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A comparison of each of the four methods discussed is found in Figure 10. Clearly, RAVI beat both the simple crossover of exponential averages and MACD over the past 11 years. RAVI produced more trades than did the simple crossover model but less than half as many as did the MACD. A look at the detailed trades shows that TMACD signaled key turning points two to three weeks before MACD. Its greater sensitivity produced more trades, which is a key limitation of the MACD approach from an investor's perspective. RAVI can also be used as an overbought-oversold indicator, since its values peak at over +10 or -10.

TO SUMMARIZE

Overall, the back testing results show that VIDYA tracks the market (as measured by the S&P 500 index) better than exponential moving averages do using a fixed smoothing constant. Trading strategies based on VIDYA seem to perform better than those based on exponential moving averages, as summarized in Figure 5.

In sum, this new class of variable index dynamic moving averages — VIDYA — adapts moving averages to the changing nature of markets.

A single formulation tracks market changes well despite the increased volatility of recent years. VIDYA serves as a variable-length exponential moving average, taking a greater "bite" out of the most recent data as market volatility increases. Like all moving averages, VIDYA also lags the market, since it is derived from past data — probably its biggest limitation.

In sum, this new class of variable index dynamic moving averages — VIDYA — adapts moving averages to the changing nature of markets. Any dimensionless market variable can be used to link these averages to the market. The figures provided illustrate well the responsiveness of these averages to market changes. Common trading strategies for moving averages can be implemented using VIDYA, demonstrated with RAVI and TurboMACD. VIDYA is also well suited for setting stops, as it closely tracks the market. VIDYA should be a formidable and dynamic addition to the trader's arsenal. Tushar Chande holds a doctorate in engineering from the University of Illinois and a master's degree in business administration from the University of Pittsburgh.

FIGURE 1: The S&P 500 weekly closes (A) are plotted along with both the long variable index dynamic moving average (B) and with the equivalent exponential moving average (C). Note how quickly the indexed moving average responds to the decline by the S&P 500 in August 1990.

FIGURE 2: The S&P 500 weekly closes (A) are plotted along with both the short variable index dynamic moving average (B) and with the equivalent exponential moving average (C). The short version of the indexed moving average follows the market closely.

FIGURE 3: The S&P 500 weekly closes (A) are plotted this time with the long variable index dynamic moving average (B) and with the short exponential moving average (C). The long version of the indexed moving average still follows the market more close/y than a short exponential moving average.

FIGURE 4: The S&P 500 weekly closes (A) are plotted this time with the long (B) and short (C) variable index dynamic moving average and with the equivalent long exponential moving average (D). The narrowing of the difference between the two indexed moving averages indicates a possible trend reversal

FIGURE 5: Using the difference between the short (A) and long (B) versions of the varriable index dynamic moving average produces the rapid adaptive variance indicator, creating a crossover method for trading signals.

The basic formulas for each column are presented in a Lotus spreadsheet. Column F is the weekly close for the S&P 500, while column G is the exponential moving average using a 0.078 smoothing constant. Column H is the EMA using a 0.15 smoothing constant, and column I is the Lotus formula for the long VIDYA. STD is the standard deviation formula in Lotus for the cell range stated within the parenthesis. Column J is the short version formula. Column K is the difference between column J and I.