Seeking Alpha

Buy And Hold Versus Moving Average Signal Performance Comparison

Includes: SPY
by: Josef Friedman
Josef Friedman
Long/short equity

The issues with moving average signal investing.

How do we design a prototype moving average trading system?

"Buy and hold" is more profitable than the prototype moving average system, but the prototype has some good points.

It is dubious to consider reinvesting profits as a feature of the prototype system.

Adjusting position size for volatility can enhance returns.

"There are three kinds of lies: lies, damned lies, and statistics." --Mark Twain

The Issues with Moving Average Signal Investing

My previous article demonstrated that prices become more volatile when they are below the 13 and 52 week averages. This phenomenon is quite well known, although I had never previously seen it expressed as something related to moving averages.

Armed with confidence about lower prices having higher volatility, I continued reading Logan’s article. Almost immediately, there was a claim about positive stock performance when above a given long term moving average. This is not a radical concept, but the usual issue with these ideas is that they do not outperform a buy and hold strategy.

A major theoretical problem with buying above a given average, is that inevitably, a much better entry must have been available below that average. This is somewhat offset by the mitigation of risk of catastrophic loss because one will exit when the stock price is hopefully just below the given average. These two factors might offset one another except transaction costs and other types of friction tend to favor not doing anything as in a buy and hold.

My previous studies of stock moving average position performance included analyzing random groups of major stocks that were above a given average on a certain date with others that were below. There was no discernible difference in performance of one group over the other with any selected moving average. Among other things, this suggests that positive price movement is not uncommon, even if a security is not in an optimal low volatility situation.

Design of a Prototype Moving Average Timing System

Let us examine the moving average decision system in more detail.

Buy Above / Sell Below Concept

The proposal is to buy SPY when it is above it’s 200 day moving average and to flatten the position when it is below. My previous article suggested, and it deserves reiterating, that the exact number used for calculating a long term average has no special significance. I use the 200 day average in my analysis here simply to be in synch with Logan's proposal.

Whipsaw Mitigation

The buy above / sell below concept is unplayable on a daily adjustment basis because of whipsaw. Whipsaw is somewhat mitigated by scheduling decisions on a weekly basis, but the most profitable and easiest to analyze solution appears to be once a month. The optimal time period between each check can be tested, but the once a month check is probably as good as any of them. It is also possible to test for the optimal time in the month to do the check/rebalance but the first trading day of a new month has to be decent, it is certainly the easiest to code for. I think optimizing this further would be counterproductive.

Buy and Hold - The Benchmark

The table below summarizes buy and hold performance for SPY from the test period of July 29, 2003 through December 14, 2018.

Start Date End Date Buy Price Shares Buy Value Sell Price Profit
07/29/2003 12/14/2018 73.37 13630.09 1000000.00 260.47 2550229.54

Buy and hold produced a profit of $2.55 million on the initial $1 million investment. Average Annual return is about 9%.

Dividends are not considered. This is standard practice and a fascinating subject in it's own right. Prices of SPY are dividend adjusted.

There are two major ways of playing this system: fixed amount buy or reinvested profits.

Fixed Amount Buy

Start Date End Date Buy Price Shares Sell Price Profit Balance
07/29/2003 01/02/2008 73.37 13630.09 116.07 582023.03 1582023.03
06/01/2009 06/01/2010 78.28 12774.57 90.60 157405.13 1739428.16
08/02/2010 09/01/2010 95.46 10475.48 91.82 -38134.26 1701293.90
10/01/2010 09/01/2011 97.55 10251.51 104.44 70670.27 1771964.17
01/03/2012 09/01/2015 111.38 8978.53 179.77 614074.46 2386038.63
11/02/2015 01/04/2016 198.25 5044.10 190.55 -38852.19 2347186.45
04/01/2016 11/01/2018 197.15 5072.21 273.51 387299.42 2734485.87
12/03/2018 12/14/2018 279.30 3580.38 260.47 -67418.55 2667067.32

The system invests $1 million on a buy signal and goes flat on a sell signal (discussed above).

The system was profitable on 5 out of 8 trades, the first 2 losing trades were relatively trivial amounts. The third losing trade is currently unrealized as it got tricked into buying on 12/3/18. The most impressive feat of the system was avoiding the financial crisis of 2008-2009, an achievement that might excuse some of it's other sins. Hopefully our prototype investor didn't decide CMOs were a good place to put his money when he took it out in 2008.

The 12/3 trade is an anomaly caused by the extraordinary technical event on 12/3, where the price popped above both the 50 and 200 day averages. One might be tempted to move the selection date to avoid this and submit the test again. However, it is more productive to look at this as an indication that the trading strategy is promising but far from a final product.

The system made $1.67 million on it's multiple $1 million investments. This is a good result, but it is almost $1 million worse than buy and hold. The return is about 7% per year.

Note the rather odd entry/exit decisions of the last six trades.

Reinvested Profits Buy

Start Date End Date Buy Price Shares Buy Value Sell Price Sell Value
07/29/2003 01/02/2008 73.37 13630.09 1000000.00 116.07 1582023.03
06/01/2009 06/01/2010 78.28 20209.67 1582023.03 90.60 1831041.57
08/02/2010 09/01/2010 95.46 19181.04 1831041.57 91.82 1761216.15
10/01/2010 09/01/2011 97.55 18055.12 1761216.15 104.44 1885681.78
01/03/2012 09/01/2015 111.38 16930.64 1885681.78 179.77 3043630.80
11/02/2015 01/04/2016 198.25 15352.38 3043630.80 190.55 2925379.09
04/01/2016 11/01/2018 197.15 14838.13 2925379.09 273.51 4058376.72
12/01/2018 12/14/2018 279.30 14530.53 4058376.72 260.47 3784767.15

This system reinvests all realized profits in subsequent buys instead of the $1 million original amount. Thus the Buy Value of the second trade is $1.58 million instead of the $1 million of the Fixed Amount Buy, etc.

In this case, the system made $2.78 million versus the Buy and Hold result of $2.55 million.

Discussion of Why Reinvested Profits is not a Suitable Performance Estimate

It is easy to see why one might conclude that reinvesting profits is a superior strategy to both the Fixed Amount and Buy and Hold strategies at first glance. However, this is quite dubious. The problem seems to be the extra risk taken on by each of the subsequent investments. Notice that the amounts of the last three trades average about $3 million, with the one on 12/3 being over $4 million.

Adjusting position size and/or reinvesting profits in a robust system in the real world is possible, but it is premature to seriously consider this during either the system development or proof of concept stages. The relationship of volatility to moving average level has been demonstrated and testing indicates that a simple strategy makes money and limits risk. The assertions of obtaining uncountable riches by reinvesting realized profits (over 90 years) are pleasant fantasies, but they do nothing to advance the implementation of a robust strategy in the real world. There is no proof, but little doubt, that our hypothetical reinvest profits investor would have found a questionable way to invest his cash in the financial crisis.

There is abundant expert advice on performance measurement and position sizing in the real world, but not too much when one is playing with monopoly money. For example, Taylor Dart discussed position sizing on SeekingAlpha last year.

From his bullet points - "This article seeks to take a deeper look at why even the best trading systems in the world can be derailed by aggressive position sizing."

Taylor's article is excellent and worth reading carefully.

Personally, I'm not an expert on statistics, so contrary opinions may have merit; but I don't see a practical value to include reinvestment options in the evaluation other than making the system seem better than it actually is. Probably the section of the wiki dealing with misuse and misinterpretation should be studied. This quote should be kept in mind:

"Mathematical probability theory arose from the study of games of chance."

My Opinion of the Concept

My overall opinion of the concept is that the prototype appears to be profitable. It has less risk than Buy and Hold, but is less profitable, perhaps because of that. I don't regard the Reinvested Profits model as a suitable estimate of profitability.

It is also important to keep in mind that in the real world, a buy and hold investor is generally saving a certain amount of money regularly for retirement or other future needs. In this scenario, a period of moderately lower prices, enhances returns because the investor is buying at those lower prices. This comparison doesn't consider that.

The tax implications of either moving average strategy are not pleasant compared with Buy and Hold.

Adjusting Position Size for Volatility Can Enhance Returns

This is hardly a new concept. Typically investment managers will hold some percentage of a portfolio in cash equivalents and adjust this balance depending on market conditions. Also many swing and day traders will have reduced their normal position sizes in these conditions.

The data suggests that position size should be reduced when markets show increased volatility and increased when volatility decreases.

Volatility near longer term moving average areas is worth further research. Volatility calculations are not easy to work with because the excess volatility happens real time, it doesn't seem to grow gradually. If we expect high volatility to positively correlate with trading areas near long term averages, this may give the investor a useful early warning. The five day average true range is a useful thing to keep track of to assess risk.

Here is the volatility table for the daily moving average combinations from mid 2003 until now:

SPY Below Both Be200 Ab50 Be50 Ab200 Above Both All
Gain Days 299 104 383 1345 2131
AvgChgPctG 1.48 1.01 0.75 0.48 0.69
AvgRngG 3.0 2.1 1.5 1.0 1.4
Loss Days 247 83 267 1116 1713
AvgChgPctL -1.63 -1.22 -0.84 -0.54 -0.77
AvgRngL 3.3 2.3 1.8 1.2 1.6

My previous article discussed the meaning of the data elements which are expressed in percentage moves. Thus SPY, below both averages, as it is now, will have an average daily range of 3.x% whether it closes up or down. Also notice that there are more up days in this relative position than down days, but the down days seem a little more serious. These ratios more or less carry over to the other situations. These numbers are useful things to be aware of.

Note that volatility also increases noticeably around the 50 day average. That suggests that attention should be paid to both averages.

Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.