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OTHER TRADING STRATEGIES All trading strategies based on moving averages can be implemented using VIDYA. For example, RAVI is a two-average crossover indicator. A buy signal is generated when RAVI turns positive from a negative value. Similarly, a sell signal occurs when RAVI turns negative from a positive value. I used weekly S&P 500 data to illustrate the smoothing characteristics using a VIDYAL and VIDYAS, representing heavy and light smoothing, respectively.

RAVI can be combined with its moving average to simulate a moving average convergence/divergence (Macd) strategy. Due to its sensitivity, this more responsive or TurboM ACD can be defined as follows:

(7) TMACDd = RAVId - (0.2 ? RAVId + 0.8 ? RAVId-1)

where the second term represents the trigger line, an exponential moving average with a smoothing constant of 0.2. A buy signal is produced when TurboMACD changes from negative to positive values, and a sell signal occurs when it goes from positive to negative values.

BACK TESTING RESULTS

The results of back testing can be divided into two parts: first, the smoothing characteristics of VIDYA, and second, long trades using RAVI and TMACD. Now let us use moving average crossovers and MACD for comparison.

I used weekly S&P 500 data to illustrate the smoothing characteristics using a VIDYAL and VIDYAS, representing heavy and light smoothing, respectively. Figure 1 covers a market period from January 1990 to July 1991 and compares VIDYAL to the equivalent exponential moving average with a smoothing constant of 0.078 . Note how the variable index dynamic average adjusts rapidly to the drop in August 1990. In contrast, an exponential moving average barely responds to the rapid price changes. VIDYAL takes small steps when the market trades in a narrow range and takes large ones when the market makes big moves in any direction. Observe how VIDYAL responded near the market bottom in September-October 1990, while rising rapidly and leveling out in May 1991 when the market entered a trading range.

The lightly smoothed VIDYAS follows the market even more closely, as shown in Figure 2. It also flattens as the market trading range narrows, as in June-July 1990. Clearly, it can be used as a trigger line in market trading systems. Even though the equivalent exponential moving average with a smoothing constant of 0.15 responds quickly to price changes, VIDYAS responds with even greater agility.

An even better picture of VIDYA's responsiveness to price changes can be seen in Figure 3, which compares the smoothing behavior of VIDYAL with a short exponential moving average with a smoothing constant of 0.15. The long dynamic average is more sensitive to rapid changes than even the short exponential average and tracks price changes more powerfully.