Risk Update: January 2020 – Convexity is the answer. Compounding is the question.

Our friends from the CME sent us this nice paper recently.


Simply put, it is an analysis on the longer term portfolio benefits of diversifying strategies, in this case looking at replacing a portion of a traditional 60/40 portfolio with a Commodity Trading Advisor (CTA). As you are all aware, we love this type of analysis, so we thought we would see how it would look against our preferred (true) diversifier – Long Vol.

The main chart from the paper compares Funding Ratios of a 60/40 portfolio against the authors hypothetical portfolio where they replace 6% of the Equity (SPXT) allocation and 4% of the Fixed Income (JPMGGLBL) allocation with a 10% allocation to CTA Trend (NEIXCTAT). We aren’t sure why they have used Funding Ratios (they refer to it as a novel methodology) when what they are measuring is only the performance of the numerator, ie. the asset side of the equation, but it does lead to an interesting follow on discussion that we will get to at the end of this section. It does allow them to compare minimum, average and final Funding Ratios, which we suppose has some value, in particular in terms of protecting against extreme minimum Funding Ratios, as a pension has to meet benefit payouts, but presumably the denominator/liability is the same for both portfolios. Still, one assumes, any effective “diversifying” strategy will show its usefulness precisely at the times that minimum ratios are occurring. As always, we care most about Terminal Capital Value, so will just focus on the “Final Funding Ratio”.

Figure 1: 60/40 Portfolio (Balanced) vs 54/36/10 Portfolio with CTA Trend (Trend)
Source: CME Group

As you can see in Figure 1, their Portfolio with Trend appears to have a positive portfolio contribution and terminates with an 11% improvement in the Final Funding Ratio; 78% versus 67%. We’ve taken a stab at replicating their analysis for the 2000-2018 period that they covered. We, inevitably, had to use an adjustment or two to get the end numbers to line up and to simplify things a bit:

  • We used LUATTRUU instead of JPMGGLBL index, giving slightly better performance.
  • We graphed it using annual points as opposed to monthly points.
  • We picked a fixed compounding rate for the presumed liabilities to match the respective start and finish ratios and held it constant through the periods.
  • Per above, to match their numbers. the compounding rate we used to construct the denominator/liability for the Balanced 60/40 portfolio was 7.00% and for the Portfolio with Trend was 6.75%. We think this relates to their assumption of 0.50% manager/CIO outperformance, but aren’t sure. Does raise an obvious concern about their results which essentially go away if we use the same compounding rate for the liabilities.
  • We have done no rebalancing on the Balanced portfolio, but have done yearly rebalancing on the Portfolio with Trend. Again, we aren’t clear on how their methodology handled rebalancing, but this was necessary to force the numbers to match.

The outcome is the below graph which replicates their results pretty well.

Figure 2: Funding Ratio Reconstructed 60/40 Portfolio vs 54/36/10 Portfolio with CTA Trend 2009-2018
Source: Convex Strategies

Of course, we would argue simply showing the compounded returns of the two asset portfolios tells you everything you need to know about the benefit of adding the diversifying strategy. Those results look like the below chart, again not rebalancing the Balanced portfolio and yearly rebalancing the Portfolio with Trend.

Figure 3: Compounded Returns Balanced vs Trend (different rebalancing)
Source: Convex Strategies

If we apply yearly rebalancing on both portfolios, the benefit goes away.

Figure 4: Compounded Returns Balanced vs Trend (similar rebalancing)
Source: Convex Strategies

We are sure it is just due to the data history of the NEIXCTAT starting at 1/1/2000 that led the authors to use that as their start date, so as to have the longest series possible, but it coincidentally is also the best possible start date for the relative performance of the Trend portfolio versus the Balanced portfolio. We will likewise choose our start date based on access to the historical data series, thus starting our comparisons from 2005 when we have data for our chosen “Convex” alternative, the CBOE Eurekahedge Long Volatility Index (EHFI451) an index of Long Volatility managers, and figure we might as well extend things through 2019, since we now have those numbers.

Using our new data series, 2005-2019, and keeping the assumptions that we used to try to match the results from the original paper, we get the below results in Figure 5. Now zero benefit in terms of final Funding Ratio, even with the differing liability compounding and strategy rebalancing assumptions.

Figure 5: Funding Ratio Balanced vs Trend Original Differing Assumption 2005-2019
Source: Convex Strategies
Figure 6: Compounded Return Balanced vs Trend Differing Assumption
Source: Convex Strategies

If we remove those differing assumptions and apply the same compounding and rebalancing, we get the following.

Figure 7: Funding Ratio Balanced vs Trend Equalized Assumptions 2005-2019
Source: Convex Strategies
Figure 8: Compounded Return Balanced vs Trend Yearly Rebalanced 2005-2019
Source: Convex Strategies

So for this time period, using the same compounding rate for liabilities (6.75%), and yearly rebalancing of both portfolios, we now get 5 percentage points outperformance on a final Funding Ratio basis, and 13 percentage points in terminal compounded NAV, of the 60/40 Balanced Portfolio over the 54/36/10 Portfolio with Trend.

So very easily we can show the superiority of our proposed “Convex” portfolio where likewise we put 10% allocation into a diversifier, the Long Vol Index, but given the superior diversifying/hedging aspect we will take all of the 10% weighting away from Fixed Income. That leaves us with a 60/30/10 portfolio of Equity/Fixed Income/Long Vol.

Figure 9: Funding Ratio “Convex” vs Trend Equalized Assumptions 2005-2019
Source: Convex Strategies
Figure 10: Compounded Return “Convex” vs Trend Yearly Rebalanced 2005-2019
Source: Convex Strategies

We see that “Convex” outperforms by 6 percentage points on a final Funding ratio basis, and by 17 percentage points on terminal compounded NAV basis.

Of course that means that this version of “Convex” does outperform, over this period, the Balanced Portfolio, but by just 1 percentage point on the final Funding Ratio basis, and by a mere 4 percentage points on a terminal compounded NAV basis.

Figure 11: Funding Ratio “Convex” vs Balanced 2005-2019
Source: Convex Strategies
Figure 12: Compounded Return “Convex” vs Balanced 2005-2009
Source: Convex Strategies

You have probably guessed where this is going, compounding is driven in the wings! If we can get better compounded performance by replacing Fixed Income with Long Vol, we should do even more and own more of the thing that performs to the upside, ie Equities. Let’s take advantage of the efficiency provided by the asymmetric and negatively correlating strategy, Long Vol, and apply leverage/partial funding to it, say 50% funded, giving us even more hedge dynamic, and shift another 10% out of Fixed Income into Equities. We will call this portfolio “Convex+” and set its weights at 70/20/20 Equity/Fixed Income/Long Vol.

Figure 13: Funding Ratio “Convex+” vs Balanced 2005-2019
Source: Convex Strategies
Figure 14: Compounded Return “Convex+” vs Balanced 2005-2019
Source: Convex Strategies

Now we are getting somewhere! “Convex+”, over this period, outperforms the Balanced Portfolio by 18 percentage points on the hypothetical Funding Ratio basis, and by 50 percentage points on a Terminal NAV basis.

We should probably note at this point the biggest of elephants in the room, namely a big part of the 60/40 performance has been driven by the overall trend and key offsetting correlation of the Fixed Income allocation. For the two time series we have looked at, Fixed Income overall has performed extremely well (though not well enough that you wouldn’t have been better off replacing it with Long Vol and more equities): 2000-2019 +4.51% CAGR and 2005-2019 +3.70% CAGR. We all know what US$ yields have done over those periods (Figure 15). It is increasingly unlikely however that those backward looking returns are going to be matched over the next decade or two when the starting yield today is circa 1.50%. Not to mention the ever-expanding uncertainty of future correlations between bonds and equities.

Figure 15: US Treasury 10yr Yield
Source: Bloomberg

That brings us to the obvious question, 30 years on from the innovation of the Central Bank reaction function to lower yields as an offset to falling asset prices, what happens when there is increasingly little room for rates to go lower? Do we want anything in our portfolio that has such a low expected return, and provides so little portfolio benefit? If we believe Central Banks will continue to do “whatever it takes” to avoid falling asset prices, and that near zero policy rates and forever QE are the way of the future, one might consider replacing the remaining Fixed Income in our “Convex+” portfolio with something that might protect against the continuing destruction of fiat currencies – like say gold. Let’s call that “Convex++” and weight it 70/20/20 Equity/Gold/Long Vol.

Figure 16: Funding Ratio “Convex++” vs Balanced 2005-2019
Source: Convex Strategies
Figure 17: Compounded Return “Convex++” vs Balanced 2005-2019
Source: Convex Strategies

“Convex++” outperforms the Balanced Portfolio by 38 percentage points on the Funding Ratio basis, and by 100 percentage points in Terminal NAV. Not a bad little three strategy portfolio. Of course we can play around with all sorts of things in our spreadsheet, but the gist is own things that participate in the up tails (and don’t pay fees on correlated returns) and own efficient protection to cut off the down tails. From there, the compounding takes care of itself.

Here is a quick summary of the various strategies we’ve discussed.

Figure 18: Summary Table
Source: Convex Strategies

This brings us back to what we mentioned at the beginning of this section that warranted further discussion, specifically the issue that the authors of the paper, for their specific time period and their results, have a preferred strategy that has seen their Funding Ratio decline from 100 to 78, and a benchmark that has gone from 100 to 67, over the last 20ish years. This is a problem! Virtually all asset markets are at historical highs, and they are still losing ground to their liabilities. It might be time to rethink their overall approach. Even over the shorter period, starting in 2005 and taking out the negative compound event of the DotCom bear market, it appears that they are still barely keeping up with liabilities, despite the greatest combined bull market in history for their two major asset classes since the 2008 crisis. What might the next eventual negative compounding event bring? What are realistic expected returns for a Balanced Portfolio starting at current valuations/yields?

There is no guarantee that a Long Vol strategy paired with more Beta will work through all scenarios and lead to superior compounding over time, but there is near certainty that things with bounded potential upside and correlation to bad market environments will not lead to superior compounding over time. It’s just math!

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