• Martyn Wild

Who wants to be normal, anyway?

Updated: Jul 25, 2021

By Martyn Wild.


It's getting on for 70 years since the arrival of the portfolio theory approach that most asset allocators still use to build client portfolios. Mean-variance optimisation (MVO), otherwise described as 'finding portfolios that have the lowest risk for a given return', is as much a part of the investment furniture as are mutual funds and active management. The problem is that the way its applied is getting a little stale...


In the recent(ish) past, professional investment advisers began using probability analysis to supplement MVO. This was a meaningful evolution because it provided for much richer analysis than using MVO alone; knowing that an outcome may occur is vaguely useful but being able to estimate how likely an outcome is to occur is invaluable.


For simplicity, many (if not most) analysts tend to assume that market returns are 'normally distributed' (remember that bell-curve we studied at school?), when they are not. This is a big problem because, among other flaws, it tends to grossly under-estimate the likelihood of bad events (like the GFC) and can therefore undermine the entire portfolio construction process. Oops!


In the chart below, we show the performance of US equities (represented by the S&P 500 with dividends re-invested) when held for periods of 10 years at a time (source: Thomson Reuters/MARQAM). We show these historical returns in grey bars, ordered into bins from lowest to highest return. We then describe this data with two continuous curves.


The first curve (in orange) is a Gaussian or 'normal' distribution used by most in the investment community to facilitate probability analysis (Chart One). Note that it really only has a passing resemblance to the returns it is trying to describe.


Chart One


The thing is, while its been useful to apply a normal distribution in the past, mathematics has evolved quite a bit. This has come in the form of a more sophisticated methodology for estimating the likelihood of outcomes. For the technically minded, we refer to this as 'non-parametric' analysis.


Chart Two

The second curve (in blue) is a non-parametric distribution (Chart Two). Notice how much better it describes the pattern of historical returns? It is precisely because it is a better descriptor of reality that we are able to use it to more accurately estimate the likelihood of any outcome. In layman's terms, the portfolios that are ultimately built from this analysis are more likely to be robust and 'all-weather' relative to their cousins that are based upon a normal distribution.


Chart Three

In the chart above (Chart Three), we compare the normal (Consensus Distribution) to the non-parametric (Realistic Distribution), directly. As illustrated by the shaded areas, we believe that the latter is a more intuitive and realistic expression of reality.

So, if non-parametric analysis is superior to using a normal distribution, why don’t advisers and portfolio managers use it more extensively? Three obvious reasons that we can see:

  1. It is mathematically more complex to derive than a normal distribution*

  2. Is computationally very challenging to apply to a portfolio construction context – you need very specialised software

  3. It can be very hard to explain to clients!

Nevertheless, we believe that just because something is hard to do, doesn't mean it should be overlooked. After all, the wealth of our clients is at stake.


For more information or to talk to a member of the MARQAM team, please click here.



MARQAM is a privately-owned, boutique consulting company focused on providing superior investment outcomes for clients and greater profitability for businesses. We are not affiliated with any other financial institution


Disclaimer: The information provided here is for interest purposes only and does not constitute investment advice or a recommendation of any kind.


*For a basic explanation of the process of estimating a non-parametric distribution, click here. Note that this link does not describe the specific methodology applied by MARQAM, which is proprietary.

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