Most long-term approaches to investing, like tactical asset allocation or factor investing, are designed to trade infrequently, generally once a month or once a quarter. This is a feature, not a limitation. Trading infrequently forces a strategy to ignore day-to-day noise and focus on long-term trends. This reduces the negative impacts of turnover, including transaction costs, taxes and whipsaw. (Corey Hoffstein has written an excellent piece on rebalance frequency here).
Day of the Month and a Basic Trend-Following StrategyFor a number of reasons (but mainly for simplicity’s sake), researchers usually show the historical performance of these infrequent trading strategies based on end of month data. But as we’re about to show, the specific day that an investor chooses to trade can have an impact on strategy performance. In the example below, we show the results of a simple trend-following strategy that trades the S&P 500 just once per month, going long when the S&P 500 will close above its 10-month moving average, otherwise investing in cash (3-month Treasury Rate). The average month has 21 trading days, so we’ve shown 21 variations of our simple strategy, each trading on a different day of the month. You can find more on the math behind this test in the article footnotes. 1 2 For now, know that we always maintain the spirit of that “10-month moving average”, so if trading mid-month for example, we use the previous 10 mid-month prices. Note the wide disparity in results, with annualized returns ranging from a low of 4.7% to a high of 8.1%. That difference of 3%+ annually, while reasonably small in any particular year, results in a 73% higher return over our 17+ year test. In short, over this time period, the day that an investor chose to trade mattered (a lot). 3 Here’s another characteristic of our simple example: trading either at the beginning or the end of the month has historically resulted in higher returns than trading somewhere in the middle. To illustrate, the graph below shows the annualized return for each of our possible trading days. Day 1 is always the first day of the month and day 21 is always the last. A similar pattern to the one below can be seen in other metrics as well (Sharpe ratio, etc.) In the remainder of this article, we’ll show that this outperformance when trading at the beginning and end of the month extends to other more sophisticated strategies as well, and talk about possible reasons why.
Real World Data: Tactical Asset AllocationOur firm Allocate Smartly provides independent analysis of one flavor of long-term investing: Tactical Asset Allocation (TAA). TAA strategies dynamically allocate to broad asset classes like stock indices, bond indices or gold. Unlike a traditional buy & hold portfolio, TAA increases allocation to assets expected to outperform and reduces allocation to those expected to underperform, in an attempt to enhance returns. We track more than 30 TAA strategies in near real-time, sourced from academic papers, books and other publications (click for the full list), including Alpha Architect’s own Robust Asset Allocation. While we don’t (yet) track every published model, those that we do are broadly representative of the TAA space and allow us to draw some general conclusions about the world of TAA. Most of the TAA strategies that we track, like our model above, only trade at the end of the month, but we show members the results of trading on other days of the month as well, because as we’re about to show, it matters. Similar to the original example, TAA strategies have also tended to perform better trading near the beginning or end of the month, rather than the middle. To illustrate, in the graph below we show the average annualized return of all of the monthly TAA strategies that we track, broken down by the day of month that one opted to execute trades. Note the similar pattern. The best days to trade tend to cluster around the beginning and end of the month. The simple model we examined in the previous section showed more pronounced differences (remember, we’re talking about a much bigger sample of assets and strategies here), but the pattern is similar. We’ve limited these results to just the year 2000 and beyond, but when looking even further into history, the pattern remains: strategies tend to perform best when trading near the beginning and end of the month (and particularly on the last day).
Why Do Begin/End of the Month Trend Strategies Work Better?One obvious possibility for the empirical result observed is pure chance. We cannot rule out this possibility. However, below we present two possible reasons for the beginning and end of month outperformance in the sample examined.
The “Turn of the Month” EffectThere is a “turn of the month” effect in many asset classes, meaning the returns for many asset classes tend to be higher near the beginning and end of each month. To illustrate, below we’ve shown the results of holding the S&P 500 for just the 4 days before and 3 days after the end of the month in blue, versus all other days in grey, since 1970. Here we ignore transaction costs and the return on cash. During our 7 “turn of the month” days, the S&P 500 averaged 0.09% per day (CAGR = 24.9%), compared to just 0.01% on other days (CAGR = 2.5%). A similar pattern exists across a number of other asset classes. A key takeaway is that there have been significant differences in asset performance around the turn of the month, and a monthly trading strategy that performs better when trading in that period may simply be exploiting a real market anomaly. In other words, the outperformance may be a feature, not simply noise. To determine if the turn-of-the-month effect drives tactical asset allocation performance, one would expect to see a cluster of outperformance around the turn of the month. In the table to the right, we’ve shown alternate trading day statistics for a real life TAA strategy from Meb Faber’s seminal paper A Quantitative Approach to Tactical Asset Alocation. Results have been sorted by annualized return. Day 21 (the last trading day of the month, when most backtests assume the strategy trades) is near the top, but note the better performing days are around the turn of the month across multiple metrics. Which brings us to the second explanation for turn of the month outperformance: overfitting.
Overfitting to HistoryConsider a hypothetical strategy that trades asset X whenever asset X crosses above its 200-day moving average. If we were to change that moving average in some minor way, by using say a 195-day or a 205-day moving average, we wouldn’t expect to see results deteriorate in any meaningful way. Moreover, knowing what we know today, we couldn’t say for sure which of those very similar moving averages (195, 200 or 205 day) would be superior out-of-sample. That’s because small changes in parameter settings shouldn’t have a significant and predictable impact on results. If they do, it’s a sign that our model was overfit to that particular set of historical data. The same could be said for which day of the month these monthly strategies trade. Unless there is something particularly special about day 21 (the end of the month), day 21 shouldn’t perform significantly better than nearby days. There could very well be a difference between trading at the end of the month and say mid-month, but days 20 and 21 for example, should perform similarly. In 27 of the 31 strategies (87%) included in this analysis, trading on the last day of the month outperformed trading on the average day. In 23 of the 31 strategies (74%), the last day of the month outperformed the adjacent two days. Again, to reiterate an earlier point, even if one were to conclude based on these stats that a given strategy was overfit to end of month data, it wouldn’t mean that the strategy was worthless, only that results as they are usually shown, trading on the last day of the month, are overly optimistic.
Accounting for End of Month OverfittingA simple “back of the envelope” approach to accounting for this end of month overfitting, might be to use statistics from the average trading day in place of the end of the month. For example, in our test of Meb Faber’s strategy above, the strategy returned 8.6% annually trading at the end of the month, but 8.3% trading on the average day (a small discount of -0.3%). Taking a similar approach with the other 30+ tactical asset allocation strategies that we track on our site, discounts to annual returns range from -1.7% (in the case of a model where end of month “outperformance” was particularly strong) to +0.2% (in the case of Gary Antonacci’s Global Equities Momentum where the average trading day actually performed better than the end of month). Alternatively, if one were to conclude that there is something special about the turn of the month, and that outperformance is a feature and not simply noise, then one could compare end of month performance to just nearby days (ex. days 19-2). By this approach Faber’s strategy suffers no discount, and the other TAA strategies that we track are discounted by between -0.6% and +0.5%. Your own conclusion about the importance of the “turn of the month” determines which discount represents a truer estimate of a strategy’s performance.
Putting It All TogetherWe’ve established that a representative sample of tactical asset allocation strategies have performed better trading at the beginning and end of the month. We’ve shown that many asset classes also behave very differently around that period as well, so the difference in strategy performance may very well be a feature. To determine if that were the case for a given strategy, one would expect to see a cluster of outperformance when trading around the turn of the month. Conversely, it could also be that outperformance when trading around the turn of the month is a symptom of overfitting. We present a “back of the envelope” approach to accounting for overfitting to the end of month and discounting strategy returns. There’s a whole world of opportunities and pitfalls in strategy design beyond the scope of this article. Here we’ve dealt with just one often overlooked aspect of strategy evaluation. To see statistics like those we’ve presented here, showing the results of trading on alternate trading days, for dozens of tactical asset allocation strategies published by the industry’s brightest, visit Allocate Smartly today.
- The following assumptions are made for all tests in this article, unless otherwise noted: trades are executed at the market close, transaction fees plus slippage total 0.1% per trade (0.2% round-trip), dividends and gains are reinvested, return on cash is equal to the 3-month US Treasury rate, and returns exclude taxes. ↩
- Every month has a slightly different number of trading days, so we first normalize the number of days each month to 21. Shorter months get stretched and longer months compressed. We normalize the day of the month as follows (in Excel parlance): round((trading_day / total_trading_days) * 21, 0). Day 1 will always be the first day of the month and day 21 the last. When calculating a “monthly” indicator for normalized day X (such as the 10-month moving average used in this article) we use previous day X values. So for example, a 10-month moving average on day 15, would be calculated based on the previous 10 day 15 values. This maintains the “spirit” of the monthly indicator even when trading on other days of the month. ↩
- One thing that is interesting to note is that all versions helped lower the maximum drawdown, a key feature of trend following rules. ↩