Equity timing models explained
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Written by Dennis Tilley   
June 30, 2008
Since 1983, we have provided market timing signals to the public, through our monthly newsletter, FundAdvice.com (formerly Fund Exchange) and (since 1998) on our Web site, www.fundadvice.com.  While we have recently stopped computing these signals and publishing them to our website, we have made the calculations readily available to those investors who are interested. The purpose of these signals is to give individual investors a practical way to manage their portfolios using market timing systems.
Our four timing systems for the U.S. equity market are not designed to “beat the market.” Our objective in designing them is to achieve similar returns to a buy-and-hold approach while reducing downside risk by 30 to 50 percent.

Why do we recommend using four systems instead of only one? In a word, diversification. Any single system could underperform the market by a significant margin, and we don’t wish to subject our readers to that much risk. In addition, we believe that psychologically it is easier to move in and out of the market in 25 percent increments rather than alternating between 100 percent equities and 100 percent money market funds.

In 2003, we disclosed the details of these systems for the first time and simplified them to make them easier to understand and follow. There are advantages to simplicity. Many timing models incorporate more market information and more complicated trading rules, but they carry a higher risk of over-optimizing to the past. Even with superb back-tested results, when complex, sophisticated timing systems are used in real time, they often underperform simpler ones.
    
These are not the systems we use in the accounts we manage for clients. For clients, our objective is to achieve risk-adjusted performance, after fees, superior to that of these four systems. With our clients’ accounts, we use fund timing rather than market timing. Fund timing involves tracking many different funds individually (we track more than 1,000 funds daily) to determine when to buy or sell any particular fund.

For a description of fund timing, see “The best retirement strategy I know using active risk management” in our article library.

These four market-timing systems focus on the entire U.S. stock market, and they are designed to apply to most non-specialty domestic stock funds spanning the range of small-cap stocks to large-cap stocks and growth stocks to value stocks.
  
These systems should work well with most general domestic equity funds, including many that are offered through 401(k) and other retirement plans. However, they should not be used with sector funds, balanced funds that include fixed-income securities or target-retirement funds.
  
We used five guidelines to choose these four systems:

1. Each model should be able to reduce risk while achieving returns similar to a buy-and-hold approach. They are not designed to beat the market, although backtesting indicates that as a group they would have done so since 1972.

2. Each timing model must be simple, with relatively few rules and variables.

3. All four systems are heavily influenced by the market trend – they are trend-following systems. Trend-following systems are simple and adaptable to changing market conditions, thus they have a good chance of working in the future (not just in the past). This philosophy is consistent with how we manage client accounts.

4. Each model is mechanical. That means trading rules are defined up front, and no human judgments or decisions are required. This is consistent with our managed programs for clients. We believe a mechanical approach is an essential element for successful money management.

5. The systems are designed to take advantage of intermediate to long-term trends and to generate only two to three round-trip trades annually.

System #1: A simple trend following system

We often cite the 100-day simple moving average (SMA) as an easy-to-understand timing system to educate investors about the benefits and pitfalls of market timing. One drawback of this system is that it sometimes dictates holding periods of 10 days or less – sometimes as short as a single day. These whipsaw trades occur when the price is near the moving average, with market volatility pushing a price above and below the moving average repeatedly before establishing a longer-term trend.

Psychologically, it’s hard to keep up with this system during a period of many losing trades. Investors can become tempted to ignore buy signals, certain they will result in more losses. This system’s frequent moves are also a problem for many fund companies, some of which may not accept future trades from investors who are too active.

We have studied this problem extensively and have found many ways to extend the holding period and reduce the trading frequency. Here are our trading rules for System #1:

  System Buy: when the S&P 500 index crosses its 150-day moving average

  System Sell: when the S&P 500 index falls 2 percent below the 150-day moving average

This is different from the 100-day simple moving average system in two ways. First, we extended the look-back period from 100 days to 150 days. This slows down the system so that it does not trade so often. Second, we use what’s called a 2 percent lower band to increase the holding period. This means that after a buy signal, the price can fall as much as 2 percent below the 150-day SMA without dictating a switch.

As with the 100-day simple moving average system, there is nothing magical or optimum about 100 days, 150 days or 2 percent. Using other combinations yields similar results. This is one of the desirable characteristics of simple trend-following systems: Their performance doesn’t vary much from changes in their parameters.

Table 1 lists the hypothetical results of using System #1 with the S&P 500 and the Nasdaq 100 from 1972 through 2005. For reference, the buy and hold returns (including dividends) for these indices and commercial paper (a proxy for a money market fund) are also shown. For now, ignore the results of System #2. 
 

Table 1: System 1 and 2, 1972-2005
  Comm. Paper S&P 500 Buy & Hold   S&P 500 System #1 Trend Model S&P 500 System #2 Interest Rate Model   NDX 100 Buy & Hold   NDX 100 System #1 Trend Model NDX 100 System #2 Interest Rate Model
TRADE STATISTICS:                    
# of Round Trip Trades:       59.5 28.0
      56.5 28.0
# of Round Trip Trades/Year:       1.8 0.8       1.7 0.8
% Winners:       43.9% 67.9%       48.2% 67.9%
% Losers:       56.1% 32.1%       51.8% 32.1%
Avg. Winning Trade Gain:       17.2% 15.8%       22.3% 21.2%
Avg. Losing Trade Loss:       -2.7% -1.9%       -5.6% -4.1%
% Time in the Market:       71.8% 36.2%       71.6% 37.3%
Maximum Winning Trade:       69.5% 49.2%       104.9% 84.5% 
Maximum Losing Trade:       -6.4% -4.8%       -16.3% -9.4%
Max. Consecutive Winning Trades:       4
7       6 7
Max. Consecutive Losing Trades:       8 3       8 4
                     
YEAR-BY-YEAR PERFORMANCE (%):
  Comm. Paper S&P 500 Buy & Hold   S&P 500 System #1 Trend Model S&P 500 System #2 Interest Rate Model   NDX 100 Buy & Hold   NDX 100 System #1 Trend Model NDX 100 System #2 Interest Rate Model
1972 4.6 18.9   18.9 9.4   17.2   17.2 17.2
1973 8.2 -14.8   -7.4 8.2   -31.1   -14.2 8.2
1974 10.1 -26.6   10.1 10.1   -35.1   10.1 10.1
1975 6.3 37.2   13.9 9.6   29.8   13.0 5.4
1976 5.3 23.7   18.9 15.4   26.1   21.1 17.3
1977 5.5 -7.4   -3.3 0.0   7.3   3.9 2.8
1978 7.9 6.4   6.6 7.9   12.3   6.7 7.9
1979 11.0 18.5   10.9 16.1   28.1   17.1 16.9
1980 12.6 32.4   30.2 32.2   33.9   34.2 42.9
1981 15.4 -5.0   -9.9 15.4   -3.2   -5.0 15.4
1982 12.0 21.5   27.9 34.7   18.7   44.6 46.4
1983 8.9 22.4   20.8 25.6   19.9   19.2 43.7
1984 10.2 6.1   3.7 9.2   -11.2   -4.0 7.0
1985 8.0 31.7   28.9 31.7   31.4   30.2 31.4
1986 6.5 18.6   13.2 17.6   7.4   3.6 6.6
1987 6.8 5.2   21.2 15.5   -5.3   18.2 14.3
1988 7.7 16.5   -1.2 7.7   15.4   -1.2 7.7
1989 9.0 31.6   31.6 14.9   19.3   19.3 4.4
1990 8.1 -3.2   -5.7 -9.4   -10.1   -13.4 -15.4
1991 5.9 30.4   26.9 21.7   65.0   47.0 40.1
1992 3.8 7.6   5.6 1.4   8.9   3.9 -0.5
1993 3.2 10.0   10.0 8.9   10.6   10.6 6.5
1994 4.6 1.2   -4.5 3.9   1.5   1.7 2.9
1995 5.9 37.5   37.5 15.3   42.5   42.5 3.6
1996 5.4 22.9   16.8 6.8   42.5   31.5 17.5
1997 5.5 33.3   33.3 7.0   20.6   20.6 1.1
1998 5.4 28.5   18.0 42.6   85.3   63.2 95.2
1999 5.2 21.0   7.1 13.6   102.0   71.6 27.2
2000 6.3 -9.1   -7.1 6.3   -36.8   -11.5 6.3
2001 3.6 -11.9   -4.3 3.6   -32.7   -15.7 3.6
2002 1.7 -22.2   -8.0 -0.9   -37.2   -16.6 -5.3
2003 1.1 28.7   25.1 28.4   49.1   34.0 39.6
2004
1.5
10.9
  10.1
3.9
  10.5
  14.4
2.5
 2005 3.5  4.9
   1.3  3.5    1.6   -2.9   3.5
 2006 5.1  15.7     9.4 5.1     6.8   1.9  5.1 
                     
  Comm. Paper S&P 500
Buy & Hold
  S&P 500
System #1
Trend Model
S&P 500
System #2
Interest Rate Model
  NDX 100
Buy & Hold
  NDX 100
System #1
Trend Model
NDX 100
System #2
Interest Rate Model
ANNUALIZED RETURN (%): 6.6 11.3   10.8 12.1   10.3   12.3 13.8
RISK PARAMETERS (%):                    
Standard Deviation:   17.0   12.6 8.6   28.0   20.8 13.5
Worst Month:   -21.5   -11.8 -8.3   -27.0   -16.3 -11.1
Worst 3 months:   -29.6   -13.2 -11.9   -38.2   -26.3 -15.5
Worst 12 months:   -39.1   -18.5 -10.2   -67.3   -28.3 -18.3
Worst 36 months:   -41.0   -21.2 4.2   -76.9   -47.6 -3.3
Worst 60 months:   -17.6   -12.8 26.3   -66.3   -24.9
13.5
Worst Drawdown:   -47.4   -27.5 -15.3   -83.0   -54.3 -23.5
Avg. of 5 Worst Drawdowns:   -32.9   -25.2 -10.6   -51.5   -31.4 -20.0
Ulcer Index (Daily):   13.4   8.5 2.9
  33.7
  19.0
5.6

Timing can reduce bear market losses, though it should not be expected to eliminate them altogether.

Using this system to time the S&P 500 provided returns that were very close to those without timing: 10.9 percent per year with timing vs. 11.2 percent without timing. Yet the risk was reduced by 26 percent (standard deviation) or 45 percent (worst drawdown), depending on how you measure risk. Results for the Nasdaq 100 had similar risk reductions, along with a higher return than buy and hold. System #1 lost money in the bear market of 2000-2002, but the losses each year were much less than without timing. Similar results can be seen in the 1973-1974 bear market, which was equally as vicious.

This system generated an average of 1.7 round-trip trades (a buy followed by a sell) per year. That is not a lot of work, and fund companies will not object to that rate of trading. Although only 41 percent of the trades with the S&P 500 Index resulted in profits, this is an acceptable level for a trend-following system because the average gain on winning trades (18.4%) was more than six times as high as the average loss on losing trades (2.7%). A similar ratio is seen with Nasdaq 100 timing.

System #2. A simple interest rate model

The premise behind this model is that stocks tend to rise when interest rates are falling. There are many reasons for this. When interest rates decline, consumers tend to spend more and save less, for several reasons: They receive lower returns on their savings, their borrowing costs are lower and they have an incentive to refinance their homes, which often gives them more cash flow to spend.

Stocks are buoyed by higher profits, and profits are stimulated by higher consumer spending and lower business costs for borrowing money, which itself is another result of lower interest rates.

For these reasons, the Federal Reserve tends to reduce short-term interest rates when the economy is growing sluggishly and needs a boost. When the Fed cuts short-term rates, the stock market anticipates better times ahead, and stocks usually go up in price. Falling interest rates also make stocks relatively more attractive when compared with bonds. At some point, falling interest rates will motivate investors to move their money from bonds and certificates of deposit into stocks.

There are many interest rates we could use in this timing model. We chose the 90-day commercial paper rate, which investment-grade companies pay for short-term loans. This rate can be found in the Wall Street Journal in the Money Rates section, or in Barron's in the Market Laboratory insert. There is nothing special about this interest rate; you can use another short-term rate as long as you’re consistent in using the same rate every day.

Here are the preliminary buy and sell rules for System #2:

Buy: when the commercial paper yield falls 1 percent below its 200 day moving average.

Sell: when the commercial paper yield rises 1 percent above its 200 day moving average.

The problem with this model, which we will call the Cp (commercial paper) model, is that on rare occasions, stock values have fallen as interest rates have dropped. This phenomenon occurs in times of severe economic stress or when stocks are extremely overvalued. Notable past occurrences include Japan in the 1990s, the United States in the 1930s, and in 2001 and 2002. Since the primary objective of this timing system must be to provide safety first, we will add a second set of variables and trading rules – what we call a trend overlay:

Buy: when the S&P 500 index rises 1 percent above its 200 day moving average.

Sell: when the S&P 500 index falls 1 percent below its 200 day moving average.

Here are the system rules that combine the two sets of variables:

  System Buy: when the Cp model AND the trend overlay are on a buy.

  System Sell: when either the Cp model OR the trend overlay is on a sell.

These rules may seem complicated, but the main idea behind them is to be in the market when stocks are trending higher and interest rates are falling. We have used 1 percent and 200 days for both the Cp and trend overlay models only to keep things simple. Other values are likely to work as well.

Table 1 shows the hypothetical results of System #2 for the S&P 500 and Nasdaq 100 from 1972 through 2005. Compared with the trend-following system of System #1, our interest rate model is more hesitant to give the all-clear signal to re-enter the market.

Notice that this system was in the market only 37 percent of the time, vs. 72 percent with System #1. Because of that, we expect the risk parameters to be much lower, and in backtesting, they were. This system cut the worst drawdown for the S&P 500 from 47.4 percent to 15.3 percent, and for the Nasdaq 100 from 83 percent to 23.5 percent. It also performed better than System #1 and buy and hold in the past. It only trades about once per year and is very easy to implement.

System #3. Simple Nasdaq Breadth Model

This model uses Nasdaq daily up and down volume to determine timing signals. Up volume is calculated by adding the trading volume for all stocks that have risen that day. Similarly, down volume is calculated by adding the trading volume for all stocks that have fallen that day. This information is published each business day in the Wall Street Journal’s Money and Investing section.

This model is called a breadth model because every Nasdaq stock has an impact on the buy and sell signal. This is in contrast to a system focused on a market index such as the Dow Jones Industrial Average, the Nasdaq 100 or the S&P 500. There are thousands of stocks that trade on the Nasdaq and New York Stock Exchange. The Dow Jones average accounts for only 30 stocks, the Nasdaq 100 only 100 and the S&P 500 only 500. This timing model tracks the health of all stocks in the NASDAQ market.

The rationale for this system is very simple. In a rising market, we expect more stocks to be rising than falling, and the up volume should be higher than the down volume. The opposite is true in a falling market. This is a variation of the trend-following System #1. The difference is that System #1 focuses on the S&P 500 while System #3 tracks all stocks trading on the Nasdaq. The trading rules are:

  System Buy: when the sum of the Nasdaq up volume over the last 8 days divided by the sum of the down volume over the last 8 days is greater than 1.5.

  System Sell: when the sum of the Nasdaq up volume over the last 8 days divided by the sum of the down volume over the last 8 days is less than 0.8.

Again, our backtesting has shown that the performance of this system was insensitive to moderate changes in the system parameters.

Table 2 shows the performance of this system with the S&P 500 and Nasdaq 100 from 1978 through 2005. Note that we cannot provide the results back to 1972 since up and down volume data are not available for years before 1978. 

Table 2: System 3 and 4, 1978-2005
  Comm. Paper S&P 500 Buy & Hold   S&P 500 System #3 NASDAQ Breadth Model S&P 500 System #4 NYSE Breadth Model   NDX 100 Buy & Hold   NDX 100 System #3 NASDAQ Breadth Model NDX 100 System #4 NYSE Breadth Model
TRADE STATISTICS:
# of Round Trip Trades:       98.0 47.5       98.0  47.5
# of Round Trip Trades/Year:       3.6 1.8       3.6 1.8
% Winners:       55.1% 40.4%       48.0% 42.6%
% Losers:       44.9% 59.6%       52.0% 57.4%
Avg. Winning Trade Gain:       7.4% 16.3%       13.5% 19.3%
Avg. Losing Trade Loss:       -2.3% -2.3%       -3.8% -4.3%
% Time in the Market:       66.9% 51.2%       66.9% 51.2%
Maximum Winning Trade:       28.7% 46.6%       56.3% 72.8%
Maximum Losing Trade:       -7.1% -6.1%       -11.2% -13.4%
Max. Consecutive Winning Trades:       9 3       4 5
Max. Consecutive Losing Trades:       5 7       7 7
                     
  Comm. Paper S&P 500 Buy & Hold   S&P 500 System #3 NASDAQ Breadth Model S&P 500 System #4 NYSE Breadth Model   NDX 100 Buy & Hold   NDX 100 System #3 NASDAQ Breadth Model NDX 100 System #4 NYSE Breadth Model
YEAR-BY-YEAR PERFORMANCE (%):
1978 7.9 6.4   13.6 13.2   12.3   25.1 18.5
1979 11.0 18.4   19.8 12.1   28.1   30.7 12.1
1980 12.6 32.4   36.6 37.6   33.9   47.2 50.7
1981 15.4 -5.0   -0.9 11.5   -3.2   2.1 17.5
1982 12.0 21.5   20.4 34.7   18.7   39.3 46.4
1983 8.9 22.4   22.5 17.9   15.2   24.1  18.7 
1984 10.2 6.1   -2.6 2.7   -18.4   -27.0  -6.4
1985 8.0 31.7   26.9 26.5   21.8   20.5  21.1
1986 6.5 18.6   6.6 2.8   6.9    -1.0 -7.7 
1987 6.8 5.2   27.4 21.7   10.5    38.3  29.0 
1988 7.7 16.5   9.7 -3.1   13.5   11.5 -2.8 
1989 9.0 31.6   25.5 26.3   26.2    25.7  30.0 
1990 8.1 -3.2   7.4 8.1   -10.4   7.9 8.1
1991 5.9 30.4   12.0 16.4   65.0   22.2 27.4
1992 3.8 7.6   -0.6 -3.7   8.9   4.2 -8.4
1993 3.2 10.0   4.4 8.8   10.6   -2.2 5.8
1994 4.6 1.2   -2.3 3.8   1.5   0.9 6.6
1995 5.9 37.5   30.2 26.5   42.5   29.2 27.8
1996 5.4 22.9   17.0 18.4   42.5   36.5 34.2
1997 5.5 33.3   20.7 22.1   20.6   15.5 6.8
1998 5.4 28.5   27.9 17.4   85.3   59.4 26.5
1999 5.2 21.0   7.0 -1.7   102.0   56.8 -6.0
2000 6.3 -9.1   0.7 -0.9   -36.1   4.1  -4.2
2001 3.6 -11.9   12.0 3.6   -33.4   18.4 3.6
2002 1.7 -22.2   -2.4 -3.2   -37.4   -1.2 -12.1
2003 1.1 28.7   5.0 22.6   49.7   -3.8 30.5
 2004  1.5 10.9     12.9 3.1     10.5    15.2  1.3
 2005  3.5  4.9    3.7  -1.0    1.6    -1.6  -6.4
                     
  Comm. Paper S&P 500 Buy & Hold   S&P 500 System #3
NASDAQ Breadth Model
S&P 500 System #4
NYSE Breadth Model
  NDX 100 Buy & Hold   NDX 100 System #3
NASDAQ Breadth Model
NDX 100 System #4
NYSE Breadth Model
ANNUALIZED RETURN (%): 6.6 13.1   12.4 11.7   13.2   16.1 11.9
RISK PARAMETERS (%):                    
Standard Deviation:   17.2   12.1  10.0   30.3   20.6 15.6
Worst Month:   -21.5   -8.5 -8.5   -27.0   -11.6 -12.6
Worst 3 months:   -29.6   -12.8 -10.9   -38.2   -18.1 -19.6
Worst 12 months:   -26.6   -8.5 -8.8   -67.3   -36.1 -16.0
Worst 36 months:   -41.0   0.2 -7.2   -76.9   -14.5  -20.1
Worst 60 months:   -17.6   19.9  -4.7   -66.3   8.9  -21.7
Worst Drawdown:   -47.4   -14.7 -15.8   -83.0   -38.5 -26.0
Avg. of 5 Worst Drawdowns:   -27.8   -13.1 -11.8   -44.8   -22.6 -23.4
Ulcer Index (Daily):   12.7   4.8 3.8   32.2    11.5  9.8 

Compared with the previous models, the Nasdaq Breadth model trades more actively, averaging about three round trips per year. The model reduces risk on the S&P 500 by 30 percent (standard deviation) and 69 percent (worst drawdown). Returns for the Nasdaq 100 are exceptionally good, along with significantly less risk. 

       

In the long run, we expect these timing systems to provide returns about the same as those of buy-and-hold, but at much less risk.  


System #4. Simple NYSE Breadth Model

System #4 uses the New York Stock Exchange (NYSE) daily advance-decline line. This is constructed each day by adding the number of advancing issues and subtracting the declining issues. The advance-decline line is also classified as a breadth indicator because it is influenced by all stocks traded on the NYSE. The trading rules for System #4 are: 

  System Buy: when the NYSE advance-decline line is 2 percent or more above its 150-day moving average AND when the S&P 500 Index is 2 percent or more above its 150-day SMA.

  System Sell: when the NYSE advance-decline line is 2 percent or more below its 150-day moving average OR when the S&P 500 Index is 2 percent or more below its 150-day SMA. 

Like System #2, the NYSE Breadth Model requires two independent models to be in sync before a buy signal is triggered. This additional hurdle limits the number of whipsaw trades. 

Table 2 shows the performance of the NYSE Breadth Model on the S&P 500 Index and the Nasdaq 100 from 1978 through 2005. Because of the additional restrictions before buying, this system was in the market only 49 percent of the time. Because of that, risk measures are all significantly reduced compared with buy and hold. This system trades infrequently, an average of 1.7 round trips per year.

The Importance of Diversification

Table 3 shows the risk-return results for the combination of all four systems (50 percent each of Systems #1 and #2 from 1972 through 1977 and 25 percent each in all four systems from 1978 through 2005). The annualized return for timing was one percentage point higher than that for buy-and-hold returns of the S&P 500. The timing returns were much better than buy and hold for the Nasdaq 100. Again, this is a consequence of the bear market in 2000 through 2002, when the buy-and-hold strategy lost 73 percent. 

Table 3: Four Systems Combined, 1972-2005
  Comm. Paper S&P 500 Buy & Hold   S&P 500 4-Systems Combined   NDX 100 Buy & Hold   NDX 100 4-Systems Combined   50% S&P 500 50% NDX 100 4-Systems Combined
YEAR-BY-YEAR PERFORMANCE (%):
1972 4.6 18.9   14.1   17.2   17.2   15.7
1973 8.2 -14.8   0.1   -31.1   -3.6   -1.8
1974 10.1 -26.6   10.1   -35.1   10.1   10.1
1975 6.3 37.2   11.8   29.8   9.2   10.7
1976 5.3 23.6   15.9   26.1   19.1   17.5
1977 5.5 -7.4   -1.6   7.3   3.4   0.8
1978 7.9 6.4   10.4   12.3   14.4   12.4
1979 11.0 18.4   14.8   28.1   19.1   17.0
1980 12.6 32.4   34.3   33.9   43.8   39.0
1981 15.4 -5.0   3.7   -3.2   7.2   5.5
1982 12.0 21.5   29.4   18.7   44.2   36.7
1983 8.9 22.4   21.8   15.2   25.2   23.6
1984 10.2 6.1   3.3   -18.4   -12.0   -4.7 
1985 8.0 31.7   28.5   21.8    21.1    24.9
1986 6.5 18.6   9.9   6.9    -0.7    4.6 
1987 6.8 5.2   21.7   10.5    29.5    25.6
1988 7.7 16.5   3.4   13.5   2.8    3.1 
1989 9.0 31.6   24.5   26.2    21.9    23.3
1990 8.1 -3.2   -0.1   -10.4   -3.8   -1.9
1991 5.9 30.4   19.4   65.0   34.1   26.7
1992 3.8 7.6   0.7   8.9   -0.1   0.5 
1993 3.2 10.0   8.0   10.6   5.2   6.8
1994 4.6 1.2   0.3   1.5   3.2   1.7
1995 5.9 37.5   27.2   42.5   25.2   26.6
1996 5.4 22.9   14.7   42.5   30.0   22.4
1997 5.5 33.3   20.8   20.6   11.5   16.3
1998 5.4 28.5   26.3   85.3   59.9   42.4
1999 5.2 21.0   6.7   102.0   35.4   20.5
2000 6.3 -9.1   0.6   -36.1   1.4    1.2 
2001 3.6 -11.9   3.7   -33.4   2.7    3.3
2002 1.7 -22.2   -3.5   -37.4   -8.6   -6.0
 2003   1.1  28.7    20.0    49.7    24.1    22.2
 2004  1.5  10.9    7.2    10.5    8.0    7.7
 2005   3.5  4.9    2.3    1.6    -1.3    0.5
                     
  Comm. Paper S&P 500 Buy & Hold   S&P 500
4-Systems Combined
  NDX 100 Buy & Hold   NDX 100 4-Systems Combined   50% S&P 500
50% NDX 100
4-Systems Combined
ANNUALIZED RETURN (%): 6.6  11.2   11.6   10.4    13.6   12.7
RISK PARAMETERS (%):                    
Standard Deviation:   17.2   9.6   28.3   14.7   11.6
Worst Month:   -21.5   -8.3   -27.0   -10.8   -9.4
Worst 3 months:   -29.6   -11.7   -38.2   -17.5   -13.4
Worst 12 months:   -39.1   -6.3   -67.3   -15.0   -8.4
Worst 36 months:   -41.0   -4.7    -76.9   -18.6   -11.7
Worst 60 months:   -17.6   14.3    -66.3   9.6    18.0 
Worst Drawdown:   -47.4   -14.5   -83.0   -51.9   -17.6
Avg. of 5 Worst Drawdowns:   -32.9   -10.1   -51.5   -28.1   -14.2
Ulcer Index (Daily):   13.4   3.4   30.7    7.7    4.7

Diversification among timing systems improves the risk parameters slightly. The average of the five worst drawdowns and the single worst drawdown are both improved by diversifying among four timing systems. The primary benefits of timing system diversification are the psychologically palpable approach of buying and selling in 25% increments, and diversification against the unknown, i.e. risks that are not captured in backtesting.  

Investors should resist any urge to rely only on System #3 with the Nasdaq, since it has the best performance record. That type of “cherry-picking” defeats the purpose of diversification and will greatly increase the risk of disappointment. However, there is no way to know whether this system will continue to outperform the others or whether it will underperform in the coming years. As Table 2 shows, this system has sometimes significantly underperformed the other three systems.

These hypothetical results make timing look quite appealing. But timing has had, and will continue to have, periods of underperformance. Investors struggled to stick with timing in 1998 and 1999 when the U.S. stock market seemed to be heading for the moon. In some ways, timing is most comforting during bear markets and panic sell-offs. In the two major bear markets in our study, these four systems showed their stuff in 1973-74 and again in 2000-02.

Studying the tables can only get you so far. The tables do not tell you about the mood of the market at the time of purchases and sales. Part of the timing system educational experience is to follow the four signals real-time, and to make a mental assessment of your mood whenever a buy and sell signal occurs. Often, a buy signal occurs at a time when the public mood is quite gloomy.

With time, patience and discipline, these four systems can help you reach your investment goals – at much less risk than buy and hold.

Assumptions used in Tables 1-3:

1.  Commercial paper rates are used to simulate money-market returns.

2.  Standard & Poor's 500 Index returns include reinvested dividends.

3.  Nasdaq 100 returns: Nasdaq Composite Index from January 1972 through December 1982; Nasdaq 100 Index from January 1983 through December 1999; QQQQ from January 2000 through December 2005.

4.  No fund expenses, transaction fees or management fees are assumed.

5.  Trading system rules are as described in text of article.

6.  Trades were assumed to take place the day following each timing signal.

7.  Combined results: From 1972 through 1977, 50 percent each in System 1 and 2; From 1978 through 2005, 25 percent in each of the four systems. Daily rebalancing was assumed. 
 
 
 

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