Blog - Investing Notes

February 13, 2008 - Update: The Mojena Market Timing Model

Mojena Market Timing, developed and maintained by retired professor Richard Mojena, presents a method for timing the broad U.S. stock market based on the combined power of eleven indicators to predict changes in intermediate-term and long-term market trends. These indicators encompass monetary, fundamental, technical and sentiment perspectives on market conditions. Professor Mojena offers a theoretical backtest of the timing model since 1970 and a live investing test since 1990. Focusing on the latter as evidence free of data mining bias, we find that:

The following chart depicts the annual live-test returns for 1990-2007 based on weekly model signals. "Buy and Hold" means buying and holding the S&P 500 index (dividends reinvested) throughout the test period. "Standard Timing" is 100% in the S&P 500 index during buy signals (dividends reinvested) and 100% in Treasury bills during sell signals. "Aggressive Timing" is 150% long the S&P 500 index (no dividends) during buy signals and 100% short the S&P 500 index (no dividends paid) during sell signals. The test uses next-day closing prices to implement portfolio changes as signaled.

Visual inspection indicates no clear winner, so we calculate simple statistics for the the three series.

The following table provides summary statistics for the three return series. The first two lines of the table show that the geometric mean returns for the three investing approaches are similar, with a modest edge for the Standard Timing alternative. Ranking of raw returns in this manner is sensitive to the start date. The Standard Timing alternative is considerably less volatile than both Buy and Hold and Aggressive Timing. The last two lines indicate that the timing signals avoid much of the downside during a bear market while capturing most of the upside during a bull market. Professor Mojena offers other risk measurements, such as maximum drawdown, that mostly favor the timing models.

For additional insight into how the Standard Timing returns differ from those for Buy and Hold, we compare results year by year using a scatter plot.

The following scatter plot relates the annual Standard Timing return to the contemporaneous Buy and Hold return (orange dots and orange best-fit line). For comparison, it also shows what the relationship would look like if Standard Timing and Buy and Hold returns were identical (green line). The chart indicates that the Standard Timing approach tends to outperform (underperform) Buy and Hold when the annual S&P 500 index return is below (above) about 12%. The flattening of the return distribution is equivalent to reduced volatility.

In summary, the Mojena Market Timing model clearly outperforms a buy-and-hold approach during 1990-2007 based on risk-adjusted returns, but not raw returns, before taxes. Evidence does not support use of long-side leverage and short-selling to exploit its signals.

The model may underperform buy-and-hold in a taxable account.

For reviews of a few other methods (as well as reviews of some books and information web sites), see Blog Synthesis: Reviews of Books and Web Sites.