Introduction  and Disclaimer

An earlier version of this article was submitted to Seeking Alpha but was rejected because it contained no "in-depth, fundamental analysis". A brief search of the SA website disclosed references to fundamentally based articles on the Acting Man website. So I sent Pater a note claiming knowledge of a fairly accurate, purely mechanical method to identify significant long-term turning points in the market. I offered to tell him a few days in advance the target point of the next signal. He graciously offered to publish my article here. If it can be arranged, I will post its buy and sell signals as they occur in the future. This information is for educational and entertainment purposes only, it will never be a recommendation to buy or sell anything. But I believe that it will prove interesting to consider and watch over time.


Method  Description

My method is similar to the so-called 4 percent method on the Value Line Geometric index, as first published by Ned Davis in the early 1980s. For those unfamiliar with this index, it is described here:

Davis’s algorithm simply bought long any 4% or greater move up in the weekly closes of this index, and sold and went short on any 4% or greater move down in the weekly closes. His algorithm captured a good portion of every major move up or down, but, as is typical of a trend following method, suffered a number of whipsaw losses, primarily due to false sell signals.  I tried a number of ways to reduce these and found two that worked well.

The first added feature uses a trend line. By dynamically constructing this line and deferring action until the market penetrated it, the method reduced whipsaw losses significantly, with little effect on total returns. I thus added this feature to the method.

The second improvement concerns short sales. Davis shorted on all sell signals. Unfortunately, most of these short sales did not end profitably. Using market breadth (advancing and declining issues on the NYSE) was found to better identify conditions for a short sale. My first pass modification identified every major downturn since 1961, except the plunge on 9/11/2001 on occasion of the WTC attack (which was hardly an economically based event), and prevented shorting of many of the smaller corrections. I added this feature to the method, unchanged from my first attempt.


Data Series

The farther an index moves (in percentage terms), the better it is suited for trend following. Davis probably was aware of this, and chose the Value Line Geometric index because it did move farther than other indexes available at the time, such as the Dow Jones Industrial Average and the S&P 500. Many small-cap indexes exhibit this tendency to make greater moves than their larger cap cousins, and are the basis for ETFs and futures contracts. Currently there are no ETFs or futures contracts based on the Value Line index, so an alternative had to be chosen.

The data series used by the method begins with the Value Line Geometric index, because there exist no readily available small-cap indexes prior to its introduction. But conversion to another index was required before the Value Line index fell out of favor. The Russell 2000 index is currently quite popular, so a continuous index was created by using the Value Line index until the Russell index was introduced in 1979, and then splicing the Russell index onto the Value Line index.



The algorithm is controlled by three parameters. Two of these are buy/sell thresholds, and the third is the slope of the trend line.  The algorithm could be optimized via backtesting, but a 'forward test' is actually far better. The typical automated trading method uses (or at least they did, for a very long time) a large number of parameters and the method is then optimized by backtesting on a great deal of historical data to determine the best set of parameter values to use. These methods work fabulously on past data when thus optimized, but often they soon begin to fail on future (out of sample) data. A forward test, where results are recorded entirely on data that the method has not used for optimization, provides a far better indication of how a method will perform in the future.

The forward test began by “training” the algorithm on the S&P 500 data from 1942 through 1960: all possible combinations of the three parameters were applied by the algorithm to the S&P 500 data, and the values that produced the best results were chosen. These parameter values then were used for the first trade on the Value Line/Russell 2000 data series, and the result of that trade was recorded as the first result of the forward test.

For the next trade, the algorithm was trained by running the Value Line/Russell 2000 data series from its beginning to the end of the first trade, with all possible combinations of the three parameters, and choosing the values that produced the best results. These parameter values then were used for the next trade on the data series, and that result was recorded as well. This process was continued for all of the data in the series, beginning each training session with the start of the data series and ending at the end of the last trade.



The results are quite impressive: close to a 14% average gain per year since 1960 was achieved, with a maximum drawdown on closed trades of about 26%. Dividends and money market interest would boost this annual gain to over 15%. For comparison, a buy and hold strategy using the S&P 500 (excluding dividends) averaged only 6.5% per year over the same period with a maximum drawdown greater than 40%.

The accompanying chart shows the results. The upper (white) line is the method; the lower (yellow) line is the Value Line/Russell 2000 index. For comparison, the S&P 500 is shown as the green line. These are results through 11/15/2013. In this forward test the method traded about 3-4 times per year, winning on 54% of all trades. Its win/loss or payoff ratio is 3.98.



MDM ChartThe return produced by the Modified Davis Method compared to the S&P 500 index and the combined Value Line/Russell 2000 Index (Value Line before 1979, Russell thereafter) – click to enlarge.



Risk of Ruin

The risk of ruin for this method, as defined in this article:

The Risk of Ruin Tables You Should Know

is quite low. To compute the risk of ruin value we need this information:


 Risk per Trade

 Payoff Ratio

 Win Ratio


The method’s Risk per Trade is difficult to estimate. Its average loss is about 2.8%, but its maximum loss has been 7.25%. In 190 trades it had only 3 losses greater than 6%.  We must interpolate between the 10% and 5% Risk per Trade tables.

Rounding the Payoff Ratio to 4:1 and the Win Ratio to 55%, the 10% table (10% of capital at risk per trade) gives a Risk of Ruin of .0438 and using the  5% table, the Risk of Ruin amounts to zero. So the method’s 'actuarial' Risk of Ruin is greater than zero, but it is obviously quite low.


Current Status, Future Results

The method last went to 100% long on 11/30/2012 with the Russell 2000 index at 821.92 (the Russell closed at 1116.20 on 11/15/2013). If it can be arranged, I will be posting future trades here as soon as possible after the close on the day they occur, and  usually hopefully before the market open of the next trading day. Stay tuned if you’re interested.


Positions Held

Disclosure: I and members of my family at present  own shares of the IWM ETF and are long Russell 2000 mini futures contracts. We will continue to buy and sell these positions as the method dictates.



Frank Roellinger is a retired software engineer who worked for a major computer manufacturer for nearly 34 years.  He has been an avid follower of markets for more than 30 years, with a strong preference for technical over fundamental analysis.  After observing the results of many different ways to approach markets, he settled upon long-term trend following.  He once hoped to develop a mathematically-based model of the stock market, but now sees little point in doing that, as his Modified Davis Method works as well as any other purely mechanical method that he thought he might ever find.




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4 Responses to “The Modified Davis Method”

  • rodney:

    Continuous walk-forward optimization?

  • Frank Roellinger:

    Intriguing thought. It probably would work on commodities, but they present special problems for testing, e.g. discontinuities at contract expiration times, and locking limits. I’ve dabbled a bit in commodities, once tracking several over about 6 months using Russell Sands’ version of the Turtles method, and found it to be profitable. But it’s a whole different world in commodities and I’ve never taken the time to investigate it fully. Historically, profitable trends have come often enough in the small-cap indexes for my tastes, and the breadth phenomenon does give them an edge. There are other measures unique to stocks (not mentioned in the article) that I have found do give some useful clues about what is going on and what is likely to happen next.

  • SavvyGuy:

    It might be interesting to see how this algorithm works on different markets e.g. soybeans, bonds, metals, crude oil, etc. Even though the market breadth parameter would not be applicable to these markets, such additional testing could help improve the trend-following behavior of the algorithm.

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