGURE
9.12
Mirror Images. Due to the principles of natural logs, the ln(NDX/SPX) always equals negative value of ln(SPX/NDX).
PART 2 Harnessing the Power of Quantitative Techniques to Create a Trading Program
264
Since this is the case, no perfect arbitrage exists in the markets. The relative pricesof UN and UL should move in tandem based on their claim on the assets of their parent—the Unilever Company. However, we find that these price ratios are not constant. As a result, the relative value of the two shares float, often reaching extremeswhere it is profitable to buy one stock and short the other stock.A similar case exists for Royal Dutch NV and Shell Transportation andTrading PLC (Figure 9.13). Both companies’ sole assets are fixed interests in theDutch-based Royal Dutch Shell. Royal Dutch owns 60 percent of the combinedfirm, while Shell owns 40 percent. Despite the fact that each companies’ net worthis tied to the same asset (the parent company, Royal Dutch Shell), the value ofRoyal Dutch shares fluctuate over time compared with Shell share prices. Theinherent relative value of the Unilever NV/Unilever PLC and Royal Dutch/Shellpairs make these markets ideally suited for our relative value trading.Commodity SubstitutesCommodity markets lend themselves well to relative value trading due to the substitution effect among related markets. If natural gas becomes too expensive forheating homes in the winter, heating oil is a substitute. Prices of soybeans will
Royal Dutch, Shell, and ln(RD/SC)500
1.00
400
0.80
Royal Dutch
0.700.60
300
0.50Shell
200
0.40
ln(RD/SC)
Performance (1989=100)
0.90
0.30100
0.200.10
ln(RD/SC)
11/16/01
11/14/00
11/18/99
11/20/98
11/24/97
11/27/96
12/4/95
12/7/94
12/10/93
12/15/92
12/19/91
12/24/90
12/28/89
0.00
1/3/89
0
DateFIGURE
9.13
Royal Dutch, Shell, and ln(RD/SC). Royal Dutch and Shell are linked through their shared ownership of Royal Dutch Shell.
CHAPTER 9 New Ideas of Markets
265
2.00
600
1.801.60
Unilever PLC
500
1.404001.203001.00200
Unilever NV
ln(UN/UL)
Performance (1989=100)
Unilever NV, Unilever PLC, and ln(UN/UL)700
0.80
ln(UN/UL)
100
0.60
11/16/01
11/14/00
11/18/99
11/20/98
11/24/97
11/27/96
12/4/95
12/7/94
12/10/93
12/15/92
12/19/91
12/24/90
12/28/89
0.401/3/89
0
DateFIGURE
9.14
Unilever NV, Unilever PLC, and ln(UN/UL). Unilever NV and Unilever PLC are linked through their shared ownership ofUnilever.
affect the prices of end products such as soybean oil and soybean meal. Gold andsilver often trade in tandem with each other. To study these and other commodityprice relationships, we create the ratios of natural log spot prices from four commodity pairs. Using spot (or cash) market prices instead of futures eliminates theneed to adjust differing futures contract cycles.Stock and Commodity RelationshipsFinally, we will look at the relationship between commodity related stocks and thefluctuations of the underlying commodities that drive their earnings.Gold producers, for example, are exposed to the absolute levels of goldprices. The producers have reasonably fixed production costs and typically do nothedge their entire production by selling gold futures or forwards. As a result,increases in gold lead to higher prices for gold stocks, and lower gold prices leadto decreases in gold stocks (Figure 9.15).A similar relationship exists between oil refiners and the price of oil (Figure9.16). The refiners’ margins increase as oil prices rise and contract when oil prices fall.As a result, there is a material link between oil stock prices and the price of crude oil.
PART 2 Harnessing the Power of Quantitative Techniques to Create a Trading Program
266
We create two series by using the Philadelphia Gold & Silver Index(XAU) as our proxy for gold stocks, the Amex Oil Index (XOI) as our proxy foroil stocks, spot gold prices, and spot oil prices. In both cases, we calculate thenew series by taking the natural log of the ratio of the stocks to the commodityprices.XAU/Gold = ln(XAU/Spot gold prices)XOI/Oil = ln(XOI/Spot crude prices)
DEVELOPING STRATEGIES FOR RELATIVE VALUE MARKETSHaving defined 30 new markets and divided them into seven asset classes (see listing, Figure 9.17), we now want to explore the profitability of applying trading strategies to these relative value markets.As in Chapter 7, we’ll start with our usual trading systems: channel breakout, dual moving average crossover, momentum, and oscillators. Expected resultsfor these new markets might be a bit different from traditional stock and futuresmarkets. In earlier chapters, I introduced behavioral evidence concerning the
Performance of XAU and Gold2.001.50150
XAU
1.000.50
100
0.00
Gold50
–0.500
–1.00–1.50
–50
ln(XAU/Gold)
–2.00
DateFIGURE
9.15
Performance of XAU and Gold. Gold and gold mining stocks tend to move in similar directions.
11/27/01
11/22/00
11/29/99
12/1/98
12/3/97
12/6/96
12/12/95
12/15/94
12/20/93
12/23/92
12/3