Testing the Rydex Asset Ratio

A reader suggested looking at Rydex asset ratios as stock market sentiment indicators. The reasoning for these indicators is that a high (low) ratio of assets in bullish funds to assets in bearish funds indicates an overbought (oversold) market. Are these indicators useful? The most timing-intensive traders arguably use leveraged exchange traded funds (ETF), thereby suggesting that bull-bear asset ratios for such funds may be especially informative. Using daily closing asset levels for the Rydex 2x S&P 500 ETF and the Rydex Inverse 2x S&P 500 ETF from the earliest available on 11/5/07 through 6/24/11 (917 trading days), along with contemporaneous daily opens and closes of the S&P 500 index, we find that:

The following chart compares the behaviors of the Rydex S&P 500 Index leveraged ETF bull-bear asset ratio and the S&P 500 Index itself over the entire sample period. The average bull-bear ratio is 1.09. Visual inspection suggests that the two series mostly move together, with the bull-bear ratio more volatile than the index.

For a more precise test of the relationship, we examine some correlations.

The next chart summarizes correlations between the Rydex S&P 500 Index leveraged ETF bull-bear asset ratio and S&P 500 Index returns for past and future intervals of one, five and 21 days. Because Rydex fund asset levels are not available until after the close, we calculate past index returns from close to close and future index returns from open to open starting at the next open after the ratio date.

Results show that the bull-bear ratio relates positively (negatively) to past (future) returns. As for many sentiment measures, investors tend to become more bullish (bearish) after a market advance (decline). Also, the connection to past index returns is much stronger than the connection to future returns. In other words, index returns predict the bull-bear ratio more reliably than vice versa.

Correlations are not very consistent for the first and second halves of the sample (break point at the end of August 2009), suggesting that the relationship may depend on overall market state or the maturity of the ETFs. Predictive power as indicated by correlations with future returns is stronger (correlations are more negative) in the second half of the sample.

These results use daily measurements, for which 5-day and 21-day return inputs overlap and potentially distort correlations applicable to an investable strategy.

Next we take a closer look at the 5-day future returns.

The following scatter plot relates the 5-day future return for the S&P 500 Index to the Rydex S&P 500 Index leveraged ETF bull-bear asset ratio with two adjustments:

1. Since the ratio may have been artificially distorted at inception, we omit the first 20 trading day readings (about the first month of data).
2. We winnow the sample, selecting every fifth daily reading, to eliminate overlap in index return calculations (with a residual sample of 179).

The Pearson correlation for these two series is -0.06. The R-squared statistic for the relationship is 0.004, indicating that variation in the bull-bear ratio explains less than 1% of the variation in the S&P 500 Index the following week.

In case the relationship is materially non-linear, we look at rankings.

The next chart summarizes average 1-day and 5-day future S&P 500 Index returns by quintile of the Rydex S&P 500 Index leveraged ETF bull-bear asset ratio, with the first 20 trading days of the sample omitted and the 5-day returns winnowed as described above. There is some indication that low bull-bear ratios indicate higher near-term index returns than do high bull-bear ratios, but the progressions across rankings are not systematic.

The sample period is too short to test quintiles of winnowed 21-day future returns (43 residual observations). However, the average 21-day future return for the 22 (21) observations with the lowest (highest) ETF bull-bear asset ratios is 0.7% (-0.9%).

As a final robustness test, we look at the longer records of two leveraged Rydex mutual funds.

The final chart summarizes average 1-day, 5-day and 21-day future S&P 500 Index returns by quintile of the Rydex S&P 500 Index leveraged mutual fund bull-bear asset ratio. The bull-bear asset ratio here derives from daily closing asset levels for the Rydex S&P 500 2x Strategy – H Class mutual fund and the Rydex Inverse S&P 500 2x Strategy – H Class mutual fund from inception on 5/19/00 through 6/24/11, with samples of 5-day and 21-day returns winnowed as appropriate to eliminate return calculation overlap. The average bull-bear ratio over the entire sample period is 1.04.

Again, there is some indication that low bull-bear ratios indicate higher near-term index returns than do high bull-bear ratios, but the progressions across rankings are not reassuringly systematic.

Some peculiarities noted in performing this robustness test are:

• The bull-bear ratio based on mutual funds is more volatile than that based on ETFs. Asset levels of the mutual funds can triple in a day.
• The correlation of bull-bear ratios based on mutual funds and ETFs is just 0.16 during the overlapping period of 11/5/07 through 6/24/11. Why is the correlation not much more positive?
• The bull-bear ratio based on mutual funds has practically zero correlations with past index returns.

These peculiarities suggest that fund flow forces are different for mutual funds and ETFs.

In summary, evidence from simple tests indicates that Rydex leveraged bull-bear fund asset ratios may have slight but inconsistent contrarian predictive power for the underlying market, so slight and inconsistent that exploitation is problematic.

Cautions regarding findings include:

• The above quintile breakdowns are in-sample across the entire available data sets. An investor operating in real time would have only data available to date for deciding what value of the bull-bear asset ratio are high or low.
• As noted above, the correlation between ETF and mutual fund bull-bear ratios is surprisingly low.

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