In 1977, long before investment analysis software made testing strategies a painless process, market researcher Arthur Merrill manually tested the idea of "filtered waves". Several years later, Martin Zweig popularized the concept as a trading model in his 1986 book, "Winning on Wall Street". In this article, we'll introduce you to this simple trading strategy and illustrate why every active trader should consider paddling out to catch these waves.

What are Filtered Waves?
Very few people read Merrill's short book, "Filtered Waves, Basic Theory: A Tool for Stock Market Analysis", when he completed it, but this work clearly demonstrated that legendary trader Jesse Livermore's swing trading methods worked.

A Wall Street

legend, Livermore had detailed his methods of swing trading late in his trading career and was able to make a complex subject understandable to all. (To read more about this trading legend, read The Greatest Investors: Jesse L. Livermore.)

While Livermore traded on a short time frame, Merrill discovered that with an appropriate filter, this strategy could form the backbone of long-term investing strategies. Swing trading is a strategy that involves holding a stock overnight, and at times for longer periods. With filtered waves, trades can last for months, and occasionally years. The goal of both methods is to take the low-risk gains from the middle of a trend, rather than trying to pick bottoms and tops. The idea is shown in Figure 1. The swing trader would hold this stock during the time indicated by the dashed line, buying after the bottom is confirmed and selling after the top is confirmed.

Figure 1: A wave

In Figure 1, the buy signal occurs when the price moves above the previous high. The sell signal is tougher to define; it can be a rule that sells after three days without a new high, or a decline equal to a percentage retracement of the previous move (for example, selling when the stock gives back half of the gains made on the upside).

Livermore defined swing buying and selling signals in percentage terms. First, Livermore identified the trend as up or down. An uptrend is a series of higher highs and higher lows; a downtrend is marked by lower lows and lower highs. During an uptrend, Livermore's system only takes long trades. The specific buy and sell points are illustrated in Figure 2. As the uptrend runs its course, prices will eventually experience a decline of at least 4% from a high (Point A in Figure 2). This is the signal to close long trades.

When price penetrates the previous swing low by 2% (B), Livermore entered short position. Shorts were closed when prices rose 4% from a recent low (C) and new longs were initiated only after the previous swing high was exceeded by 2% (D). This is also the point where Figure 2 started, with the buy signal shown on the left side of the chart. (For more insight, see Introduction To Types Of Trading: Swing Traders and The Daily Routine Of A Swing Trader.)

Figure 2 - Trading the waves

However, Livermore never offered proof that his tactics worked. Merrill picked up where Livermore left off, and quantitatively tested the idea of buying and selling based on percentage moves. He simplified the rules, backtesting on the Dow Jones Industrial Average, switching from long to short whenever price rose or fell by 5%. Merrill's results showed that despite a lot of losing trades in trendless markets, these rules beat a buy-and-hold strategy.

The name filtered waves comes from the idea that the market moves in waves. These waves ebb and flow just like ocean waves. Up waves are followed by down waves and they all come in different sizes and strengths. Merrill ignored the minor waves, filtering out any moves of less than 5%. The filter allowed him to identify the long-term trend, and formed the basis of a trend following trading system. (For more, see our Trading Systems Tutorial.)

Building a Trading Strategy
Zweig extended the work of Merrill by providing a complete trading history in his book, crediting Ned Davis with developing the trading rules. Using the Value Line Index, a popular trading vehicle at that time, buy signals were generated whenever prices closed 4% above the most recent low. Sells occurred when prices declined 4% from previous highs.

From 1966 until 1993, the period Zweig tested in his book, the strategy significantly outperformed the buy-and-hold investor. Taking both short and long trades, Zweig reported that this simple rule posted a 12.6% annualized gain, compared to a 2.7% gain for the index. The system was also profitable on long-only trades, switching to cash instead of shorting the market. (For more, see Riding the Momentum Wave.)

Of course, this system can still lose. For example, if we take a trade at the beginning of a bull market, the averages may increase by 20%. This would lead to a trade with a profit of 12%, because entry is delayed until the market has gained 4% and an additional 4% of profits are given back before the sell signal is taken.

While this would be a respectable trade, most swing moves are smaller than that. On a 10% move, the trader would show a profit of only 2% before trading costs are considered. On a 5% move, the trader would actually lose 3% or more after trading costs are considered.

Advanced Trading Strategies
Traders can think of filtered waves as a trend identification tool rather than a standalone trading strategy. While the results are certainly impressive, in a trading range market, the patience and equity of most traders will suffer. Simple modifications to the basic idea should help reduce the risks of being caught in a series of whipsaw trades.

Using asymmetrical signals is one way to limit the size of drawdowns. This means setting the buy and sell points at different percentages. Ned Davis Research has published impressive results for the S&P 500. The rules are to buy when the index rises by 8.4% from an extreme low closing price, and sell when it falls by 7.2% from a top. Long-only, this system returned 11.5% per year between 1969 and 2001, easily beating the market return of 7.9%.

More advanced students of the market can consider substituting a multiple of the average true range (ATR) instead of percentage changes to define the strategy. The ATR indicator was designed to change with market volatility by measuring the absolute level of change within the market over a certain time. As an example of this approach, traders could use a filter of three times the 10-day ATR as the trigger for buy and sell signals. From a high or low, the ATR calculation would be completed and added or subtracted to identify the trade trigger.

Using ATRs as the wave filter would have the benefit of accommodating market conditions, allowing a trader to stay with the trend longer during volatile times. Unfortunately, it can also increase the amount given back by traders during those volatile times. As such, this approach might be better suited for short-term, risk-tolerant traders.

Conclusion
No matter how it's applied, filtered waves are a valuable addition to an investor's toolbox. With them, traders are guaranteed to always be on the right side of the trend without being overrun by the crashing wave. With refinements, this versatile technique can be useful as part of a long-term trading strategy and can be applied to mutual funds, ETFs, or volatile stocks.

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