Predicting the future by looking at the past.

An analysis of trading strategies with backtesting.

You decide to invest in the stock market and buy a few shares of XYZCorp, you suddenly wake up one day and decide that you are going to day trade to capture the profit from the price movements but have nothing else to guide your decision but your gut, technical analysis is also starting to look interesting even though it all sounds a little fishy*, you trust fundamental analysis but see it more as a long term tool, you wish there was a reasonable way to capture all these ups and downs…

* Note: I've never been a fan of Technical Analysis but to each its own, my main beef is that it lacks a proven track record and hinges on a mostly absolute certainty that the past will repeat itself; and that there are rules governing behaviors across markets, exchanges and participants we can describe, yet the basis for these rules is usually not explained, a fertile ground for snake oil.

Don’t ! You stand a better chance of turning a profit in your investment if you Buy and Hold than if you day trade; this strategy (Buy and Hold) while not without risk (global/local economy, market, sector, company) has a few things going on for it that others don’t:

  • It’s cheap : Day trading can chew your principal capital via commissions and taxes.
  • It’s low maintenance: You literally have to do nothing for years on end but provide capital, XYZCorp then uses your capital to generate monetary value and you get a cut via your stock price and/or dividends.
  • It’s less risky: The risk here comes from missing out on the big swings that can happen in a matter of minutes, being on the wrong side of a trade during a swing is usually devastating.
This post is not about financial advice, but for an overview that expands on the risks of day trading and other financial follies I can recommend The Investment Answer (Goldie, Murray) 

First things first, let’s call what we are about to do by its proper name: Gambling, we are placing our money at risk expecting a reward on an uncertain event => Here the uncertain event is what will happen with XYZCorps price during a time period.

You could argue that all of Investing is gambling and you wouldn’t be entirely wrong, even guaranteed investments like government bonds fail from time to time, so what is important to note is the risk amount which in turn is correlated to how uncertain we are of the outcome, in other words, how confident are you that XYZCorps price will behave in such and such way in the following days.

Confronted with this seemingly impossible problem ( uncertainty ) we usually turn to the past, not because the past is a perfect or even good predictor of the future, but rather ( humbly ) because we don’t have anything else to look at for clues about the future, and that’s unfortunately all we get, clues…

Backtesting as its name implies is simulating or testing a certain action with past data and confronting the result with the present, it also gives us valuable insights about future strategies, if you have ever thought about your life in terms of the choices you didn't take ( what if I had pursued a medical profession ) and then confronted that with present data ( Jim is a doctor and he’s wealthy but overworked ) you are backtesting. When your own son or daughter then asks you what to study, you can tell them: from what I understand you have a good chance of becoming wealthy and overworked, the certainty /risk is left out, but it depends on many factors like your sample size, data quality and external or intrinsic factors, if medical robots suddenly become the norm your offspring might not fare that well, ( but you had no way of knowing ), as I said the past gives us clues, uncertain ones, nothing more…

To the Past !

But first we would need something to compare the past with along with some data.

Note: from here on, I’ll use real data, but momentarily obfuscate the identity of the investment, so for now XYZCorp it is, I'll also simplify considerably our analysis by only using close prices and zero commissions, in reality you'd need to take into consideration Bid/Offer spreads and other subtleties.

The data itself is simply a YTD time series of the closing price, here in chart form along with some basic volatility measures:

Our baseline strategy then would be the profit or loss during this period Year to Date Profit/Loss, any other trading strategy will be measured on top, in excess or loss against this baseline:

YTD P/L = (( Last Price / First Price ) - 1) * 100YTD P/L = (( 271.77 / 140.82 ) - 1) * 100YTD P/L = 93% If you had invested $100 you would have around $193 now, not bad.

The strategy is more or less simple, instead of buying your investment on the first day of the year all at once, you would divide your money in a number of periods and then buy accordingly, so why would you do that ?

If you had perfect knowledge of the future, you would save your money and buy late in a downward market, likewise you would hold onto your investment in an upward market and sell, the issue here is that we don’t know where the trend is going, so this strategy serves as a way to invest when there is a lot of uncertainty in this regard, the fact that we usually have savings available on a monthly or biweekly basis also makes it a popular strategy…

So let’s start there, let’s say you got paid twice a month, that would roughly translate to 10 buy periods of 10$ each. To backtest this strategy we simply divide our data and capital into 10 periods and create imaginary buy operations, it is easier to grasp in table form:

Date        |    Close   |   Amt  | Buy   Qty |  cumSumQty |   #
----------- +------------+--------+-----------+------------+-----
2019-01-14 | $129.07 | $10 | 0.0774773 | 0.077477 | 1
2019-01-27 | $113.41 | $10 | 0.0881756 | 0.16565 | 2
2019-02-10 | $124.81 | $10 | 0.0801218 | 0.24577 | 3
2019-02-23 | $158.8 | $10 | 0.0629723 | 0.30874 | 4
2019-03-08 | $135.13 | $10 | 0.0740028 | 0.38275 | 5
2019-03-22 | $137.18 | $10 | 0.0728969 | 0.45564 | 6
2019-04-04 | $158.05 | $10 | 0.0632711 | 0.51891 | 7
2019-04-17 | $166.95 | $10 | 0.0598982 | 0.57881 | 8
2019-05-01 | $160.82 | $10 | 0.0621813 | 0.64099 | 9
2019-05-14 | $217.15 | $10 | 0.0460511 | 0.68704 | 10

We can get our P/L by deriving it from our final quantity bought:

P/L = ((( SumQty * Last price )/ Amount) - 1) * 100P/L = (((0.68704 * 271.77)/100)-1) * 100P/L = 86.71%After investing $100 you would have around $186 now, still not too shabby.

We can also ask the very valid question, what would have happened if instead of 10 periods we bought in 2, 4 , 20 etc, well we can answer that:

The first thing to notice is that there is not much difference to our baseline strategy of buying at the start of the year, even though we won’t be able to capture a better return, at least we are not that much worse. The other thing to notice is the worst and best performing periods 2 and 3 , here it is implied that you are better off buying in a few periods, but not too few.

Going back to the start of this article, what you/we are after is some sort of validation or insight on the more frequent movements of the investment so as to improve the odds of turning a profit.

What backtesting needs to provide here is a simulation of a trading algorithm along with a trading schedule of operations, we can then tally our P/L and compare it to our baseline P/L…

Let’s start with a trading algorithm that buys on the first of the year, sells when the price goes UP by 8% or more and rebuys the day after, here’s each one of those trades:

Date        |   CloseP  |   chg1D | chg1D% |   BuyP  |    P_L
----------- +-----------+---------+--------+---------+-----------
2019-01-02 | 155.05 | 0.1011 | 10% | 149.14 | 1.03963
2019-01-14 | 129.07 | 0.1041 | 10% | 122.03 | 1.0996
2019-02-08 | 119.27 | 0.1409 | 14% | 119.43 | 1.09813
2019-02-17 | 133.6 | 0.0839 | 8% | 146.1 | 1.00418
2019-02-18 | 146.1 | 0.0936 | 9% | 145.35 | 1.00936
2019-04-02 | 163.96 | 0.156 | 15% | 161.46 | 1.02499
2019-05-11 | 194.3 | 0.1222 | 12% | 187.33 | 1.06312
2019-05-14 | 217.15 | 0.1031 | 10% | 247.15 | 0.934078
2019-05-15 | 247.15 | 0.1382 | 13% | 264.01 | 0.874427
2019-05-19 | 261.29 | 0.1138 | 11% | 251.86 | 0.90716
P_L in excess/loss : -9.28%
Accumulated P/L : 75.08%
Note that here we are calculating our P_L just for the relevant trades, additionally you need to also take into consideration the Start/End prices to properly compare this backtest with the baseline, this is the Accumulated P/L.

As you can see everything was going well until mid May where we had 2 consecutive days where the price rose more than 8% and our P/L turned negative, bummer.

Technical Notes: The code I am using here to backtest is unfortunately part of a side project that is not ready for release, but if you want to roll your own, you can start like I did, with excel, then move onto python data frames to expedite the process, if you have any specific questions let me know.

The cool thing with backtesting is that you can get extravagant and demanding with your trading strategies and sample a huge number of combinations, let’s run the previous strategy, but now let’s expand our dimensions by waiting a number of days before rebuying and adding more days to our original strategy, here are 49 backtests :

❗️Note that unlike our first trading strategy ( 1D Change -> Sell -> reBuy ), here, unless the reBuy period is 1 day, we can't do consecutive operations since we are out of stock to sell, if you don't incorporate this small but crucial detail, your backtest will be incorrect.

Dissecting these strategies, out of 49 only 5 return a profit, and all of them require we re buy our stock within one day, it makes sense when confronted with the price chart due to the up trend.

More tests that you might want to try:- Make the Day change variable, so if the stock goes up X percent or more in a period of 2,3,4, etc days -> Sell -> Rebuy after Y days, for a period of 7 days you are looking at 343 backtests. - Try the opposite strategy, start long cash, then buy when the stock goes DOWN x percent or more and resell y days after (another 343 backtests).- Mix and match, combine both strategies. 

Going back to the start of this article, we now have something to guide our decision making ( besides our gut ), but how sure or certain are we of these results ?

Well, a good strategy is to test our previous group of tests on a different time period and see how well they hold up, for instance we could ask what if we tried our last set of strategies in the previous 6 months ?

For period June- Dec 2018

Would you look at that, our ugly duckling of a strategy suddenly turned into a mostly positive swan, you’d also be more impressed if I mentioned that our baseline P/L is a negative -76.5%, what’s happening here ?

If you look at the price chart things start to make more sense:

Selling and then rebuying afterwards on a downward market can be quite lucrative, the only gotcha is that you need to be sure the trend is going your way.

Backtesting is an important tool for gaining insights into the future via past observations. In this specific case ( day trading) , they point to a real difference in performance depending on the overall trend and strategy, so while they might not serve as an indication of what is to come, they do help us by pointing out some potential downfalls…

Closing Notes:More specifically I would interpret these backtests as follows: -If I had $100 to invest passively for this stock I would divide them in 3-4 periods spread out during a few months.- When considering day trading strategies, the market trend needs to be taken into consideration.-Hundreds if not thousands of backtests need to be performed in order to gain further insights that are suited to an individual investors risk profile, and even then, they are no guarantee of a repeat performance but can save you costly mistakes.
THE DATA: Close prices of Ethereum ETH from June 2018 to May 2019.

Thanks for reading !

About the Author:

Born Eugenio Noyola Leon (Keno) I am a Designer, Software Developer & Artist currently living in Mexico City, you can find me at

AI, Software Developer, Designer :

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