The Seasonal Timing Strategy (STS) was published by Sy Harding in the book Riding the Bear back in March 1999, and again in Beat the Market the Easy Way on November 2007. It attempts to improve the Best Six Months strategy by optimizing the entry and exit dates using a technical indicator called Moving Average Convergence and Divergence (MACD).
Sy Harding is the founder of Asset Management Research Corp. and a long-time publisher of the Street Smart Report newsletter. He’s primarily a market technician, and he times the markets with the use of technical indicators in a subjective manner. The STS strategy, however, appears to be entirely rule-based, and the Hirsh organization (inventor of the Best Six Months strategy) strongly advocates this strategy in their yearbook Stock Trader’s Almanac.
The basic premise of the strategy is that every year is different, and the stock market does not necessarily start going up exactly on the first of November (when the best six months normally begins), nor does it start declining precisely on the first of May (when the best six months normally ends). So what Harding did was to “relax” the entry and exit dates such that the model can enter or exit the market a bit earlier or a bit later, depending on the market momentum.
In this study, our goal is to recreate the model using our own software and data so we can verify the numbers ourselves. We’re skeptics when it comes to the investing and trading marketplace, so we never follow anybody’s advice blindly.
We also like to move the research result forward and keep it current indefinitely. This way, you can follow the strategy in real-time and you never have to wonder… “Is that strategy still working?”
In the next few sections, we’ll give you the background information to understand the strategy along with its buy and sell rules. Then we’ll discuss a summary of our findings. If you’re already familiar with this material and just want to see the reports, feel free to jump right to the programs.
In writing this article, we’ve made the assumption that you’re already familiar with the concepts we’ve introduced in the Best Six Months, Fabian, and Pentad timing models. If you haven’t read those studies in a while, consider reviewing them before you continue.
In case you’re curious, you can see the most recent trades made by STS in Chart 1.
The Seasonal Timing Strategy is a 100% mechanical timing model for the stock market that’s based off the Best Six Months seasonal pattern. Unlike the original strategy, the entry and exit dates of STS have been fine-tuned and made elastic. That means it no longer enters or exits the market on exact dates. Instead, it first waits for a confirmation from the MACD indicator before placing the actual trades.
The system is long-only and does not sell short.
The model enters the market anytime the market momentum surges after October 16th. So this means the strategy can enter the market as early as mid-October if the market is strong, or well past November 1st if the market is weak.
Conversely, the model exits the market anytime the market momentum wanes after April 20th the following year. So this means the strategy can exit the market as early as mid-April if the market is weak, or well past May 1st if the market is strong.
The model operates on a daily timeframe, so it might be a bit of a hassle for investors who prefer to manage their investments on the weekends or at the end of the month. But the good news is you only need to pay attention to it twice a year for a period of one day to about a month, right around when the best six months begins and ends. The model makes one round-trip trade per year, and the average holding period is a little over six months.
Our target portfolio for this study is the US stock market, and we’ll use the S&P 500 Total Return Index as our proxy. Since STS is an attempt to improve the Best Six Months strategy, it is only fitting that we use it as our benchmark for this study.
We use total return data, as opposed to cash or nomimal return data (what you see in the news), when simulating investment returns. Why? That’s because total return series accounts for the compounded effect of reinvested dividends, interests, and other distributions over a period of time.
This can be as much as 50% of the total gain if you buy and hold high-yield instruments like dividend stocks, bonds, and REITs. Keep this in mind the next time someone proclaims they “beat buy and hold” but are using nominal prices for comparison.
Both Harding and Hirsch use the Dow Jones Industrials as their target instrument, and we believe they are using the nominal prices, so our results would diverge. We opted to use the S&P 500 because we believe it’s more representative of the US stock market, and we would like to compare the results of this strategy with the other timing models we have in equal terms.
To understand the MACD indicator, we first need to introduce one more type of moving average – the Exponential Moving Average, or EMA for short.
At this point, you should now be familiar with two types of moving averages – the Simple Moving Average (SMA) and the Weighted Moving Average (WMA). If not, please take a look at our discussions on these two indicators in the Pentad timing model.
If you recall, the main difference between SMA and WMA is that the former gives equal weight to the past n data points, while the latter applies a linearly increasing weight starting from the oldest data in its lookback window, and all the way to the newest. The reason for front-weighting the moving average is to make it more responsive to the price changes on more recent data (i.e., reducing the lag).
Like WMA, EMA is another form of front-weighted moving average, except it uses an exponentially increasing weight. In other words, the highest weight is given to the most recent data and the weights decreases geometrically as you go back further in time.
Figure 1 illustrates how a 10-period SMA, WMA, and EMA weigh their input data. The vertical axis represents how much weight is given to a data point, and the horizontal axis represents the 10 data points starting today (0) up to nine days ago (9).
Notice that SMA weigh each data point at 10% (simple average), so it just forms a flat line. WMA weighs the oldest data at 2%, and proportionally increases the weight until it reaches 18%, resulting to a straight line with a positive slope. Finally, EMA starts at around 3%, and the weights are increased exponentially until 18%, giving us a rising curve.
Between the three, SMA and EMA are the most popular when it comes to investment and trading systems. Why? For SMA, it’s because of its simplicity, and one could argue that a front-weighted moving average would increase the occurrence of whipsaws. But for those who prefer front-weighted moving averages, we think EMA won out because it’s less laborious to compute compared to WMA, which is a big deal back when indicators were computed by hand.
Ultimately, however, the three moving averages produce about the same result, and all three are equally effective in generating smoother versions of the input data.
Now that we have basic understanding of EMA, let’s move on to the MACD.
The MACD (pronounced as MAC-Dee or M-A-C-D) is a popular momentum indicator that was invented by Gerald Appel back in the 70’s. Momentum indicators measure the speed at which the price changes through time.
MACD measures the momentum indirectly by comparing the relationship of fast exponential moving average (Fast EMA) and slow exponential moving average (Slow EMA). The Fast EMA have shorter lookback period and would therefore follow the input data more closely.
The momentum is positive if the Fast EMA is above the Slow EMA, and the momentum is negative if the Fast EMA is below the Slow EMA. The larger the difference between the two moving averages in terms of magnitude, the stronger the momentum (and the sign determines the direction). Mathematically, this is expressed simply as: Fast EMA – Slow EMA.
The two main components of the indicator are the MACD Line and the Signal Line, and they are computed as follows using the standard 12-26-9 settings:
Fast EMA = EMA(Price Close, 12) Slow EMA = EMA(Price Close, 26) MACD Line = Fast EMA – Slow EMA Signal Line = EMA(MACD Line, 9) MACD Histogram = MACD Line – Signal Line
Figure 2 illustrates the different components of the MACD indicator. The top pane shows the price, along with its Fast EMA and Slow EMA, while the bottom pane shows the MACD Line, Signal Line, and the MACD Histogram.
The MACD Line measures the momentum of closing prices of the instrument by comparing the relationship of the fast and slow moving averages (as we described earlier), using a 12-period and 26-period lookback, respectively.
The Signal Line is the 9-period average of the MACD Line, and it is used as a reference to determine if the MACD Line itself is gaining or losing momentum. In other words, if we compare the relationship of the MACD Line to the Signal Line in the same way we compared the Fast EMA and Slow EMA, then we can determine if the momentum is speeding up or slowing down (i.e., the momentum of a momentum), and at which direction. This relationship is expressed mathematically as MACD Line – Signal Line, and it is typically plotted as a histogram.
In this study, we will use the daily closing prices of the S&P 500 Index (nominal version of our target instrument) to calculate the MACD indicator.
Here are the buy and rules of the Seasonal Timing Strategy:
Buy Rule:
Sell Rule:
So instead of entering exactly on Nov 1, the model could enter as early as Oct 16 provided that the momentum is positive. Otherwise, it could delay its entry, possibly missing the entire best six months. But of course, this doesn’t happen in reality, and in our test going back to 1950, the latest entry ever recoded was the last week of November. So the rule could have said Current date >= Oct 16 of this year, and <= Apr 20 of next year, but we simplified it for clarity. We took this possibility into account in our software program, however, just in case it ever happens.
The same goes for the exits. Instead of selling exactly on May 1, the model could exit as early as Apr 20 if the momentum is negative. Otherwise, it could hang on to the position, possibly through the entire worst six months. This possibility also didn’t happen, and the latest exit ever recorded in our test going back 1950 is the last week of May.
When the strategy is not in the market, we assume that the cash in the sidelines earns 90% of the going T-Bill rate. This is similar to what you’ll get if you park your cash in your brokerage account or money market fund.
The ultimate question we have when we decided to look into this strategy is this:
Does STS perform better enough compared to the Best Six Months strategy to make all the extra complications worth it?
Apparently not, but this is just our opinion. We’ll present the data so you can judge for yourself.
You can see the equity curves of STS and Best Six Months in Chart 2. The equity curve is shown in the top part of the chart, and it illustrates how the strategy’s equity grows over time. The underwater equity curve is at the bottom, and it demonstrates the drawdowns or setbacks you have to go through. Ideally, you want to see the equity growth to go up in a straight line at about 30 to 45 degree angle, and you want the drawdown pane to be completely blank. Typical investors won’t be able to stomach more than 20% of drawdowns.
It shouldn’t be a surprise that both have similar equity curves, since their core strategy is the same. STS and Best Six months performed on par to each other from 1980 to 2000, but it looks like the former gained a slight edge afterwards. We think the model’s MACD filter enables it to handle bear markets much better by fine tuning its entries and exits, hence, the outperformance.
The underwater equity curves look identical so it’s hard to see, so we plotted them separately in Chart 3. Even then you really need to have a sharp eye to discriminate the small differences.
This is when the numbers come in handy, and you can see them in Table 1. The four statistics we normally look at – compound annual return, max drawdown, MAR ratio, and longest drawdown duration – have improved across the board, but only very slightly.
| STS | Best 6 Months | |
|---|---|---|
| Starting Equity | $100,000.00 | $100,000.00 |
| Ending Equity | $8,200,258.84 | $7,261,012.32 |
| Time Elapsed | 45 years, 5 months | 45 years, 5 months |
| CAGR % | 10.19% | 9.89% |
| Max % Drawdown | (33.78%) | (35.63%) |
| MAR Ratio | 0.30 | 0.28 |
| Win Rate % | 84.4% | 80.0% |
| Longest Drawdown Duration | 44.6 months | 45.2 months |
| Avg Trades Per Year | 0.99 | 0.99 |
It’s interesting to note that STS, as of this writing, has a tiny edge in compound annual return of less than 0.5%. Yet, this miniscule difference, compounded over many years, got it ahead by nearly half a million dollars. Talk about the power of compounding!
Finally, you can see the yearly performance of STS and Best Six Months in Table 2. We see the same story here – their performances are nearly identical.
In this study, we looked at a different twist to the original Best Six Months strategy. The basic premise of STS is that the market doesn’t necessarily start going up exactly on Nov. 1st, and it doesn’t necessarily start going down on May 1st the following year. So it fine tunes its entries and exits using market momentum with the help of the MACD indicator.
In the past 30+ years of our test, STS demonstrated a slight outperformance over the original strategy. However, we think that whatever edge it has right now is too small that it could be easily be wiped out by a trade or two.
We also like to keep things simple, and the facts show that we’ll get 99% of the benefit by just following the original strategy, without the additional complications of the MACD indicator, or the extra hassle of monitoring the markets daily when it’s time to buy or sell.
Of course, we could be wrong, and only time will tell.
The result of this study demonstrates one of the most frustrating parts of what we do. Sometimes, you’ll see a strategy that’s promising on paper, and after putting in a lot of the time and effort in coding, checking and double checking our implementation, we get results that are not exactly what we hoped for.
But then again, this is the price for due diligence, and it’s better to find out this way compared to testing with real money.
Not that STS is a bad strategy per se (it still beats buy and hold on risk-adjusted basis after all), it just didn’t meet our expectations.
Nevertheless, we’ll keep this research up to date so we can monitor how it is doing. We believe in documenting both winning and losing strategies, because each type has important lessons you can learn from. It’s also a handy reference if you plan to do your own testing so you can get an idea on what to expect and what to avoid.
We actually tested this timing model going back to 1950, and we also isolated the more recent period from year 2000. We obviously cannot fit all those reports in this article, so if you want to see those studies, feel free to browse the available programs we have for this model.
Overall, we hoped you’ve learned something from this study. We’ve introduced the EMA and MACD indicators, and we’ll encounter these two indicators again in our future studies since they are favorites among system developers.
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