Cursed By Randomness – Cantab Capital PartnersDR EWAN KIRK – see original article and formatting here.

For all investors there has always been a strong desire to “pick winners” or beat the market. In the presence of randomness this can be extremely challenging.

Investors are driven, whether they be high net worth individuals or institutional pension funds, to focus a great deal on the trades, positions or underlying investment thesis of a potential investment. Quite naturally, this results in analysis of the past performance of a manager or similar trades in the hope that this will dimly illuminate the uncertain future.

Given our focus on systematic and statistical analysis, we would be the last people to be dismissive of analysis of historical data. After all, it is our “thing”. However, the tools of historical analysis are frequently used by market participants without a clear understanding of the limitations of the data set. And sometimes it is those who think they are the most sophisticated and clever statisticians who are prone to these errors – perhaps more so than investors who take a strong dose of common sense with their porridge in the morning.

The limitations of data and analysis rear their heads in a variety of situations. Investors want to answer questions such as:

  • Will investment A perform better than investment B? The “Is the investment a winner?” question.
  • What effects will investing in A have on my portfolio? The “Have I already got this investment?” question.
  • Will investment A make money in the future? The “Am I going to look like a hero?” question.
  • Will investment A lose money? The “Am I going to look like an idiot?” question.

…and so on. An investor’s life is full of difficult questions and, given there is so much data around, it is natural to seek answers to these through statistical analysis.

All of the questions above (and many others that are asked by managers, investors and the media) boil down to one question: “What is going to happen in the future?”. It is a clichéd old chestnut but Niels Bohr was right: “prediction is very difficult, especially about the future”.

Furthermore, few of the questions that investors seek to answer have simple binary answers. The answers that managers give need to be (and should be) hedged with phrases such as “on balance…”, “it is likely that…” or “over the long term…”.

Outside finance, this is not unusual in the real world. Smoking cigarettes has a relatively low probability of causing lung cancer (about 1 in 5) but a very high certainty that the life time risk increases if you smoke (from 1 in 100 to 1 in 5). The LHC spent two years collecting data to be 99.99997% certain that the Higgs Boson exists. But there is still a small chance it doesn’t exist. There are some things which truly are binary: “Can I beat Sir Bradley Wiggins in a bike race?”(1) but in reality many of the answers to difficult real world questions are really statements about relative probabilities.

It’s therefore surprising(2) that, despite randomness, uncertainty and error bars in finance being larger than in almost any other field of human endeavour, there are such high expectations of generating insight from superficial analysis. There is a widespread belief that a transparent window into the future is opened through statistically suspect analysis of the performance of existing investments.

I’m sure we will return to this theme in future pieces but at the moment we’re going to discuss one particular sub-issue: the desire investors have to deeply understand the constituents of their managers’ portfolios. Investors want to have position-level transparency to aid this understanding. Occasionally this can be a source of friction between managers and investors. In some very specific cases (distressed debt or other illiquid investments, or some forms of activist investing) telling your investors what your positions are could be an issue, but in most cases, investors will be given information about positions and trades and they want to know more about what happened to these positions. This is entirely justified – it is, after all, their money.

But how much can an investor (or indeed the manager themselves) glean from this information about positions, trades and what they have done in the past? Sadly, the answer is “not much”.

Those of you who have met me probably realise that I have a penchant for “toy models”. The financial world is a hugely complex place with an uncountable number of factors which could affect the solution to a problem or the answer to a question. Simplified models can often allow us to gain insight into a complex process.

This is not unlike the situation facing physicists. The real world is complex. Newton wouldn’t have made much progress attempting to explain gravity by trying to model the motions of every single molecule inside the apple, the effect of air resistance on the falling apple, the Coriolis effect from the Earth’s rotation and the minute general relativistic effects where time appears to slow for the apple as it drops into the Earth’s gravitational well.(3) No, Newton considered two idealised point masses and came up with this equation


Newton’s toy model was so good that it was 229 years before Einstein published a better one.

I’m always keen to come up with simple toy models which explain (or rather “illuminate”) a problem so let’s look at the problem of understanding the returns of managers by analysing the returns of their individual assets.

Let’s imagine that we have a set of assets. In the case of a managed futures or CTA style strategy, this could range from say 70 to 250 futures contracts and foreign exchange forwards. For a systematic equities stat arb fund, it could be many thousands of individual stocks. But in our case, we are going to assume that our simple manager has 100 assets, because it’s a nice round number and it makes arithmetic easy.

Let’s also assume our manager truly has a Sharpe ratio of 1.0 after fees. Whilst there are managers who have consistently outperformed this, it’s fair to assume that this is a reasonable ex-ante expectation. Despite the well-known (and often overblown!) concerns regarding using Sharpe ratio as a measure, it is going to work fairly well for this simple example. As we all know, volatility is something you

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