June 20, 2016                         Also available in PDF

(Part 2 of 3)

An Inquisitive Backtest

I opted to test the protective stop loss hypothesis starting with the notion of having a 10% trailing stop loss. The intention is to buy stocks on their way up and sell them later at higher prices (see the intro, Part 1). To execute a trailing stop, you first need to buy some shares, so I also put in a 10% trailing buy order from a bottom.

The price will need to go up by 10% after having reached some lower point. Then a purchase will be automatically initiated after that 10% rise, actually the day after. It is the same kind of operation as the trailing stop but on the buy side.

Based on these simple conditions one should profit long term since stock prices over extended periods of time tend to go up. You wait for the stock to go up 10% and buy, then wait until a 10% drop in price from its next high mark to get out. If the stock price does not drop by 10%, it will result in you holding on to the shares for as long as it takes to get a 10% dip. The method almost guarantees you to have some winning trades. The probability of having some profitable trades is asymptotically approaching 1, if not almost surely equal to 1. Overall long-term portfolio profitability is another question.

Designing such a trading script is relatively easy to code, but if you do only the 10% trailing stop case, it might not be that revealing or conclusive. So, I went for changing the stop loss setting from 1% to 40% by 1% increments and doing the test over a 20-year period, actually over 5,281 trading days (20.9 years). More than sufficient to make a point. At least long enough to silence those that would say: you selected too short a period where it works or didn't work.

The purpose of doing the test is to also answer questions like what should be the preferred stop loss setting? How many stops will be executed over the trading interval? How much ending profits overall were generated using this supposedly "protective" stop-loss technique?

Initially, trades were set at \$10k each with a \$100k reserve, thereby starting with a 10% portfolio bet. The outcome of the test - using the same stocks as in previous recent tests - is shown in chart #1 below.

#1  ABT - Trailing Stop    (1% to 40% trailing stops)

(click to enlarge)

In 39 of the 40 scenarios, the simulation ended with a positive result over the 20-year trading interval. However, when one looks at the result from a profitability standpoint, it is not so hot. In fact, those are dismal performance results. The APR column shows that none of the scenarios produce anything above a 1.5% CAGR (compounded annual growth rate), and that is over a 20-year investment period. Drawdowns were tolerable, as could be expected, since they were set by design at a 10% mark. After all, you were only risking \$10k at a time. The exposure column can attest to that too.

What stands out is the diminishing number of trades as the percent stop loss setting is increased from 1 to 40 (see second column #OptVar1 on chart #1).

#2  ABT - Number of Positions vs APR

(click to enlarge)

The above chart is also revealing. It shows that as the % trailing-stops increased (#OptVar1 in chart #1), the number of executed trades decreased (fifth column in chart #1), and a lot faster than might be expected. This is normal since there are a lot more 1% drops than 10% or 20% ones. As the trailing stop percent increases, we see fewer and fewer trades. This is perfectly depicted in the above chart.

So, technically, nothing of note except maybe gaining a better understanding of the stop-loss scenario process. With a \$10k bet out of a \$100k stake, the 10% trailing stop is not that interesting after all, especially in the CAGR department. It surely suffers from low market exposure or has a real allocation problem. However, in building a diversified portfolio, one might find a 10% portfolio stake to be quite high for a single stock. Most often, that figure is much lower, especially if you put 50 to 100 stocks in your portfolio.

#3  ABT - Number of Positions vs Profit

(click to enlarge)

This can raise the question that the number of trades over the lifespan of a trading system will more than matter, and most probably a lot. In the above chart (#3), only the right-hand scale changed compared to chart #2. Both charts express the same thing, one as a percent, the other as a dollar amount.

ABT did the most trades at the 1% trailing stop level (664), but it could not even come close to achieving the performance level of a single trade as in a Buy & Hold scenario. Even the most favorable outcome came in short by a factor of 20 to 1. This saying that the Buy & Hold scenario was by far more rewarding.

There is no surprise in these results. It is what logically should have been expected.

Anyone could have reached the same conclusions without even doing this kind of test. The more you increase the stop loss level (from 1% to 40% in this study), the less the number of trades.

It is like measuring how many trading opportunities were available over the entire trading interval. The larger the trailing stop, the smaller the number of opportunities or trades. This is not for just one stock, as depicted above, but can stand on its own as a general rule.

By increasing the stop loss level, one is also increasing the average percent profit per trade, as can be seen in the average profit % column of chart #1. But, this is done on a diminishing number of trades. To the point where at about the 10% stop loss level, one might consider that the trading method is losing statistical significance due to the reduced number of trades (42 trades) over the 20-year period. The best behavior appears to be between the 17% to 29% stop loss level. At those levels, it is not everyone that would trade like that knowing beforehand they will underperform even the averages of index funds. There is no alpha there.

A trading program applies a set of trading rules. In this case, rather simple ones: rise by x% from a bottom, get in; drop by x% from a top, get out. And none of the trailing stop scenarios proved worthwhile, even though almost all came out positive. It is just that it really was not enough for the efforts deployed, and furthermore, this was a scenario requiring constant monitoring of the situation over the years, day in and day out.

The trailing-stop scenario, as presented, could be viewed as a variant of a simple moving average crossover system. Instead of having variable entries and exit points, these points are pre-set as a fixed percent of price moves (from highs and lows). It becomes like changing the length of the lookback period for a moving average, and as in this test, simulates a range of lookback settings.

This view of variable entry and exit points has been covered before, for example, in the Stock Trading Strategy Experiment or, more recently, in the Value of a Stock Trading Strategy.

## Too Much Reserves

Was it a case of too much reserves? After all, bets were only \$10k on a \$100k stake. This can easily be answered. Simply redo the simulation with a \$10k portfolio with \$10k bets. Here is that test:

#4  ABT - Trailing Stop with \$10k Bets & \$10k Reserves

(click to enlarge)

Since this test is totally scalable, if you want to see bigger numbers, just add zeros to the profit figure as well as the bet size and reserves. However, it should not change the number of trades, the APR column, or the average profit % column, as presented in chart #4. This is to say you would get the same CAGR as can be seen in chart #4.

A more visual representation of the profit distribution in chart #4 is given below:

#5  ABT - Trailing Stop with \$10k Reserves - Profit Distribution

(click to enlarge)

From the above chart, the profit distribution does not appear to be part of a robust system. The highest profit occurred at the 20% trailing stop setting, and you could get 8 times less by setting it to 23%. Not that desirable a characteristic, too much dependence on a slight variation. In no case, any of the trailing stop settings exceeded the Buy & Hold profit (\$72.879) or its long-term CAGR (9.9%), see chart #6.

The general drawdown level increased significantly compared to chart #1. This goes as well for the exposure ratio which is more elevated. However, the number of trades was reduced compared to chart #1. This is understandable too. The excess reserves in the first case allowed for more trading. So, limiting the reserves does have an effect on performance.

#6  ABT - Trailing Stop with \$10k Reserves – APR Distribution

(click to enlarge)

Maybe the most important point being presented is that as the trailing stop setting is increased, the number of trade opportunities decreases to a point where only one trade might remain in the portfolio and thereby asymptotically approaching the Buy & Hold scenario from under, just as the trend seems to suggest in chart #6.

At the 40% trailing stop level, there were only 2 trades executed over the 20-year period. Another way of saying not statistically significant. And a system that trades only twice in 20 years is more a variant of a Buy & Hold proposition than anything else. One could call it a system, but not that much a trading system.

It is, however, quite understandable that as you increase the trailing-stop percentage, fewer and fewer trade opportunities exist. This is quite explicit in chart #3, where the number of trades decreases significantly, having a steep negative slope at the lower stop loss levels. Levels at which profitability is also decreasing, especially below the 10% trailing stop level. Above the 10% trailing stop mark, one has to consider that such a system becomes statistically not that relevant or significant even if it can show some profits.

Operating with a 30% trailing stop, which I think requires character, is shown in chart #5 as not that productive, whereas the 31% level produced 5 times more. It makes it a system that is too sensitive to slight setting variations, and you don't know if another stock would respond the same. Well, in fact, you do: they won't. Each stock will behave differently.

... to be continued