A subscriber suggested comparing intrinsic momentum (IM), also called absolute momentum and time series momentum, to simple moving average (SMA) as alternative signals for equity market entry and exit. To investigate across a wide variety of economic and market conditions, we measure the long run performances of entry and exit signals from IMs over past intervals of one to 12 months (IM1 through IM12) and SMAs ranging from 2 to 12 months (SMA2 through SMA12). We consider two cases for IM signals and one case for SMA signals, as applied to the S&P 500 Index as a proxy for the stock market and the 3-month U.S. Treasury bill (T-bill) as a proxy for cash (the risk-free rate). The three rule types are therefore:

- IMs Case 1 – in stocks (cash) when past index return is positive (negative).
- IMs Case 2 – in stocks (cash) when average monthly past index return is above (below) average monthly T-bill yield over the same interval.
- SMAs – in stocks (cash) when the index is above (below) the SMA.

We estimate S&P 500 Index monthly total returns using monthly dividend yield calculated from Shiller data. This estimation does not affect index timing signals. We focus on net compound annual growth rate (CAGR), maximum drawdown (MaxDD) and annual Sharpe ratio as key performance metrics, with baseline stocks-cash switching frictions 0.2%. We use buying and holding the S&P 500 Index (B&H) as a benchmark. Using monthly closes of the S&P 500 Index during December 1927 through November 2019 (92 years), and contemporaneous monthly index dividend and T-bill yields, *we find that:*

The monthly T-bill yield per the linked source is available only back to January 1934, calculated as average daily T-bill yield during each month. To estimate T-bill yield further back to December 1927, we: (1) calculate the average monthly spread between Shiller’s long-term yield and the available T-bill yield during January 1934 through November 2019; and, (2) subtract that average spread from Shiller long-term yield during December 1927 through December 1933.

Assumptions for all switching rules are:

- Switches occur at monthly closes coincident with monthly signals (the investor must slightly anticipate signals).
- As noted, baseline stocks-cash switching (trading) frictions are 0.2% (with sensitivity testing). This value is probably very low (somewhat high) for many investors during the older (newer) part of the sample period.
- Ignore tax implications of trading.

The following chart summarizes net CAGRs for all IM and SMA rules and B&H. Notable points are:

- Across lookback intervals, there is no clear winning rule type.
- IMs-Case 1 mostly beats IMs-Case 2 (likely by accruing more dividends).
- The top performance overall is for IM10-Case 1.
- Top performances for other rule types are IM10-Case 2 and SMA12.
- Only three of 35 rules beat B&H.

What about MaxDDs?

The next chart summarizes MaxDDs for all IM and SMA rules and B&H. Notable points are:

- Across lookback intervals, there is no clear winning rule type.
- The best performance overall is for SMA5, IM9-Case 1 and IM9-Case 2 (tie).
- All rules/lookbacks beat B&H.

However, even long series have just a handful of crashes.

What about annual Sharpe ratios?

The next chart summarizes net annual Sharpe ratios for all IM and SMA rules and B&H. For these calculations, we treat January 2019 through November 2019 as a full year. Notable points are:

- Across lookback intervals, there is no clear winning rule type.
- The best performance overall is for IM5-Case 1.
- Top performances for other rule types are IM5-Case 2 and IM10-Case2 and SMA10, SMA11 and SMA12.
- Most rules/lookbacks beat B&H.

How often are the rules exposed to equity risk?

The next chart summarizes percentages of time in stocks for all IM and SMA rules. In general:

- Percentages range from 57% to 68%. Rules with longer measurement intervals spend a little more time in stocks.
- IM-Case 2 rules spend less time in stocks than corresponding rules for the other two sets.

How often does each rule switch between stocks and cash?

The next chart summarizes number of stocks-cash switches for all IM and SMA rules. In general:

- Short measurement intervals switch more frequently than long measurement intervals and are therefore more sensitive to assumptions about switching frictions.
- IMs mostly switch a little less frequently than corresponding SMAs and therefore are somewhat less sensitive to assumptions about switching frictions.

How sensitive are the best rules to assumed level of switching frictions?

The next chart summarizes effects on net CAGRs of varying the level of switching frictions from 0% to 1% for SMA12, IM10-Case 1 and IM10-Case 2 over the full sample period, with CAGR for B&H shown as a benchmark. Breakeven levels of switching frictions are about 0.2%, 0.3% and 0.7%, respectively, for these rules.

Are findings consistent for a recent subperiod?

The final chart summarizes net CAGRs for all IM and SMA rules and B&H since the beginning of 2000. For this short recent subperiod, which includes two severe bear markets:

- There is considerable variation in performances across rule types and lookback intervals, with longer intervals generally working better than short ones.
- The best rules by type are SMA9, IM10-Case 1 and IM5-Case 2.
- Many longer-interval rules beat B&H.

Note that even random timing tends to boost performance for a relatively short sample containing deep bear markets.

In summary, *evidence from simple tests indicates no clear winner among the three U.S. stock market timing signals considered, but IM based on raw cumulative return appears to be better than IM in excess of the risk-free rate.*

Cautions regarding findings include:

- The available sample period favors market timing in that it begins with the severe 1929 stock market crash. The subsample starting January 2000 likewise favors market timing by beginning with the 2000-2002 stock market crash. This recent subsample is small for testing.
- Testing multiple rules on the same data set introduces data snooping bias, such that results for the best (worst) rules overstate (understate) expectations. Lack of consistent patterns across measurement intervals amplifies this concern.
- Modeling of S&P 500 dividend flow is crude.
- Trading frictions vary considerably over the long sample period (see “Trading Frictions Over the Long Run”). The crude assumption of constant switching frictions may affect findings.
- As noted, the above analysis ignore tax implications of trading to, for taxable accounts, the disadvantage of B&H and the disadvantage of variations that trade infrequently.
- Results may differ for other equity indexes and other asset classes (see “Optimal Intrinsic Momentum and SMA Intervals Across Asset Classes”).