As we mentioned in the last post, our raison d'être is using science – namely machine-learning tools and statistics – to help small investors achieve decent returns with low volatility. OK, great. But what does this really mean? Well in this post we show what is possible with a simple strategy, which uses our public data and strives to beat a traditional buy-and-wait strategy for a difficult index such as the CAC 40. What is important to remember in this example is the underlying message of how statistics can help you make consistent, data-based decisions to achieve modest yet stable returns. All without passively waiting decades, using expensive financial advisors, or relying on subjective "gut-feelings".
So what exactly is our simple strategy? Well as you know each night in Paris just after markets close in New York, we publish a forecast over the next four days for the CAC 40 (we also publich a similar forecast for the S&P 500). Each forecast contains two probabilities: one probability for the ceiling, which is above the last closing price; and one probability for the floor, which is below the last closing price. These two probabilities are important because they serve as buy-triggers for our simple strategy as follows.
▪ Go above ceiling: 50%, 60%, or 70%
▪ Stay above floor: 70%
We also have two sell-triggers. If our forecast is correct, then we should be able to sell at the end of four days with a gain. However there is always a chance that our forecast is incorrect. Therefore in those cases in which the price falls below the floor contrary to the forecast, we sell at the floor before the end of four days as outlined below.
▪ Sell if price goes below floor
▪ Otherwise sell at end of four days
The process is straightforward. If the next day's forecast for the CAC 40 satisfies the buy-triggers, we buy shares in a CAC 40 index fund the next day immediately after market-open. Then we track the position over the next four days. If the price ever drops below the floor, then we sell the position. Otherwise we sell the position after four days. We repeat this process every time there is a buy-trigger.
Seems simple enough, right? So how did we perform in back-testing against a traditional buy-and-wait strategy for the CAC 40 over the past twenty-five years since 1990?
CAC 40 Results
In the following chart we list our annual returns* and variances** without dividends as well as the returns and variances from a buy-and-wait strategy without dividends for the CAC 40 (see our previous blog entry). The timespan is 1990-2015.
Now let us focus on the results from individual decades as shown in the table below. Note that the identical returns from 1990-1999 and 2010-2015 for our simple strategy (labeled STATS4TRADE) are coincidental and only due to rounding.
Now consider the following decade from 2000-2009, which witnessed two large declines at the beginning and towards the end during the global financial crisis in 2008. During this decade we yield almost 6% more return than the buy-and-wait strategy: 1.7% compared to -4.2%. Again our variance is about 8% less.
Last consider the period from 2010-2015, during which the trend from the previous decade continues. We achieve a 12.8% return versus 2.7% for the build-and-wait strategy. As during the previous two decades we still have less variance but the difference this time is less at about 3%.
What About Trading Fees?
Until recently small investors have not been able to avoid trading fees. However just like in other service sectors such as transportation (Uber and Lyft come to mind), new companies are beginning to disrupt and challenge the traditional fee structures in financial services. One good example is Robinhood, a California-based discount-broker, which charges no fees to trade in the United States.
According to its website, Robinhood is presently expanding into Australia and China. Therefore it is in the realm of possibilities that a European version of Robinhood will be launched soon. Or perhaps DEZIRO will actually launch? If so then one could avoid trading fees for the CAC 40 as well.
Unfortunately however trading fees are still a fact of life today in France and the rest of Europe. Therefore we must now show you the drastic effect that trading fees have on our returns. In this case we have assumed a 0.2% fee each time we trade (0.2% subtracted from each individual return). See the following chart.
Like before let us look at the results with fees from individual decades as shown in the table below.
Second during the decade from 2000-2009 we now yield -4.1% instead of 1.7% without fees and the unchanged -4.2% for the buy-and-wait strategy. However we still have about 8.5% less variance.
And last from 2010-2015 we now only achieve 6.5% return instead of 12.8% without fees and versus the unchanged 2.7% for the buy-and-wait strategy. The difference in variance is unchanged at about 2.5%.
Wrapping It All Up
As you have just seen, even a simple data-based approach for making trading decisions can yield decent, stable returns compared to a traditional buy-and-wait strategy. However the simple strategy outlined in this post is certainly not without its limitations – namely trading fees, which essentially strip away any excess returns versus a buy-and-wait strategy. Nonetheless the message is clear. A data-based approach works. Moreover with the advent fee-free trading portals like Robinhood, trading fees will decrease even in Europe. It is just a question of time. Therefore data-driven approaches like ours will become increasingly attractive to small investors across the world as companies like Robinhood proliferate.
At this point we must emphasize a point that we made in an earlier post. Namely please do not trade with our public data using any strategy including the simple example outlined in this post. We have not yet clearly outlined all the limitations associated with our data (trading fees are just one example). These limitations embody significant risk especially over the short-term. We are working now to reduce these risks with improved approaches, which we outline in coming posts. However if you insist on trading with our data then we must be clear: you assume full responsibility for any outcomes. Therefore please just wait for now!
Presently we are back-testing improved strategies with other types of statistical data and forecasts longer than four days. We are certain that these efforts not only yield better results over shorter timespans but are also more useful for the small investor. We plan to publish these approaches and their results in upcoming blog posts.
However our next blog post is not about improved strategies or even finance. Instead we take a step back and show you process of generating our stastical data as well as historical success rates from our back-testing. Statistical data underpin all of our processes; hence an understanding of these data – including limitations – is essential for understanding our overall approach.
As always if you have any questions, please do not hesitate to contact us anytime. Just fill out the comment form next to this text with your name, email address and question. Please do not be shy – we sincerely look forward to hearing from you!
**Variance is calculated using the standard method. More specifically we caclulate the arithmetic mean of the individual returns within a year, sum the square of the difference of each return with the mean, and normalize the sum by dividing by the number of returns.