The Pentad timing model was developed by Nelson Freeburg, editor of Formula Research. Nelson investigates and develops systematic investment and trading strategies for stocks, bonds, and commodities (similar to what we do here), and publishes his findings with all the rules fully disclosed.
If you follow his work from the start, you’ll notice that at first, he was just pursuing his own ideas for research, probably based from what he read in books and magazines. Later on, he attracted the attention of successful money managers, and they started sharing their own models for Nelson to test and eventually publish (at least those that pass his rigorous tests). This is what makes his body of work powerful, and if you’re into this type of research, then this is a goldmine waiting for you to be discovered.
Pentad was featured on the October 1995 issue of Formula Research, as well as in his DVD course Timing Models and Proven Indicators for Today’s Market. The strategy was named Pentad because it looks at five indicators, and it is actually a simplified version of Ned Davis Research's (NDR) “12-indicator Trend Model.” (For those who are not familiar, NDR is a highly regarded research firm that focuses on quantitative models but caters only to institutional investors).
Even though the model is already “simplified,” the rules are actually quite complex for beginning systematic investors. However, we think it’s worth the effort for you to study it, since it’s one of the most powerful timing models we know for the US stock market. If you haven’t done so, we highly suggest that you first familiarize yourself with simpler models like Best Six Months, Faber TAA, and Fabian before continuing.
Our main objective for this study is to verify if the model actually works as the author claims, using our own test methods and data. There are just too many misguided advice and snake oil salesmen out there that we firmly believe in verifying an investment idea ourselves before risking real money.
We also would like to update the research result forward, and keep it current as long as there’s enough interest. This way, we can witness the effectiveness of this strategy first hand as it navigates through the ups and downs of the financial markets.
We’ll first take an in-depth look at the model and discuss how it works. Then we’ll look at the latest backtest results we have to see how it performed in the past and in recent times. If you want to skip all of these and just look at the numbers yourself, then check out the accompanying programs for this model.
Just to whet your appetite, Chart 1 shows how Pentad did recently. Not bad eh? Considering this has been around since 1995 and it only cost less than $50 to learn about it!
Pentad is a 100% mechanical, long-term, inter-market timing model for US the stock market. It looks at five indicators: three are trend-following, one measures market breath, and the other is based on interest rates. All indicators are derived from the US markets, so it doesn’t work as well in foreign equities.
This strategy works in weekly timeframe, so that means you only need to check it once a week to see if you need to take any action. The model makes about an average of 0.61 round-trip trades per year, and the average holding period is 388.8 days. Overall, it’s a fairly low-maintenance strategy, and it might suit your needs if you can’t devote a lot of time in minding your investments. For shorter-term traders, you can use this model as a “filter” to make sure you’re on the right side of the big trends.
It employs what we call the Board of Indicators pattern. This pattern essentially uses several indicators, and each indicator can independently “vote” on what to do. The votes are then tallied to create the total, and this value is used to make decisions based on pre-defined levels.
The system is long-only and does not sell short.
The parameters look to be optimized, probably by the Ned Davis folks, so it’s a little convoluted. But this model works well that we didn’t want to change it to keep its track record intact.
Our target investment vehicle for Pentad is the US stock market as represented by S&P 500 Total Return Index, and our benchmark is to buy and hold this same instrument.
Unlike nominal or cash prices, total return data have been adjusted to make it appear that all the interests, dividends, and other distributions are automatically “reinvested.”
This is critical, since more than half of the returns of an instrument may come from interests and various distributions, especially high-yielding ones like the bonds, dividend stocks, and REITs. It’s the cash or nominal prices that are typically quoted on websites and newspaper, and not the total return.
Pentad is an inter-market strategy, and that means it looks at other markets with proven predictive relationship to the overall US stock market to make its decisions. It does this on the theory that a more diversified indicator would provide signals with less noise.
In a way, this is similar to using different instruments – like satellite images, barometers, and thermometers – in concert to forecast the weather. Had you just used different types of thermometers in various locations, then your forecast won’t be as good, arguably.
The specific markets and indicators that Pentad looks at are the following:
Similar to Fabian’s Timing Model, we’ll use the nominal prices for S&P 500, Dow Jones Utilities, and Dow Jones Transports for signal generation. We’ll assume you’re already familiar with these indices, since we’ve discussed them before and are widely quoted in newspapers.
The Dow Jones Corporate Bond Index is an index of investment-grade bonds issued by large companies to fund their operations. Why look at the bond market to time the stock market? That’s because interest rates have a strong influence in the economy.
If the interest rate is going up, then money becomes tight, so individuals and corporations alike would cut costs and the overall economy tanks. If the interest rate is going down, then money becomes easy to obtain, so spending goes up and the overall economy booms (check this video out by hedge fund manager Ray Dalio to learn more).
By looking directly at the Corporate Bond Index, as opposed to a Government Bond Index for example, we can measure how the businesses are affected by the interest rates more precisely.
The NYSE Weekly Advance / Decline Line (or A/D line for short) is a market breadth indicator that measures strength or weakness of the market based on the number of advancing or declining issues in the New York Stock Exchange. It’s basically trying to measure the trend of the population changes between stocks that are going up and the stocks that are going down.
You calculate it by taking the number of advancing issues minus the number of declining issues (based on weekly closing prices), and adding the difference to the indicator’s previous value. Why do the last step? Because we want to accumulate the population changes so we can see the trend as shown in Figure 1. Otherwise, it would just oscillate between two extremes like in Figure 2.
If you’re kind of confused by the details, don’t worry about it. All you need to know is that the NYSE A/D line is another way to measure the strength of the market based on participation (as opposed to a more direct measure like price).
At this point, you should now be familiar with the way we use simple moving averages to generate market signals. If not, a review of Fabian or Faber models is recommended, because we’re going to introduce more advanced concepts here.
Pentad uses two types of moving averages – the Simple Moving Average (SMA) and the Weighted Moving Average (WMA).
If you can recall, SMA is simply a straight average of the most recent x number of data points, so we are essentially giving each data point the same importance.
The basic theory behind WMA is that the older data shouldn’t be given the same importance as the most recent one, so we apply a linearly increasing weight from the oldest to the newest data points so the latter is given the most emphasis (see this link for an example computation). The effect is that the WMA becomes more sensitive and would respond faster to the price as illustrated in Figure 3.
Does it make a lot of difference? Not really. Our experience shows that different types of moving averages produce about the same result. However, we won’t second guess the system and we’ll stick to the original rules.
One of the problems of using moving averages, and trend-following in general, is the dreaded whipsaw. Whipsaws happen when the indicator flip flops between buy and sell signals causing a string of losses and missed opportunities. This can be reduced using different techniques, but it cannot be completely eliminated.
The specific technique Pentad employs to reduce whipsaws is to place buy and sell filters above and below the moving averages, respectively, as shown in Figure 4. You calculate the buy filter by adding a fixed percentage to the moving average, and you calculate the sell filter by subtracting a fixed percentage. The percentage used for the buy and sell filters may or may not be equal.
When filters are used, the moving average buy and sell signals are generated differently. Instead of simply buying and selling when the price cross overs the moving average, we now buy only if the price goes above the buy filter, and we now sell only if the price goes below the sell filter. In effect, we added a buffer zone that would minimize the rapid changes in signal.
From the figure, you can see that without the filter, you would have been whipsawed in and out of the market between Nov. 2008 and Mar. 2009.
So far, we’ve used only price crossovers to generate signals based off moving averages. That means we buy if the price becomes greater than the average by a certain amount, and we sell if the price becomes lower than the average by a certain amount.
Another way Pentad generates signals from moving average is to look at the slope or direction of the moving average itself. If the moving average is going up, we buy. If the moving average is going down, we sell. Price doesn’t play any direct role in generating the signals.
This method also suffers from frequent whipsaws, so Pentad uses a Percent Swing filter to minimize it. For those who have read the book Winning on Wall Street, this is the filter that Martin Zweig and Ned Davis used in the “Value Line 4% Model,” except they applied it to the price, while Pentad applies it to the moving average slope.
With Percent Swing filter, a buy signal happens only when the moving average slope goes up by x% from the most recent low point, and a sell signal happens only when the moving average slope goes down by y% from the most recent high point. In other words, we ignore the small wiggles made by the slope and only take action on larger swings.
To illustrate, let’s say we used 4% for our buy and sell filters (they may not be equal in practice) and assume we currently have a sell signal. If the slope goes up by 3% from the most recent moving average low, then there will be no change in the signal. Why? Because we need an additional 1.01% move to exceed the 4% threshold before we take any action. If the slope then retraced back by 1%, there will still be no change in signal, and we are now just 2% off the most recent low. Only if the slope jumped by at least 2.01% from this point forward would the signal change to buy. The sell filter is the exact mirror of the buy filter, except we’re comparing the slope’s movement with the most recent moving average high.
Whew! After laying out all that groundwork, the rules for Pentad should now be easy to understand. Each of the five market index we’ve discussed earlier creates a buy and sell signals independently based on the following parameters:
| Market Index | MA Type | MA Period | Signal Type | Buy Filter | Sell Filter |
|---|---|---|---|---|---|
| S&P 500 | WMA | 65 weeks | Crossover | 0% | 3% |
| DJ Transports | SMA | 25 weeks | Crossover | 0.5% | 2.5% |
| DJ Utilities | SMA | 27 weeks | Slope | 0% | 3% |
| DJ Corporate Bond | WMA | 38 weeks | Crossover | 1% | 2% |
| NYSE A/D Line | WMA | 14 weeks | Crossover | 0.5% | 2% |
Notice that the MA lookback periods are not typical and looks as if it has been picked randomly. The buy and sell filters are no different. This is what an optimized system looks like.
Optimized systems use parameters that have been determined through lots of trial and error using computer simulations. It’s a form of data mining, which is useful, but if not done properly, would lead us to pick parameters that works well in the past but fails in the future. Obviously the NDR folks or Nelson knows what they were doing because the system didn’t fall apart after its release.
Pentad uses asymmetric buy and sell filters wherein the buy filter is more sensitive than the sell. Why? That’s because markets tend to go down a lot faster than they go up, so we give it a bit more leeway to reduce whipsaws.
Finally, here are the buy and sell rules for Pentad:
Buy Rule: If all five indicators are flashing buy signals, and we are out of the market, then enter the next day at the open.
Sell Rule: If only three indicators or less are flashing buy signal, and we are in the market, then exit the next day at the open.
In other words, we can only enter the market if the votes are unanimous. Once in, we need at least two down votes to exit the market.
When the strategy is not in the market, we assume that the cash in the sidelines earns 90% of the going T-Bill rate. This is similar to what you’ll get if you park your cash in your brokerage account or money market fund.
In order to calculate the risk, volatility, other metrics more precisely, we use daily data with the open, high, low, and close (OHLC) in our testing, even though the strategy operates on a weekly basis. The model still make trade decisions at the end of the week as you might expect.
Chart 2 shows the equity curve of the Pentad timing model. The equity curve is shown in the top part of the chart, and it illustrates how the strategy’s equity grows over time. The underwater equity curve is at the bottom, and it demonstrates the drawdowns or setbacks you have to go through. Ideally, you want to see the equity growth to go up in a straight line at about 30 to 45 degree angle, and you want the drawdown pane to be completely blank. Typical investors won’t be able to stomach more than 20% of drawdowns.
As you can see from the chart, Pentad’s equity grew in a healthy fashion without huge downturns. There are long flat times during the 2002 and 2008 bear markets, but that’s better than losing money. The drawdowns are a bit higher than normal recently, but it is still well contained under 25%.
Note that the “P” flag indicates when the model was published, so anything after that is out-of-sample (unseen data). This is usually the critical juncture when “magic” systems sold to the public would deteriorate due to over-optimization. Evidently, Pentad did not suffer that fate, and the equity curve is still taking the same trajectory as it did almost 20 years ago! How’s that for staying power?
We show the same equity chart as before in Chart 3, except we added the equity curves of our benchmark as an overlay so you can easily compare them. We also magnified the underwater equity curve in Chart 4 so you can contrast the risks involved in each strategy.
You can see that Pentad was able to participate in the major rallies, and yet avoid all the major declines. The drawdowns, in general, are also very mild compared to buy and hold. It suffered some whipsaws back in 2012, and that’s why the drawdowns got deeper than the benchmark, but it has since recovered and made new equity highs.We don’t often see timing models that outperform the buy and hold strategy with such a wide margin over a long period of time, so we’re very impressed.
We view long-only market timing strategies for market indices as defensive plays, which means their first priority is to reduce risk (as measured by maximum drawdown), and their second priority is to increase the risk-adjusted returns (as measured by MAR ratio). So if you just look at the returns without factoring in the risk, it would normally underperform its buy and hold counterpart for long periods of time, and its true value would only surface when buy and hold suffers from catastrophic losses.
With this in mind, we’re happy to see if a long-only timing model could:
If you look at the stats summary in Table 1, I think you’ll agree that Pentad did very well and met all our expectations. In fact, it was actually able to exceed the returns of buy and hold by several percentage points, which is a very strong showing.
| Pentad | S&P 500 | |
|---|---|---|
| Starting Equity | $100,000.00 | $100,000.00 |
| Ending Equity | $13,450,761.05 | $14,681,720.46 |
| Time Elapsed | 44 years, 3 months | 44 years, 3 months |
| CAGR % | 11.71% | 11.93% |
| Max % Drawdown | (23.26%) | (55.25%) |
| MAR Ratio | 0.50 | 0.22 |
| Win Rate % | 66.7% | 0.0% |
| Longest Drawdown Duration | 49.6 months | 73.5 months |
| Avg Trades Per Year | 0.61 | 0.00 |
From Jan 1980 to Apr 2024, an initial investment of $100,000.00 in this strategy would now be worth $13,450,761.05. That’s a compounded annual return of about 11.71%. The maximum drawdown that the system underwent is (23.26%), which leads to a MAR ratio of 0.50. The longest period where it didn’t make any money is 49.6 months.
On the other hand, the same initial investment on S&P 500 (our benchmark) over the same period would now be worth $14,681,720.46, which is about 11.93% compounded. The maximum drawdown, however, is (55.25%), and this yields to a 0.22 MAR ratio. If you invest in this strategy in the worst possible time, you have to wait up to 73.5 months just to break even.
Table 2 shows the year-by-year percentage returns of this timing model. What we want to see here are stable returns year in and year out with very few or no down years. You don’t want consecutive losing years or double-digit negative returns (low teens might be acceptable). As you can see from the table, Pentad delivers.
If you would like to see more, check out the program for the full report.
One of our favorite ways to stress test the logic of a system is to reverse its rules. Specifically:
Buy Rule: If only three indicators or less are flashing buy signal, and we are out of the market, then enter the next day at the open.
Sell Rule: If all five indicators are flashing buy signals, and we are in the market, then exit the next day at the open.
In other words, if the original strategy tells us to buy and get into the market, we sell and stay on the sidelines. If it tells us to sell and stand aside, we buy and get into the market instead.
Interest earnings from cash on the sidelines have been disabled in this test. We do this to isolate the strategy’s actual performance, since high-interest rate environment tend to make unprofitable strategies look better than it is.
So, what should be the expected outcome? If the logic of the system truly identifies the best time to stay invested, then reversing it should make our equity decline, get nowhere, or earn a tiny rate of return with unjustifiable risk. If you look at Chart 5, this is exactly what happened.
The equity never had any significant run-ups, and the strategy is pretty much in a state of perpetual drawdown. If you compare the equity curves of the inverted version of Fabian Timing Model, Best Six Months, and Faber TAA, you’ll see that this chart looks the worst. This suggests that Pentad is better at isolating profitable opportunities in the US stock market.
| Pentad Inverted | S&P 500 | |
|---|---|---|
| Starting Equity | $100,000.00 | $100,000.00 |
| Ending Equity | $207,985.79 | $14,681,720.46 |
| Time Elapsed | 44 years, 3 months | 44 years, 3 months |
| CAGR % | 1.67% | 11.93% |
| Max % Drawdown | (57.67%) | (55.25%) |
| MAR Ratio | 0.03 | 0.22 |
| Win Rate % | 75.0% | 0.0% |
| Longest Drawdown Duration | 236.5 months | 73.5 months |
| Avg Trades Per Year | 0.63 | 0.00 |
Table 3 shows the strategy’s performance statistics.
Had you followed this strategy and invested $100,000.00 on Jan 1980, your nest egg would have compounded at 1.67% annually and would now be worth $207,985.79. To achieve this return, you would have to endure a maximum equity drawdown of (57.67%) from peak to trough, and the longest dry spell took 236.5 months to end. The strategy’s MAR ratio is 0.03.
Judging from these results, we’re convinced that the performance of the original system did not happen just by chance, and it really helps pinpoint the best time to be in the market.
To see the rest of the report, check out the program.
Congratulations for getting this far!
Pentad is definitely not an easy timing model to grasp, especially if you’re just a beginning systematic investor. However, it’s worth it, as you can see from the results. It uses five inter-market indicators, four of which are technical, and one is fundamental. Pentad enters the market when they are unanimously bullish, and exits the market when at least two are bearish. The rules are kind of complex and the parameters looks optimized, but it has performed very well even decades after its publication.
In the 30+ years that we’ve investigated, Pentad outperformed the buy and hold on an absolute and risk-adjusted return basis. It also handily beats the other timing models we’ve looked at so far in this series. We like this model, and we put a lot of weight in its opinion about the stock market.
You don’t have to use this timing model in an all-or-nothing fashion as we did in this study. For example, you could choose to be always 50% invested, and rack it up to 100% when the model gives the go signal. You could buy conservative stocks when the model is bearish, and turn to more speculative issues when it is bullish. You could use it in conjunction with other timing models to form a consensus opinion.
We’ve covered a lot of groundwork in this study, and the good news is that you can leverage this knowledge going forward, because a lot of strategies use the same building blocks.
Here are the summary of the new concepts we’ve introduced:
If you are overwhelmed by the details or are too busy to follow this strategy on your own, consider joining us – we’re here to help. We do all the calculations and heavy lifting, so you don’t have to. You get to follow investment and trading strategies in a calm objective manner without the hype or hassle.
You should check out the available programs for this model. Programs are variation of a model that we independently maintain. For example, we have programs that focus on older and more recent periods. We may also have programs that trade different portfolios. Each program features in-depth reports like performance distributions, trade-by-trade log, and more. And, unlike books, magazines, and every other websites out there… we keep all our research up to date.
If there’s enough interest, we would like to expand this research even further. We’d like to investigate how an un-optimized version of the strategy would perform. For example, instead of using odd lookback periods like 25 and 27 weeks, we could just round it to something more logical like 26 weeks (two quarters worth of data). Or maybe we could standardize with 0.5% buy filter and 2.5% sell filter for all indicators. We’d also like to try if this model would be good for shorting applications. For example, we could sell if all indicators are bearish, and then cover when two or more becomes bullish.
If you find this study worthwhile, please help us spread the word and share so we can get more traction!