# A Closer Look at the Relationship Between Return and Volatility

Updated: May 18, 2022

It is generally agreed and understood that to enjoy higher returns over the longer term one must accept higher levels of volatility in the shorter term. One of the most interesting features of the last ten years has been the breakdown in this relationship.

"Neither FX exposure nor commodities are likely over the long term to produce high volatility adjusted returns"

The below scatter chart shows the relationship between volatility (x-axis) and return (y-axis) for a range of asset classes for two periods: the last year (CY2016) and the last ten years (2006 to 2016). It also shows the best fit line for both periods, together with the correlation statistics (R-squared) for each. Please note that each dot refers to a particular asset class. Also that I have not labelled each dot because a) it would clutter the chart and b) the emphasis is on the general relationship rather than the specifics (Table 1 further on presents the detailed underlying numbers for each of the asset classes depicted in the below chart).

There are two key parameters to note for each of the two series (periods): the slope of the best fit line and the correlation. The slope defines the relationship between return and volatility (i.e. whether it is positive or negative) while the correlation statistic defines how well the data fits the relationship.

It is not too surprising that over one year there is neither a positive relationship between return and volatility, nor a high level of correlation (in fact the R-squared of 0.03 says that there is none whatsoever!) However, it is interesting to note that over ten years there is an inverse relationship between return and volatility and that the correlation is quite high. This is completely at odds with the aforementioned generally accepted positive relationship between return and volatility. What is going on?!

The table below shows the return and volatility statistics for the various sub asset classes used in the above chart. They have been sorted by 10 year volatility-adjusted return (proxy for the Sharpe Ratio).

Here are some observations:

There are in total nine bond-related sub-asset classes and they are all in the top 10 by 10 year volatility-adjusted return

Volatility of risky bonds has on the whole been lower than that of safe haven bonds

US high yield has produced some very impressive volatility-adjusted returns over the last ten years

US high yield (<=CCC) had a fantastic 2016, generating a return of 36% with annualised volatility of just 7%

Equity markets generally appear in the lower half of the table, with some markets such as Japan and Europe ex UK producing miserable volatility-adjusted returns

Of all the equity regions, the US’s numbers are the most impressive, but they are still not great – the 6% return over the last 10 years is lower than the 9.5% one has seen over the last 30 years

The bottom of the table is generally occupied by commodities and other “non-traditional” asset classes such as REITs, listed private equity and infrastructure

One important point to note is that neither FX exposure nor commodities are likely over the long term to produce high volatility adjusted returns. FX returns are essentially a zero-sum game – for example, when a Yen-based investor who is holding Sterling wins, a Sterling-based investor holding Yen loses. There is a small net positive utility in holding foreign exchange since a 10% gain for one investor is a 9% loss for the other - the average for the two is thus +0.5%. Once one takes account of the relatively high volatility of FX spot rates, one can understand that volatility-adjusted returns over time will be poor (one can also understand why FX hedging can make so much sense).

As for commodities, there is little reason why over the long term their prices should rise more than the prices of other goods and services. If you own Nickel for example and are not doing anything with it, you are firstly not generating an income and secondly you are paying for storage (not directly but via losses incurred at futures contract rollover). In other words there is little reason why commodities prices should rise in real terms over the long term (this is indeed the case in practice as well as theory). The volatility of commodities prices is even higher than for FX exposure (as can be seen in the above table) and so volatility-adjusted returns over time will tend to be even worse.

What this all means is that there are some sub asset classes which fail in both theory and practice to adhere to the aforementioned positive relationship between return and risk. Notwithstanding this, over the last ten years, weird things have been happening between risky bonds and safe haven bonds and between bonds in general and equities.

My own conclusions from the above observations are fairly simple: over the next ten years, returns from safe haven bonds will be poor, returns from risky bonds will be moderate, and returns from equities will be moderate to good. I might get excited about commodities or FX if they are close to long term lows on an inflation adjusted basis, but this is not generally the case at the moment (Sterling on a real effective basis is now trading close to all-time lows but it is possible nay probable that Brexit will keep it there for the time being). The inflation-adjusted oil price is well below its long term trend but as with Sterling there are structural issues that may keep it there.

In my next letter I will go into more detail with respect to our 2017 macro and market outlook.

*Published in Investment Letter, January 2017*

The views expressed in this communication are those of Peter Elston at the time of writing and are subject to change without notice. They do not constitute investment advice and whilst all reasonable efforts have been used to ensure the accuracy of the information contained in this communication, the reliability, completeness or accuracy of the content cannot be guaranteed. This communication provides information for professional use only and should not be relied upon by retail investors as the sole basis for investment.