Testing the McClellan Oscillator and Summation Index

A reader commented and asked: “Several of my friends swear by the McClellan Summation Index for timing medium term bull/bear moves. Have you any evaluation of its usefulness?” The McClellan Summation Index derives from the McClellan Oscillator, a technical indicator developed in 1969 by Sherman and Marian McClellan, for which the daily input is the number of stocks that closed higher (advances) minus the number that closed lower (declines). The McClellan Oscillator smooths and seeks to concentrate the information in this daily breadth input stream via the difference of two exponential moving averages. The McClellan Summation Index is a running total of the daily values of the McClellan Oscillator. McClellan Financial Publications describes how to calculate the McClellan Oscillator. Advances and Declines is a public source of the historical numbers of advances and declines for U.S. exchanges. Using the daily numbers of NYSE advances and declines for 3/1/65-7/12/10 and daily dividend-adjusted closes of S&P Depository Receipts (SPY) for 1/29/93-7/12/10 (about 18.5 years), we find that:

In setting up the calculations for the McClellan Oscillator and McClellan Summation Index, we make the following assumptions and corrections:

• NYSE data from Advances and Declines for 11/26/99 are missing. We ignore that date.
• There are quite a few entries in the NYSE data from Advances and Declines in the latter part of the available sample that fall on market holidays. These entries appear to be duplicates or post-close revisions of data from the immediately prior trading session. We delete the holiday entries.
• There are minor differences in the numbers of advances and declines between the data from Advances and Declines and the recent sample from McClellan Financial Publications. These differences may stem from post-close revisions. We accept the data from Advances and Declines.
• The value of the McClellan Summation Index depends on the calculation start date. We calibrate the index by taking its 7/12/10 value as calculated by McClellan Financial Publications and then step backwards over the sample period.

The following chart summarizes Pearson correlations between the McClellan Oscillator and the McClellan Summation Index and returns for SPY during future intervals of 2, 5, 10, 21 and 63 trading days over the entire SPY sample period. All correlations are small, and all are negative except for that between the McClellan Summation Index and the SPY 63-day future return.

For a closer look at the McClellan Oscillator, we focus on the SPY 5-day future return.

The following scatter plot relates the SPY 5-day future return to the value of the McClellan Oscillator over the entire SPY sample period. The R-squared statistic for the relationship is 0.00, indicating that the McClellan Oscillator explains nothing about the SPY 5-day future return.

Daily observations overlap, tending to overstate sample size and potentially distort statistics. Winnowing the data such that no two 5-day future return intervals overlap (878 winnowed observations) results also in an R-squared statistic of 0.00.

In case there is a material non-linearity in the relationship, we calculate average SPY 5-day future return by decile of McClellan Oscillator value.

The next chart summarizes average SPY 5-day future return by decile of McClellan Oscillator value based on the winnowed data over the entire SPY sample period. Results are far more indicative of randomness than any systematic relationship between the value of the McClellan Oscillator and future stock returns.

What if we consider a signaled, rather than fixed, future return interval?

For signaled entry and exit based on the McClellan Oscillator, we consider the following guidance from Decision Point: “When the McClellan Oscillator moves below the Zero Line a SELL Signal is rendered, and a BUY Signal results when it moves above zero…” Applying this guidance to the unwinnowed data over the entire SPY sample period generates 320 buy signals and 321 sell signals. The average duration of the buy (sell) signals is ten (nine) trading days. Assuming trades at the close with the signals (requiring slight anticipation of indicator values), the average return between buy and sell (sell and buy) signals is 0.19% (0.24%), with standard deviation per trade 2.74% (2.38%). In other words, return from sell to buy is comparable to that from buy to sell (perhaps better).

For a closer look at the McClellan Summation Index, we focus on the SPY 63-day future return.

The next scatter plot relates the SPY 63-day future return to the value of the McClellan Summation Index over the entire SPY sample period. The R-squared statistic for the relationship is 0.00, indicating that the McClellan Summation Index explains nothing about the SPY 63-day future return over the sample period.

Daily observations overlap considerably, tending to overstate sample size and potentially distorting statistics. Winnowing the data such that no two 63-day future return intervals overlap (only 68 winnowed observations) results in an R-squared statistic of 0.01, indicating that variation in the McClellan Summation Index explains 1% of the variation in the SPY 63-day future return.

In case there is a material non-linearity in the relationship, we calculate average SPY 63-day future return by tercile of McClellan Oscillator value.

The final chart summarizes average SPY 63-day future return by tercile of McClellan Summation Index value based on the winnowed data over the entire SPY sample period. Results suggest that low values of the index may be more favorable for future returns than high values, but the difference is modest given the small sample size (removing a single observation can change the order of the tercile returns).

What if we again consider a signaled, rather than fixed, future return interval?

For signaled entry and exit based on the McClellan Summation Index, we consider the following guidance from Decision Point: “Movement below the Zero Line is considered bearish, while movement above +2000 is considered bullish.” We apply this guidance to the unwinnowed data over the entire SPY sample period based on the following assumptions:

• Since the McClellan Summation Index is above 2000 at the beginning of the sample period, we start with a buy signal at that time.
• The guidance sometimes generates consecutive buy and sell signals. Since repeat signals are not tradable, we assume trading on the first buy or sell signal in any sequence.

Based on these assumptions, there are 17 buy signals and 16 sell signals over the sample period. The average duration of the buy (sell) signals is 248 (132) trading days. Assuming trades at the close with the signals (requiring slight anticipation of indicator values), the average return between buy and sell (sell and buy) signals is 4.8% (4.4%), with standard deviation per trade 17.2% (10.4%). All in all, considering the small sample sizes and differences in signal durations and per-trade volatilities, return while on a sell signal is no worse than that while on a buy signal.

In summary, evidence from simple tests on available data generally does not support a belief that the McClellan Oscillator or the McClellan Summation Index usefully predict stock returns at either fixed or signaled future horizons.

There may be methods of applying these indicators that do exhibit predictive power, but failure of these simple tests makes data snooping bias a concern for such methods.

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