‘Be water my friend.’ Elegant, insightful, evocative, and one of the best-known quotes of perhaps the greatest martial artist of all time, Bruce Lee. But is it an appropriate start for a research piece examining the historical relationship between performance and volatility over the last 30 years? I think so, and by the end of this piece you’ll see why. As an investor you will have to deal, or had better make your peace, with volatility. It’s ever present, mostly in a dormant (even docile) state, just waiting to unleash its ferocity – forcing its consequences on the discerning investor when least expected. Lee’s advice is about adopting flexibility, and it might just help you navigate markets while using the predictive power of volatility as a helping hand rather than a foe to inevitably fight.
The Question
With stats, you must know the right questions to obtain meaningful answers. If you get the answer ‘42’, you had better already know the question. Like every good finance teacher, I ferociously preach to my students that volatility eats performance. Fine. But how does volatility do that? Are there any pointers, mechanics or divine insights that reveal when it might be prudent to invest, divest or crack open a Cherry Diet Coke and do nothing? I do not know. The question of ‘how’ volatility hits is probably answerable via analysis of market participants’ motivations and their deepest and darkest desires/fears. So, clearly, it falls within in the field of behavioural finance. But let’s not open that can of worms. The question I can ask, and answer, is the following: what happened when volatility did hit the market?
The Methodology
We’re going to analyse the relationship between the performance of the S&P 500 and the implied volatility of the S&P 500 represented through the VIX Index over a period of 30 years. As the S&P 500 represents the biggest equity market in the world, it appears to be a good proxy for average equity returns. The VIX Index will be the proxy for ‘expected market volatility’, thereby measuring the expectations of option traders about the future volatility of the S&P based on the pricing for ‘at the money’ options with a maturity of (roughly) one month.
The correlation between the VIX closing levels and the realized volatility of the S&P 500 amounts to 88%. This correlation is reduced when the VIX Index, as it is so often described as predictor of future realized volatility in the S&P 500, is shifted one month into the future to 73%. This means there is a good chance that the VIX is not just displaying anticipated moves in the S&P randomly and is therefore a good enough indicator to run some awesome spreadsheets and explore the question of what happened. Why 30 years? The appropriate answer would be ‘quality of data’; the honest one is that this is pretty much the time I started my life in the industry as a market maker, and I was always interested in reconciling my subjective impressions with some statistical voodoo.
Having 30 years of data available will predictably let you start with a year-on-year analysis, only to realize that (even though satisfying) 29 full one-year periods to compare will fail to yield the full picture. Instead, I opted to create roughly 7,500 rolling ‘year-on-year’ periods covering the whole 30 years to facilitate for the uncertainties of life – namely that an investor could have pretty much picked any of those 252-day investment horizons at random, and we want to exclude ‘smart’ or ‘dumb’. Shorter or longer periods are of course subject to further investigation; but as a starting point, rolling annual portfolios (here the S&P 500) will yield a general understanding of what happened when volatility hits performance. All these performance sets correspond to an individual set of volatility represented through the VIX Index and can therefore be matched.
As a starting point for my investigation, I revisited my own very subjective gut feeling. Which levels of volatility from an investor’s point of view might they consider good, mediocre or just plain evil? Traders and speculators might attribute different adjectives to these levels, but the information contained within this observation in relation to the returns of the S&P are unambiguous. The long-term average for the VIX Index, calculated on closing levels, computes to 19, confirming my cognitive bias that things get dicey above this level. We might consider the next 10 VIX points, bringing you up to 30, as symbolizing a feeling of heightened alert on the side of investors. If you are still playing the long side above a VIX of 30, you a) have failed to check the data, b) are below 20 years of age, or c) have an account at Robinhood.com (possibly all of the above). For the purpose of this study, I have therefore focused on volatility brackets of 0 to 20, 20 to 30, and 30 and above.
The Results
A simple buy and hold strategy in a random 252-day S&P portfolio, would deliver an average return of 7.4% with a positive to negative return ratio of 80:20 (80% of 252-day periods would be have positive returns, and 20% would have negative ones). Now we can determine the contribution to these returns during different VIX regimes. Let’s start with the bad news for investors and work our way toward investment Nirvana.
Were an investor to have invested over a random 252-day period, but only when volatility was above 30 (as indicated by VIX) then the performance contribution would be -6% with only 5% of the periods delivering positive returns and 95% delivering negative returns (Charts 1 and 2).
In periods when the VIX was trading between 20 and 30 points, the average performance contribution was -2.6%, with only 27% of period delivering positive returns and 73% delivering negative returns.
So, where did all the performance we have seen over the last 30 years generate? You guessed it. Below a VIX level of 20, the performance of all rolling 252-day portfolios generated an average return of 16%. If you had chosen to be only invested on those days with volatility below 20, while neutralizing your S&P 500 investment during ‘those difficult days’ of heightened volatility, on average 98% of the performance contributed by following this strategy was positive. In only 2% of all observations could negative returns be observed.
Chart 1
Chart 2
To complete this rather crude approach, let’s now compare the portfolios an investor might want to hold.
Portfolio 1, the classic buy and hold over a 252-day period averages a performance of 7.4%. Had one bought the S&P at the worst of times this would have delivered a return of -67%, bought at the best of times 52% – all maintenance free (Chart 3).
Portfolio 2, the riskier version when the portfolio goes neutral above VIX levels of 30. This yielded on average 13%. The worst of all portfolios you could have bought set you back -23%, and the best buy option would have yielded 43%.
Portfolio 3, only holding the S&P when the VIX is below delivers average returns of 16%, more than twice the return of a buy and hold strategy and over 2% more than the slightly riskier version 2. However, the real beauty in the eye of the beholder of boring, low-volatility investing has to focus on the worst portfolio you could have bought. The worst return out of 7,500 portfolios that did not hold investments above VIX levels of 20 realized a negative return of just -2.6% and might have realized you a whopping 58.4% in a best-case scenario. The downside might be positive periods in the S&P 500 with heightened volatility when this strategy would not be invested at all and your investors ask what you did with all their money. ‘Protect it’ is a very good answer.
Chart 3
As a final point of interest, I was wondering how an investor would perform if he or she always bought a portfolio that ended up trading lower after 252 days. We know that happened in 20% of all observed periods (Charts 4 and 5). As you might guess, the maximum drawdown is still at -2.6% as this is just a subset of all the observations that we made earlier. However, even in these pesky little 20% bear market portfolios, the investor would be profitable 96% of the time with an average return of 8.4% and a potential top-line return of 33.8% if only invested at VIX levels below 20.
Chart 4
Chart 5
For everyone who is now turning around shouting at their quants demanding to know why you didn’t play those odds earlier, let’s pour some water in your wine. Observing the facts of life is one thing, transferring them into actionable strategies quite another. For one, you would need to know in advance when volatility will spike above your chosen and acceptable volatility levels and neutralize your portfolio before that happens. Not easy. Those little differences between trading closing vs. opening price will eat away a substantial bit of the ideal returns.
Another questionable point is the volatility reference you chose. Is it the VIX in absolute terms as I did for the purpose of this brief, or is it something else? Will these levels still be relevant into the future? Should you use a percentile ranking, a weighted high-low ranking system or employ a sophisticated Kelly-Criterion money management algorithm? What impact will result from these uncertainties? Are the last 30 years a good indication for future developments? Maybe you want to feed a long-term bear market, let’s say Japanese style, into your models; and, of course, you always wonder what the Fed will do.
What stands, however, is the clear historic relationship between performance and volatility. And, now we even have the numbers to make a case. Everything else is in the hands of the ‘Thinking Investor’, for whose benefit I now finish by quoting Bruce Lee in full:
“Empty your mind, be formless, shapeless — like water. Now you put water in a cup, it becomes the cup; you put water into a bottle it becomes the bottle; you put it in a teapot it becomes the teapot. Now water can flow, or it can crash. Be water, my friend.”
Bruce Lee, Philosopher & Martial Artist
Thorsten Roland Wegener spent twenty years trading equity derivatives and was a partner at Bear Stearns. Currently, he teaches as well as cooking, driving, and cleaning lots.
(The commentary contained in the above article does not constitute an offer or a solicitation, or a recommendation to implement or liquidate an investment or to carry out any other transaction. It should not be used as a basis for any investment decision or other decision. Any investment decision should be based on appropriate professional advice specific to your needs.)