Mojena Market Timing Model

The Mojena Market Timing model, developed and maintained by retired professor Richard Mojena, is a method for timing the broad U.S. stock market based on a combination of 11 monetary, fundamental, technical and sentiment indicators to predict changes in intermediate-term and long-term market trends. He adjusts the model annually to incorporate new data year by year. Professor Mojena offers a hypothetical backtest of the timing model since 1970 and a live investing test since 1990 based on the S&P 500 Index (with dividends). To test the robustness of his model’s performance, we consider a sample period bounded by the availability of Standard and Poor’s Depository Receipts (SPY) as a conveniently investable proxy for the S&P 500 Index. As benchmarks, we consider both buying and holding SPY and trading SPY based on the 10-month simple moving average (SMA) of the S&P 500 Index. Using the trade dates from the Mojena Market Timing live test, daily dividend-adjusted closes for SPY and daily yields for 13-week Treasury bills (T-bills) over the period 1/29/93 through 8/27/10 (nearly 18 years), we find that:

In performing analyses, we make the following assumptions:

• Start with an initial investment of $10,000.
• Use of dividend-adjusted values of SPY assumes reinvestment of dividends.
• For the Mojena Market Timing strategy, trade between SPY and cash at the close on the first trading day after the dates (Sundays) specified. Trading at the open would be a feasible alternative.
• For the 10-month SMA benchmark strategy, invest in SPY (cash) when the S&P 500 Index is above (below) its 10-month SMA at the end of the month. Assume this strategy can anticipate signals sufficiently to trade at the monthly close with the signals. This benchmark strategy generates 17 switches between stocks and cash over the sample period (not counting the initial position), compared to 30 switches for the Mojena Market Timing strategy.
• The return on cash is the T-bill yield.
• Assume one-way trading friction (transaction fee plus bid-ask spread) is 0.1% of the balance for the Mojena Market Timing strategy trades and the 10-month SMA strategy trades. Ignore trading frictions for reinvestment of dividends.
• Ignore tax implications of trading.

The following chart compares the cumulative values of $10,000 initial investments for the Mojena Market Timing strategy and for the buy-and-hold and 10-month SMA benchmark strategies over the period 1/29/93 through 8/27/10. The cumulative values of the Mojena Market Timing strategy, the buy-and-hold benchmark strategy and the 10-month SMA benchmark strategy are $36,751, $32,910 and $58,646, respectively. The Mojena Market Timing strategy sometimes lags, sometimes tracks and sometime beats the buy-and-hold benchmark strategy. It generally lags the 10-month SMA benchmark strategy.

Since cumulative value analyses are sensitive to start and stop dates, we look at annual returns.

The next chart compares the calendar year returns for the Mojena Market Timing strategy and the two benchmark strategies, with 1993 a partial year commencing 1/29/93 and 2010 a partial year ending 8/27/10. The Mojena Market Timing strategy beats the buy-and-hold (10-month SMA) strategy during eight (six) of 18 years.

For additional perspective, we look at some return series statistics.

The following table provides the geometric mean annual returns, arithmetic mean annual returns and standard deviations of annual returns for the Mojena Market Timing strategy and the two benchmark strategies over the entire sample period (treating 1993 and 2010 as complete years). The geometric mean is arguably the better estimator of long-term strategy performance, while the arithmetic mean is arguably the better estimator of next year’s return. Results indicate that the Mojena Market Timing strategy beats the buy-and-hold benchmark strategy but loses to the 10-month SMA benchmark strategy for long-term performance. The 10-month SMA strategy wins for all three statistics.

These results for the Mojena Market Timing strategy differ from those presented by Professor Mojena for 1990-2009 because sample periods are different and perhaps because of trade modeling assumptions and SPY tracking error relative to the S&P 500 Index. Professor Mojena presents other return statistics for the 1990-2009 period.

For additional insight into how the Mojena Market Timing strategy differs from buy-and-hold, we relate annual returns using a scatter plot.

The following scatter plot relates annual returns for the Mojena Market Timing strategy and the buy-and-hold benchmark strategy over the entire sample period (again treating 1993 and 2010 as complete years). The R-squared statistic for the relationship is 0.87, indicating that SPY annual returns explain 87% of Mojena Market Timing strategy annual returns. Results indicate that the Mojena Market Timing strategy generates some alpha relative to SPY for the sample period and that it tends to underperform (outperform) an advancing (declining) stock market. Its performance relative to the market over a given sample period therefore depends on the mix of bull and bear states during that period.

In summary, evidence from simple tests over a modest sample period supports a belief that the Mojena Market Timing strategy tends to outperform a buy-and-hold benchmark strategy (depending on the mix of bull and bear states) but may not outperform a simple long-term trend following strategy.

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