Risk Update: August 2019 – Compounding through Convexity.

With ever greater extremes in global monetary policy, what some might call currency debasement wars, and the resulting unprecedented historical lows in interest rates the world over, it is tempting to write a piece on the structural damage that is being done to society: the pulling at the thread of socio-political stability as wealth segregation reaches breaking points in country after country. Instead, however, we will go back to our bread and butter, and pull together some of our past work on portfolio strategy and expound further the ever-increasing benefits of strong risk mitigation, and the ongoing supremacy of “barbell” strategies.

This could be a longer update than normal, but a lot of it is pictures from previous notes, in order to set the stage.

The simple question is, what solutions are available to savers, that almost universally function within a standardized “balanced portfolio” world, when interest rates get near/to/through zero? How much of one’s long-term retirement savings should be held in securities with little to no yield, and increasingly questionable risk mitigating dynamics? The key to answering these questions, as is so often the case, comes down to one’s perception of time and basic mathematics. If your time horizon is longer than shorter, and your objectives are terminal geometric compounded values, not short-term arithmetic returns, then the answer is quite clear: optimize performance in the wings, don’t target the mean.

To refresh from past notes, the below is a wonderful bit of work from our friends at Deutsche Bank. The boxes represent the contribution to long-term compounded returns over 30+ years by the percentiles of monthly returns. The point we like to focus on is the Equity bar, which simply put tells us that only 40% of the total compounded returns are contributed by the 90th percentile of monthly returns. That leaves 20% contribution to the 5th percentile of upside returns, and a whopping 40% contribution (negative!) from the 5th percentile of downside returns. A manager targeting the mean, at the expense of the wings, is destroying long term compounding.

Figure 1: Contribution to Compounded Returns
Source: Deutsche Bank

In our May 2019 monthly letter we showed in greater details the implications of this distribution in our version of a fantastic presentation given by our friends at the University of Chicago. In that letter we created a hypothetical portfolio return that is concave relative to a simple 60% beta benchmark. The below chart shows what is far too common an outcome amongst asset managers. We discussed what sort of behaviour leads to these types of outcomes, e.g. bounded upside correlated exposures (carry, short vol, etc), performance linked fees/pay on correlated risks, flawed risk measurement practices allowing leverage on things that portray low vol/low correlation in the mean of distributions.

Figure 2: Hypothetical Concave Portfolio vs 60% Beta Benchmark
Source: Convex Strategies, Bloomberg

As we discussed, however, many fiduciary investment managers seemingly operate very much with the wrong incentive/objective. The industry has standardized along the lines of annual performance benchmarks, with naturally asymmetric incentives linked to the upside only. They are able to mask the long-term wealth destruction relative to compounded returns through the practice of reporting returns on an annualized arithmetic basis, ie start over at zero every year!

In the below breakdown of our hypothetical returns, the manager of our hypothetical portfolio might tell the end capital owner that in 2004 they did a great job, earning an annual return of 5.53% versus their benchmark target of 5.39% (they perform relatively well near the mean of the market distribution). In 1995, the fiduciary could boast about his exemplary efforts of achieving returns of 13.56%, well above long term average annual returns. However, they would likely fail to mention, much less explain, why they fell so far short of the benchmark return of 20.47% in that year. Then of course in 2008, after a crushing -34.75% return, the fiduciary could assure the end capital owner of his prudence in avoiding the total pain of the market’s -39.49% drawdown. What happened to the 0.6 beta? All the while, compounding is destroyed and the manager’s incentive restarts at zero the next year.

Figure 3: Hypothetical vs Targeted Annual/Arithmetic Return
Source: Convex Strategies, Bloomberg

The truth of the matter is truly laid bare when the hypothetical performance is geometrically compounded. The results are little less than stunning. We like to refer to Figure 4 as the “Where is my money?” slide. The realized returns, over the life of the theoretical portfolio data, generates an annual average return of 2.79%, but a CAGR of just 2.24%. The targeted beta benchmark has an average annual return of 5.02% and a CAGR of 4.62%. Using the basic Rule of 72, the actual return series indicates that the value of the portfolio will double every 32.14 years, versus the target benchmark which would have doubled every 15.58 years. Thus, over the 46 years of performance, the realized returns have grown $100 to $277, while the benchmark would have achieved $800. Hence, were this to be a real example, we think the end investor might reasonably ask “Where is my money?”

Figure 4: Hypothetical vs Targeted Compounded/Geometric Return
Source: Convex Strategies, Bloomberg

That’s the background. The solution, for the last 30 or so years, has been driven by such stalwart academic work as Modern Portfolio Theory (MPT) and Capital Asset Pricing Model (CAPM), leading to what we broadly refer to as the overwhelming market standard of the Balanced Portfolio. The simple, and wonderfully successful, premise is a portfolio balanced between weightings in Growth/Equities and Defensives/Fixed Income. Fixed Income has proven to be the perfect complement to an equity portfolio (at least since Alan Greenspan innovated the Central Bank reaction function of slashing interest rates when asset prices fell). It provided running yield in the 90th percentile of markets, helping asset managers perform well in the mean of the distribution, and negatively correlated to equities in the tails, creating improved portfolio risk dynamics. It truly has been a gift to a generation of savers. This brings us back to where we started this note. What happens to this “gift” when interest rates get to zero? What to do when there is no running yield in quiet markets, increasingly uncertain negative correlation in equity sell-offs, reduced scale of the potential capital gains to offset equity losses and a whole bunch of unprecedented risk in the event of some future normalization of interest rate levels?

Figure 5: US 30y Treasury Yield
Source: Bloomberg

As all regular readers will know, our proposed solution is what we like to call the Barbell Portfolio. Replace ineffective defensive strategies with explicit hedging strategies, e.g. Long Vol, and take more risk. Of course we hear, over and over, how the cost of owning vol has been a killer, while owning bonds has performed wonderfully, particularly 2019 YTD. Interestingly, just randomly pegging as proxies, the CBOE EurekaHedge Long Volatility Index and the Barclays US Treasury Total Return Index, have almost identical total performance since May 2005, though with quite different paths.

Figure 6: CBOE EurekaHedge Long Vol Index vs Barclays Treasury Total Return from 2005
Source: Bloomberg

In a nutshell, the Long Vol index performed more strongly during the market dislocations of 2008 through to early 2012, but the cost of owning volatility, along with the continued declines in interest rates, have the two indices back to the same levels as of today.

Let’s give the Long Vol leg of the Barbell the maximum disadvantage and start our comparisons at the peak of its performance in May 2012, so emphasising the period where Fixed Income most outperformed Long Vol.

Figure 7: CBOE EurekaHedge Long Vol Index vs Barclays US Treasury Return from 2012
Source: Bloomberg

So now we can use these, along with SPXT (SPX total return), to compare Balanced Portfolios with Barbell Portfolios, where we replace the entire Fixed Income allocation with 50/50 weightings of SPXT and CBOE EurekaHedge Long Vol over a period when, supposedly, owning volatility has been excessively expensive.

Let’s compare to good old traditional low/medium/high growth Balanced Portfolios.

Figure 8: Low Growth Balanced Portfolio: SPXT 30% / US Treasury 70%
Source: Convex Strategies, Bloomberg
Figure 9: Medium Growth Balanced Portfolio: SPXT 50% / US Treasury 50%
Source: Convex Strategies, Bloomberg
Figure 10: High Growth Balanced Portfolio: SPXT 70% / US Treasury 30%
Source: Convex Strategies, Bloomberg

Then, using our simple premise of replacing fixed income with a 50/50 basket of Long Vol/Long Equities we can generate these comparisons (with net new % allocations to equities and hedge).

Figure 11: Low Growth Barbell: SPXT 65% / CBOE Long Vol Index 35%
Source: Convex Strategies, Bloomberg
Figure 12: Medium Barbell: SPXT 75% / CBOE Long Vol Index 25%
Source: Convex Strategies, Bloomberg
Figure 13: High Growth Barbell: SPXT 85% / CBOE Long Vol Index 15%
Source: Convex Strategies, Bloomberg

So, there you have it. If you believe in the protection of your chosen Long Vol strategy, thus allowing you to carry more risk, one could certainly argue that it has come with no cost whatsoever! Remember, we have done this over the period with the greatest outperformance of Fixed Income relative to Long Vol we could find. Starting our analysis any earlier only makes the numbers for the Barbell Portfolios look even better. To recap:

Of course, we don’t know precisely what or how much protection resides within the Long Vol Index at any given point in time, but past performance would seem to indicate that it is more than what was provided by Fixed Income, and that is back when Fixed Income still had some room for interest rates to fall! If anybody wants to argue about the implications of the traditional portfolio risk measures, Sharpe / Sortino or Portfolio Vol etc, feel free to get in touch and we can chat about things that measure performance at the mean during historically low vol environments and how they tend to fare in market dislocations, as well as just generally perform in the wings. If a ‘Barbell’ approach was a good idea in May 2012, and obviously a massively good idea in May 2005, we believe it is an even better idea today. Of course, when it comes to correcting the compounding and convexity of your portfolio, the best time to address this was yesterday. Next best is today….and so on.

Read our Disclaimer by clicking here