expression, “A Dollar Today Is Not Worth a Dollar Tomorrow.” We’ll go into this becausemany popular stock valuation models derive a company’s worth by estimating thepresent value of future earnings.Let’s say I have $100 today and have to decide whether to loan it to my friendJoe or deposit the $100 in the bank and earn 5 percent interest.Option 1
Option 2
Loan Joe $100 todayReceive $100 from Joe a year from now
Deposit $100 in a bank at 5% interestReceive $105 from the bank a year from now
The fact that I can deposit my $100 today and receive $105 from the bankin a year is the principle of the time value of money. When we look at cashflows in the future, we need to adjust their value back by an interest rate todetermine their present value. For example, the $100 loan to Joe may seem likea wash to most, but when we discount that repayment by the 5 percent we couldbe earning from the bank, the loan becomes a money-losing proposition. If allwe care about is money, we’re better off by putting our $100 in a bank and earning 5 percent.Option 1
Option 2
Loan Joe $100 todayReceive $100 from Joe in 5 years
Deposit $100 in a bank at 5% interestReceive $127 in 5 years
The concept becomes very important as the length of time increases.Suppose that Joe wishes to borrow the money for five years. Now the trade-offbecomes whether to receive the original $100 from Joe after five years or toreceive $127 back from the bank in five years. This example details the power of
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compounding. If I deposit $100 with the bank at 5 percent annual interest, atthe end of year one, I will receive $105. At the beginning of year two, I deposit the$105 with the bank again at 5 percent annual interest. My $105 grows to $105 ⭈(1 + 5%) = $110.25 at the end of year two. Again I deposit the $110.25 at thebeginning of year three at 5 percent and receive $110.25 ⭈ (1 + 5%) = $115.76 atthe end of year three. This process continues until the end of year five, where myoriginal $100 becomes $127.The same principle is applied when valuing companies.From annual reports, we can determine a company’s net profit. SupposeXYZ Inc. had $5 in profits during 2001 and is projecting this level of profitability for the foreseeable future. If we bought XYZ Inc. for $100 we would need tocompare the trade-offs between paying $100 for annual cash intake of $5 and thealternative of depositing the $100 in the bank to earn interest.AlternativesInterest rate
Bank interest
XYZ returns
1%5%10%
$1$5$10
$5$5$5
As we see in the table above, the level of interest rates can dramaticallychange our preference from either buying XYZ Inc. or depositing our $100 in thebank and earning interest. Similar decisions are made in the trade-off betweenbuying stocks and buying bonds. As a result, interest rates become very importantwhen valuing a company’s worth.There are three theories why lower interest rates lead to higher stock prices.First, as yields fall, a company’s cashflow looks more attractive versus bonds. Thiscan raise the value of the company. Second, lower interest rates cause waves ofhome mortgage refinancing, and the extra cash from lower mortgage paymentsoften finds its way into the stock market. A third potential link between interestrates and equities is that companies have greater ability to finance capital expenditure projects when interest rates are low. These expenditures modernize plants,raise productivity, and create new products through research and development.This spending often leads to improved profitability in the future.Historical data support the theory that lower interest rates boost equityprices. If we look at monthly percentage returns of the S&P 500 versus themonthly percentage changes in the 10-year Treasury yield between 1970 and2001 (Figure 10.2), we can see a distinct relationship. In Figure 10.2, as interestrates decline—measured by yields on the 10-year Treasury note—stocks are morelikely to rise when interest rates rise. We can use this relationship to design strategies for timing the equity market.
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Scatterplot: S&P 500 Returns vs. Change in Interest Rates20%
Monthly Change in S&P 500
15%10%5%0%–20%
–15%
–10%
–5%
0%–5%
5%
10%
15%
20%
–10%–15%
y = –0.2494x + 0.0107R2 = 0.0603
–20%–25%Monthly Percent Change in 10 Year Rates
FIGURE
10.2
Scatterplot: S&P 500 Returns vs. Change in Interest Rates. Stock prices appear to increase when interestrates fall and fall when interest rates rise.
TESTING MEDIUM-TERM STRATEGIESWe test monthly returns of the S&P 500 using total returns—price changes plusdividends—from 1970 through the end of 2001. Positions can either be invested inthe S&P 500 or cash. If invested in cash, the account receives the then going threemonth T-bill rate. We will base investment decisions on past returns of the S&P500, recent changes in 10-year Treasury note yields, and recent changes in oneyear Treasury bill yields.Most of these strategies can be considered simplistic—certainly whencompared to other ideas tested previously in this book. Despite their simplicity,however, many of these strategies lead to outperformance of a buy and holdmethodology, and with less risk.When reporting results, we calculate the ending value of a $100 startingaccount balance. In order to better evaluate the performance of our trading methodologies, we’ll calculate the ending account value of a contrary strategy, which investsexactly opposite our strategy, and compare it to our chosen strategy. When our strategy is invested in the S&P 500, the contrary account is in cash. When our strategyis in cash, the contrary strategy is invested in the S&P 500. I also report the percentof the time a strategy is invested in the market, which is a surrogate measure for risk:The less time we’re in the market, the less risk we’re taking with our money.
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As listed in Figure 10.3, 25 strategies based on moving averages and momentum changes were tested on monthly data. The signals are generated using themonthly closing price of the S&P 500 total return index, a cumulative measure ofthe S&P 500 total return. For comparison purposes, the buy and hold account endswith $3661 in 2001, while the strategy always invested in cash finishes with only$944. Remember, each strategy starts with $100 in 1970.What do these results tell us?First, 54 percent of the strategies outperform the buy and hold case and takeless risk in doing so. These performance numbers suggest that there may be anadvantage to market timing.The next important feature is that the best performing strategies were longthe market when rates were falling. Buying stocks when the 10-year yield was lessthan its three-month average led to an ending account balance of $6819. Thisamounts to annual returns of 14.1 percent, compared with 11.9 percent annuallyfor the buy and hold and 7.3 percent annually for the all cash strategy.The other interesting performance detail is that buying the market duringtimes of strong market returns produced some of the worst performance. The worstperforming strategy bought the market when the S&P 500 was greater than itsaverage over the past three months. This strategy turns $100 in 1970 into only$1310 in 2001—an annualized performance of only 8.4 percent—despite beinginvested roughly 63 percent of the time.Perhaps the most interesting strategy is the one that invests in the marketwhen both one year and 10-year interest rates are below their 12-month averageand the stock market is above its 12-month average. Despite only being invested38 percent of the time, this strategy produces annualized returns of 12.8 percentand handily beats a buy and hold return.
SHORT-TERM TRADING METHODOLOGIESFor those with shorter term trading horizons, we’ll also develop a number ofshorter term models and shed light on some market inefficiencies that are tradable using S&P 500 futures, exchange traded funds, or no-load index funds.Index Funds and ETFsIndexing and index funds grew tremendously during the 1990s, as equities rose inpopularity with American households. Contrary to a typical mutual fund managerwho picks stocks which he anticipates will beat the market, an index fund will buyall the stocks in an index and attempt only to match the performance of the index.Index funds have the advantage of being low cost. Typical mutual fundscharge 1.5 percent per year or more in expenses. This money is used to pay theportfolio manager and research analysts who pick the stocks held in the portfolio.
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EndingAccount
Percentof TimeInvested
Opposite RulesEndingAccount
10 year yields<3 month average
6,819
50%
500
1 year yields<6 months ago
6,610
52%
523
1 year yields<12 month averageSPX>12 month average and 1 year yields
4,855
54%
712
Strategy
<12 month average and 10 year yields<12 month average1 year yields<12 months ago10 year yields<12 month average
4,735
38%
730
4,4424,379
53%54%
778789
1 year yields<6 month average
4,337
51%
790
10 year yields<6 month averageSPX>12 months ago
4,2904,211
51%81%
798821
1 year yields<3 months ago
4,202
48%
822
SPX>12 month average1 year yields<3 month average
4,1234,089
76%50%
838834
3,7733,661
38%100%
904944
SPX>12 months ago and 1 year yield<12 months ago and 10 year yield<12 months agoBuy and Hold10 year yields<6 months ago
3,531
51%
979
10 year yields<12 months ago10 year yields<3 months agoSPX>6 months ago and 1 year yields
3,1653,135
49%49%
1,0921,102
2,732
33%
1,248
2,491
32%
1,369
2,4152,132
34%72%
1,4181,621
2,0061,879
71%71%
1,7221,823
1,8171,310
30%63%
1,8762,603
<6 months ago and 10 year yields<6 months agoSPX>3 months ago and 1 year yields<3 months ago and 10 year yields<3 months agoSPX>6 month average and 1 year yields<6 month average and 10 year yields<6 month averageSPX>6 months agoSPX>3 months agoSPX>6 month averageSPX>3 month average and 1 year yields<3 month average and 10 year yields<3 month averageSPX>3 month average
FIGURE
10.3
Performance of Market Timing Strategies. Over 54 percent of the strategies beat the S&P 500 while taking less risk.
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Because index funds simply match the holdings within a popular index, investment decisions are reasonably automatic and there is no need to pay for expensivestock research. Most index funds charge less than 0.3 percent in annual expenses.One of the largest mutual funds in the country is the Vanguard 500 Index Fund,which is designed to match the performance of the S&P 500. It has over $85 billion in assets.Stock exchanges, quick to realize an opportunity, began to offer exchangetraded funds in the early 1990s to compete with investors using index funds. ETFsare unit investment trusts or depository receipts that hold a basket of stocksdesigned to mimic a defined benchmark such as the S&P 500, the Nasdaq 100, orthe Russell 2000. The ETFs are listed on stock exchanges and represent the assetsthat hold these baskets of stocks. As a result, individual investors can now tradestocks that behave exactly like index funds.Unlike most index funds, which are only open to money inflows or outflowsonce a day, ETFs trade very actively throughout the day. They’re like stocks in almostevery way: ETFs trade on exchanges, they can be sold short—some even without theneed for an uptick—they can be purchased on margin, and they’re bought and soldthrough brokers. Due to their popularity, ETFs representing specific sectors andcountries have been designed to give investors exposure to very precise asset classes.Day of Week and Day of Month EffectsEarly research on day of week effects was conducted in the early 1980s to determine if Monday was more volatile than other days of the week. If informationdrives prices, and the amount of information is disseminated equally everyday,then, the reasoning goes, Monday should be three times as volatile as Tuesdaythrough Friday due to the news buildup over weekends. In fact, researchers discovered that, on average, Monday was equally volatile as every other day of theweek. What was not equal were the average returns that each day of the week generated. Monday had significantly worse returns than Friday.Over the years, it appears that the day of week effect has become muted.Well, how about the day of month and its effect on market returns?Examining daily returns of the S&P 500 since 1990, we average returns byeach day of the month. Note that we’re talking specifically about calendar days.Although March 3 may be the first trading day of the month, it would be recordedas Day three in our study. Figure 10.4 details the market ups and downs by day ofthe month.I first noticed the day of month pattern in my days at Salomon Brothers in1997 while part of the equity derivatives research group. I found that stock market returns had a bias based on where they occurred within the month. Distinctperiods of outperformance and underperformance emerged.
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Average Return by Day of Month0.40%
0.30%
0.20%
0.10%
0.00%
FIGURE
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
–0.20%
1
–0.10%
10.4
Average Return by Day of Month. Returns at the beginning, middle, and end of the month are higherthan average.
Looking at the above graph, you’ll see three intervals of above average returnsand two intervals of below average returns. If we divide the month into five periods, there’s a visible tendency. The beginning (Days 1 through 5) and end of themonth (Days 27 through 31) have the strongest returns. The second (Days 6 through11) and fourth (Days 19 through 26) parts of the month have less than averagereturns. A small positive hump exists in the middle of the month between Days 12and 18. We look at two strategies that capitalize on this day of month effect:1. We are long the market during Days one through five and Days 27 through 31.Assets are invested in cash for the remainder of the month.2. We are long the market during Days one through five, 12 through 18, and 27through 31. Assets are invested in cash the remainder of the month.In Figure 10.5 we see the importance of the day of the month in the two strategies we outlined. Despite being invested less than 30 percent of the time forStrategy 1 and only 54 percent of the time for Strategy 2, both strategies outperforma buy and hold methodology. A $100 investment beginning in January 1990 yields$454 for Strategy 1 and $758 for Strategy 2, compared with $419 for buy and hold.There are some possible explanations as to why the day of the month effectexists. Much of the American workforce now receives defined contribution retire-
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Day of Month Effects in the Equity Market1000Long the tails and middle800Buy and Hold600
400
200
7/2/01
1/2/01
7/2/00
1/2/00
7/2/99
1/2/99
7/2/98
1/2/98
7/2/97
1/2/97
7/2/96
1/2/96
7/2/95
1/2/95
7/2/94
1/2/94
7/2/93
1/2/93
7/2/92
1/2/92
7/2/91
1/2/91
7/2/90
0
1/2/90
Long the tails
Date
FIGURE
10.5
Day of Month Effects in the Equity Market. Our day-of-month strategy outperforms a buy and holdstrategy.
ment benefits. In contrast to 30 years ago, when retirement pay was based on apercentage of ending salary—so-called defined benefit plans—most currentretirement savings plans allow the individual flexibility in their savings options.These new plans, called defined contribution, usually involve a matching of fundsby the employer. If I contribute $100 each pay period to my 401(k), my companymight contribute $50 as part of a benefits program. The catch here is that I amresponsible for making investment decisions with this pool of money.Typically, 10 to 15 options are offered, including discounted company stock,equity mutual funds, corporate bond mutual funds, and government bond mutualfunds. With each pay date, money flows from my paycheck into the mutual fundmanagers. Given that most are paid biweekly, a large amount of 401(k) funds flowinto these mutual funds around the beginning, middle, and end of the month.When these funds are invested in stocks and bonds, the buying pressure couldmove prices higher and result in the day of the month bias we see above.Using the Volatility Index to Trade the S&P 500The price of volatility is determined by market forces, just like the price ofa stock or future. Investors, nervous that a stock will fall, will rush to buy putoptions in order to protect against a precipitous decline in a stock. Investors who
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are convinced that the market will rally sharply will buy call options to participate in violent rallies. This option buying pressure, which pushes up the price ofvolatility, increases the value of both calls and puts.When complacency arises, investors typically sell options. Overwriters willsell call options against their long stock position in order to generate extra incomein exchange for less upside in a stock. Other investors will sell put options as amethod to get long a stock at a lower price. When these sellers of options enter themarketplace, volatility declines. The resulting struggle between option buyers andsellers can be seen in the CBOE Volatility Index, commonly referred to as the VIX.The VIX is calculated from real-time option prices. As this index rises, itindicates that option buyers are outweighing option sellers and are pushing theprice of volatility higher. As the VIX falls, it indicates that option sellers are outweighing option buyers and pushing the price of volatility lower.The VIX is a measure of implied volatility using S&P 100 options. Volatilityis the main driver fueling option prices. Typically, high levels of implied volatility signal that the market is nervous and pessimistic in its outlook of futurereturns. Conversely, low levels of implied volatility signals complacency andoptimism. We can use the VIX to measure this fear or complacency and trade theS&P 500 accordingly. We want to be long the market in times of fear, and investedin cash when complacency is prevalent. In the graph in Figure 10.6, we see thatperiods of high VIX values usually coincide with market bottoms, while low values of the VIX are prevalent near market tops.I know of two popular methods of using the Volatility Index to trade the S&P500. One of them is discussed in Big Trends in Trading, in which author PriceHeadley utilizes Bollinger bands in conjunction with the VIX. Bollinger bands,popularized by market technician John Bollinger, plot price channels that adjustbased on market volatility. The middle band is drawn using a simple moving average, while the upper and lower bands are displaced by a multiplier of recent standard deviation of prices. Headley’s strategy utilizes a 21-day moving average withBollinger bands two standard deviations above and below the 21-day moving average. Long positions are entered when today’s S&P 100 close is above its 10-daymoving average and the VIX crossed below its upper Bollinger band five days ago.This strategy requires that an oversold condition presents itself before a long signalis generated. This oversold condition is signaled by the VIX rising above its upperBollinger band. An easing of this fear is set up by the VIX declining and fallingbelow its upper Bollinger band. A trade occurs five days after the VIX falls belowits upper Bollinger Band if the S&P 100 close is above its 10-day moving average.The other proponent of using the Volatility Index to trade the S&P 500 isLeon Gross, managing director of the Equity Derivatives Research group atSalomon Smith Barney. Gross suggests fixed levels to enter and exit positions.Currently, he advocates entering long positions in the S&P 500 on VIX crossesabove 30, and exiting into cash on drops below 20.
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S&P 500 and VIX80S&P 50070
S&P 500
VIX1300
60
1100
5040
VIX
1500
90030700
20
12/4/01
9/4/01
10/22/01
7/23/01
6/8/01
4/26/01
3/14/01
1/30/01
12/14/00
11/1/00
9/20/00
8/8/00
6/26/00
5/12/00
3/30/00
2/15/00
101/3/00
500
Date
FIGURE
10.6
S&P 500 and VIX. High values of the VIX usually signal market bottoms, while low values of the VIX signal market tops.
Both these methodologies use extreme highs in the VIX to enter long theS&P 500, and use low VIX readings to exit long positions. As we see in Figure10.6, bottoms are typically made during periods of high VIX readings, while topsare generally made during periods of low VIX readings.If we’re to create our own VIX trading strategy for the S&P 500 (since neitherabove method is ideal, in my opinion), we must first set out to identify periods ofextremes in the Volatility Index. We start by taking a 120-day average of the VIX todevelop a “mean” volatility. VIX readings above this mean signify higher than averagevolatility, while readings below the 120-day average signify lower than average volatility. Next, we quantify the deviation from normal volatility by comparing today’s VIXreading to the 120-day average reading and then dividing by the standard deviation ofchanges in the VIX over the past 120 days. Here’s the operative equation:VIXToday − VIXAverageVIX score = ᎏᎏᎏσVIXToday − VIXYesterdayPositive VIX scores denote that the VIX is higher than average and suggestequity market fear and pessimism. Negative scores denote that the VIX is lowerthan average and suggest equity market complacency.
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VIX and Standard Deviation Bands
VIX
45
30
12/2/01
11/2/01
10/2/01
9/2/01
8/2/01
7/2/01
6/2/01
5/2/01
4/2/01
3/2/01
2/2/01
1/2/01
15
Date
FIGURE
10.7
VIX and Standard Deviation Bands. By plotting bands around a 120-day average, we quantify periodsof high and low VIX readings.
Figure 10.7 graphs levels of the VIX, its 120-day average, and the averageplus two standard deviations, plus four standard deviations, minus two standarddeviations, and minus four standard deviations. These bands appear to highlightrelative extremes in the VIX readings quite well. Even more interesting is the wayin which the market behaves depending on the current Volatility Index score.Figure 10.8 calculates the average return of the S&P 500 based on yesterday’s VIXscore using daily returns from 1990 through 2001.VIX scores of +4 or greater lead to above average returns the following day,while scores of –2 or less generally lead to negative returns the next day. We canuse this tendency to create a new more robust VIX strategy to market time theS&P 500.Our new VIX strategy buys the market when today’s VIX score is greaterthan +2. We stay long until the current day’s score falls below –2. Figure 10.9graphs the portfolio value of following our new VIX strategy compared to a buyand hold strategy. Note that not only does our strategy outperform the buy andhold, but does so by being in the market only 53 percent of the time.
Average S&P 500 Return1.0%
Average Return
0.8%
0.6%
0.4%
0.2%
0.0%–5
–4
–3
–2
–1
0
1
2
3
4
5
6
7
8
–0.2%Yesterday’s Standard Deviations from VIX Mean (VIX Score)
FIGURE
10.8
Average S&P 500 Return. Returns are highest following days where the VIX was far above its 120-dayaverage. Returns are lowest following days where the VIX was far below its 120-day average.
VIX Strategy vs. Buy and Hold600500Portfolio Value
Buy and Hold400300200VIX Strategy100
6/29/01
12/29/01
6/29/00
12/29/00
6/29/99
12/29/99
6/29/98
12/29/98
6/29/97
12/29/97
6/29/96
12/29/96
6/29/95
12/29/95
12/29/94
6/29/94
6/29/93
12/29/93
6/29/92
12/29/92
6/29/91
12/29/91
6/29/90
12/29/90
12/29/89
0
DateFIGURE
10.9
VIX Strategy vs. Buy and Hold. Our VIX strategy outperforms a buy and hold strategy.
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CHAPTER
11
New Techniques in Money ManagementOptimizing the Results of Our Strategies
Money management deals with the amount of leverage we employ in our quantitative trading programs. With leverage of up to 20:1 obtainable in today’s financialmarkets, the money management question becomes very important. In this chapterwe’ll explore some of the popular methods for determining optimal leverage.
THE IMPORTANCE OF MONEY MANAGEMENT“Money management is the most important part of a trading strategy.”You will often see this quote in books about trading, but I disagree with thepremise of the statement. In reference to this, let’s introduce two important tenetsof money management:1. No money management technique can turn an unprofitable trading strategy intoa profitable trading strategy.2. Poor money management technique can turn a profitable trading strategy into anunprofitable trading strategy.According to the first tenet, we need a winning idea in order to trade profitably. Because of this, I believe that designing a profitable strategy is the first andforemost key to a successful trading program. The previous 10 chapters have beendesigned to teach readers to design, create, and evaluate trading strategies. I couldeasily end the book here and send readers out into the real world to trade. My guess305
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is that if you follow the concepts we’ve highlighted, your trading would more thanlikely be profitable. But even with a profitable trading strategy, many would suffer losses or wipe out their trading accounts. Why? The second tenet of moneymanagement says it all: Poor money management can transform a profitable strategy into a losing strategy.To understand the importance of money management, imagine a commoditythat you’ve studied over the past 10 years. It typically trades between $12 and $18,and studies have shown that selling highs near $18 and buying lows near $12 hasbeen quite profitable.Now, let’s say the market makes a new high at $20, and you decide to implement your strategy using your $45 bankroll by selling one contract. Despite theresearch that suggests lower prices, the market pushes higher after your first saleand trades up to $