Data 101: How To Separate The Signal From The Noise


Scale matters.


Whether it is global vaccine production capacity, the financial system in a small country like Ireland, or your favourite pair of jeans in early January, things need to be the right size for the jobs they were intended to do. When we get the scale of our interventions wrong, we can create a whole new set of problems for ourselves.


Let’s take a look at an example from the financial markets[1].


The equity market returns about 7% a year on average, with a volatility of almost 20%.


To put those numbers in context, imagine the chart of an equity index like the FTSE 100 or the S&P 500. The average return is the slope of the straight line joining the starting value of the index to its current price, and the volatility is the random variation around that upward-trending line. (If the volatility was 0%, the price chart would be a perfectly straight line, with a 7% slope.)


Now consider an asset that returns 15% a year, with a volatility of 10%. This asset produces twice the return of the stock market but with only half the variation, and both the higher sloping trend line and the narrower price range would be clearly visible, were the asset plotted against one of the equity indices mentioned above.


For an asset to produce twice the return of the equity market at half the risk is almost unheard of. Only the very best hedge fund managers (or the occasional Bernie Madoff) could produce these kinds of returns over time. If you were lucky enough to have this asset in your pension pot, you would be very happy when you retired.


Let’s imagine that you had, in fact, invested your pension in that asset, and that every December you received a statement from your pension provider informing you of its performance over the previous year.


Over the course of a 20-year holding period, you would expect 19 of those annual statements to report a positive return (strictly – 93%) and you would be very happy with yourself. Although with such a strong asset in your portfolio, you might be tempted to admire its performance more often, and that is where things start to get interesting.


If you checked the asset’s performance once a quarter, you would see a positive return 77% of the time. So even though 19 of the 20 years had produced positive returns, only 62 of the 80 quarters would be expected to do so. Meanwhile, the ‘bad news’ proportion has more than tripled to 23%.


Does that seem strange that you? It is the same asset, with the same performance, over the same 20-year time period, so why does the performance appear to be deteriorating?


It may seem paradoxical, but there is no error. If we continue the analysis, we will see the pattern repeat itself.


Check the performance monthly, and the positive proportion becomes 67%. Check it daily, and it falls to 54%. Check it several times a day (as many investors do) and the outcome would be little better than a coin toss: half the time up, half the time down, and no evidence of the long-term trend.


You might even come to the conclusion that it was all random, so why bother investing at all?


But it’s not random.


We know that this is the same asset that returns 15% a year with an annual volatility of 10%. We know that its full price chart displays a clear, strong upward trend. We know that if we hold the asset for 20 years, whether we check it hourly or annually, we will capture all of those returns.


The only thing that changes in this example is the frequency at which we monitor its performance – but that is the curious thing! Just as an image will blur the more you magnify it, the data really does become less clear the closer you look.


On longer timeframes the random fluctuations have more opportunity to cancel each other out, so there’s less ‘noise’ and the underlying trend can reveal itself (the ‘wisdom of crowds’ effect works in a similar way). But on shorter timeframes, the volatility dominates the trend, which then fades into the background.


So, what’s the moral of the story – that you should invest for the long-term? That you should only check your pension once a year?


I’m sure it is good advice, but this piece is not about investor habits. It is not about investment at all. This piece is about scale, and how an awareness of scale – in this case, timescales – can help us to make sense of the world.


With that in mind, let me ask you: how often do you check the news?


Once a year, or once an hour?


In the past, we might have read the paper in the morning and watch the news on TV in the evening. Then the internet arrived, so we could check the news at lunch too. Then we put the internet on our mobile phones, so we could check the news on the commute to work, on a cigarette break, while we were standing in a queue, or wherever else we happened to be when the impulse struck.


But given the previous discussion, what do you think these media consumption habits would do for your ability to process all that additional information? Would you be able to identify the long-term trends among all the short-term volatility and noise? Would it help you to understand the world as it truly is, and to make more informed decisions in your life?


Or would they be more likely to leave you feeling confused, frustrated, or possibly even angry, like a trader whose stock picks aren’t going the right way?


I’m not here to scold anyone for their online media habits – mine are no better. The point is that the timeframe over which we observe events can distort our perception of those events, so we should be aware of the implicit ‘scale’ choices we are making every time we check Twitter, read the paper, or watch the news.


The events of the day are merely the latest in a sequence of events which will often trace their origins back centuries, or more. They are the continuation of much longer stories, not independent prose, isolated from history, or from each other – even if that is how they are presented in the daily media.


We can follow these stories for entertainment or distraction, if that is what we want, but it will be very difficult for us to understand their causes and likely consequences without first understanding the timeline of events which led us to the current moment.


Put simply, the long-term trends influence the medium-term trends, which influence the short-term trends, which create the events you see and hear in the daily news. But we can’t see the long-term trends – the true drivers of history – on a short-term timeframe. We need to change the scale of our perspective to match the scale of the undertaking.


The moral of the story, then, is to zoom out. In a data-heavy world, choosing less frequent but higher quality information will help you to separate the signal from the noise.



[1] This example comes from Fooled By Randomness, by Nassim Taleb. The calculations assume a Normal distribution for the asset’s returns.