The financial industry classifies assets according to their risk profile and, for the sake of comparison, adjusts the actual performance of the risk taken. Measuring risk, be it ex-ante or ex-post, is a highly complex matter. Most of the time, it is done by using volatility as a risk indicator (second-order moment of the normal return distribution). In other words, an asset that "moves a lot" is considered riskier than one that "moves little”, irrespective of performance.

In the real world – or in the eyes of any person blessed with a modicum of common sense – true risk is the risk of loss. How much did I pay for it? What is the current price? How much am I up? How much am I down? In short, the risk reflects, ultimately, the performance of the asset over a given period of time.

Case in hand: YoY volatility of the daily returns, for 2015-2017, of: the S&P 500, Italian bonds and Indian bonds:


According to this measure, the S&P 500 is a risky investment, riskier than Italian or Indian bonds, whose return volatility is quite similar over the period. At the end of 2017, the prudent investor might have said: I prefer to invest in Italian bonds as they are less risky than US bonds and emerging market bonds like India. Another investor might have preferred Indian bonds whereas a risk-taker investor might have gone for the S&P 500.

As at the end of September 2018, these 3 investors’ portfolio performance would have delivered as follows:

Italian bonds: -4.5% | Indian bonds: -0.3% | S&P 500: +10.6%

Imagine their reactions:

  • I’m happy: I’ve posted a 10% gain.
  • I, on the other hand, am 4.5% down.
  • Yes, but …  you took less risk.
  • What d’you mean by "risk?? All I know is that I’m down and you’re quids in.
  • Yeah, but, I could have lost big time!
  • Ok, but you won, a lot, and I still ended up losing.

The risk of loss is above all a question of market timing. It is the risk involved in buying an asset at a given moment and selling it at a loss at another. The volatility, in a way, comes from the probability of being the victim of poor market timing. The higher the volatility, the higher the risk of buying at the wrong time (or, indeed, of selling at the wrong time). From this, we may deduce that an asset’s risk is inextricably linked to the holding period, rather than to its ability to move in the short term. However, this idea is not widespread within the financial industry as the time horizon is very tight, with performances assessed in the space of a few months.

This study, rather than dwell on the right way of measuring an asset’s risk, seeks rather to understand whether the performance of the US equity index has been exceptional over this particular cycle (which started in 2009). Because, these past few years, it has – Fact! – been difficult, for long only investors, to lose money with the S&P 500, we’ve been wondering about how risky this index actually is. What are its main features? How risky is the purchase of a basket of US securities such as the S&P 500 or the MSCI USA?


We are currently checking the MSCI indices from 1969-2018 (up until the end of September), taking a sample of developed countries with highly diverse economic cycles over the past 50 years: Japan, Sweden, the UK, Switzerland, Australia, Belgium and Spain.

The chart above shows that, since 1969, the performance of the S&P 500 compared to its volatility has been one of the best, but not strong enough to call it an anomaly. It has been outperformed by one country (Sweden), with two others (Switzerland and Belgium) not far behind.

Fact (2): economic performance does NOT explain the long-term performance. We know that, for the period at hand, the Australian economy was one of the better-performing, with Switzerland one of the worst. Nonetheless, the MSCI Switzerland index has a better Ri/Vol ratio than the MSCI Australia.

N.B. This Ri/Vol ratio can be understood as the risk-aversion coefficient found in the utility functions of asset selection models. The fragility of the concept lies, nonetheless, in its varying from one country to another and in its not being correlated to economic fundamentals …

The question now is: is the cycle the US index began in 2009 unique or not? Could there be a ”before” and an “after” 2009?

Having split accordingly the period into two sub-periods, we again present the results below. The message is crystal clear: 2009 does indeed look like a turning point, with a pre- and a post- period. Post-2009, the indices’ Ri/Vol ratios widen significantly from their pre-2009 average.

With respect to the US index, the data are eye-catching, showing that the MSCI USA is the only index whose ratio improved. Other countries’ ratios dropped, with some even collapsing (as was the case with Spain) while the MSCI USA reached a ratio of 1.0 – the highest of the levels recorded for our pre-2009 sample.

At this point, we may conclude, as previously, that this performance of the US index is, albeit quite impressive, not unique. Although it is exceptional post-2009, this type of performance had already been delivered by Sweden. We are continuing our analysis by studying the distribution of these annual returns to calculate the skewness and the kurtosis – both measures of dispersion enabling an understanding of how the average and the volatility are calculated. More specifically, it lets us differentiate the median and the average, as well as the influence of the extreme values. In theory, both measures have zero values, as it is assumed that the financial asset returns are normally distributed. Nonetheless, practical knowledge of the financial markets tells us that this distribution is abnormal and that equity prices are more reactive on the downside than on the upside.

The result is actually very unsettling, and one that flies in the face of financial theory. Since 2009, the distribution of the MSCI USA’s annual returns has been unique. Beyond the particularly high Ri/Vol ratio, these indicators tell us that returns have been anchored – with a small dispersion - around a very positive median performance. 

The diametric opposite would be Spain, where index returns have varied widely, from very positive to very negative but where they have been, on average, low. We may therefore conclude that the US index has posted positive returns firmly embedded in a substantially positive value (+10.1% on average) while the Spanish index has delivered highly volatile returns around a value near 0 (+0.9% to be more precise). 

The investment risk attached to these two indices has, therefore, differed greatly.

A more intuitive way of grasping this feature is to just count the positive months versus the negative months since 1969 (cf. Table below).

Number of Positive and Negative Months – MSCI Indices


This is an equally incredible result. Since 2009, there have been 4.8 times more positive months than negative months in the United States. This cycle is therefore quite unique for the US index, not from a risk/return or from a pure return point of view, but from a “risk of loss” standpoint. The distortion of the distribution of returns was striking, and quite clearly buyer-friendly.

So why is this topic on the agenda today? The answer is: simply to put into perspective the recent equity sell-off, which should make October a negative month for most indices. Many investors see this as an exaggerated move, out of kilter with fundamentals.

In our opinion, this conveys an inability to accurately appraise the current cycle. The US index, the benchmark for the world’s equity markets, has been almost unrecognisable over the last decade. There are good (more or less) reasons (micro or macro) for this but from a statistical point of view (distribution of returns), it’s an anomaly. In 2009, the ex-ante probability of having only 17% of negative months in the following 10 years was extremely low.

If we believe in cycles, in probabilities, that equity indices are risky, that sunshine follows rain, then this exceptional behaviour will always come at a price. We don’t have any other details and don’t even know if we’re going to be billed this year, next year or thereafter, but, when dealing with the financial markets, equities, it must be remembered, can rise or fall irrespective of “fundamentals” and we must be wary of the  illusion of control (“Nothing strange about me winning as I’m a good stock-picker; something unusual about me losing, it’s disconnected from fundamentals.”).

The recent index correction is rather reassuring as, by and large, it is consistent with intrinsic equity risk. The risk premium is a random form of compensation that offsets the extra risk. It should not be taken for granted and, for it to exist, risks must – occasionally or regularly – arise.

The comments and opinions expressed in this article are those of the authors and not necessarily those of Candriam.