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A New Era of Positive Stock/Bond Correlations and What That Means
I read recently – I can’t find where – that stock/bond correlations in the US are the highest (most positive) they have been in decades. This of course is bad news for investors who commonly allocate to both stocks and bonds with the expectation that adding bonds will reduce the risk of a portfolio not only because they have a lower natural volatility than do stocks but also because the expectation of negative correlations between them have the effect of lowering the volatility of the portfolio further (since the variance of a 2-asset portfolio is equal to the weighted sum of the variances plus 2 times the product of the weights and the covariance between the two assets. So, when two assets are negatively correlated, total portfolio variance is lower than the sum of the weighted variances of the assets; when they are positively correlated, total portfolio variance is higher than the sum). That’s sort of Portfolio Management 101, but since most of my readers are not professional portfolio managers: think of one person pushing another person on a swing. If they’re pushing in rhythm with the swing (positive covariance), then the person on the swing goes higher and higher. But if they’re pushing in the opposite rhythm (negative covariance), then the swing goes up less and less and Dad is telling the kid it’s time to go home.
So, this matters a lot for portfolio construction and optimization, of course.
By the way, it isn’t like this just started happening. I’ve been warning about this (and showing the chart I am about to show) since at least 2019. In 2022 I even had a nice table to go with the chart (see this year-end piece, and scroll to the “Other Things” part at the end https://inflationguy.blog/2022/12/22/2022-year-end-thoughts-about-2023/ ). But let’s update it.
This heavy line in this chart shows the rolling 3-year correlation of monthly returns of stocks and bonds, going back to 1948 (I sourced equity returns from Ken French’s site based on CRSP data; bond returns I estimated based on Shiller’s lengthy series). You will notice that stock/bond correlations are not guaranteed to be negative – in fact, for the 35 years or so prior to 1998, correlations were positive. The shaded area illustrates the salient point, and that is that correlations tend to flip when inflation gets sustainably over about 2.5% (the shading is positive when 3-year compounded inflation is above 2.5%, and negative when it is below). That’s not coincidence. The simple way to explain it is that stocks and bonds react very similarly to the inflation factor and very differently to the growth factor. That is to say, when there’s news about good economic growth, then stocks tend to rise and bonds tend to sell off (yields rise because real yields rise). But when there is bad news about inflation, then stocks tend to fall and bonds also tend to fall (yields rise because inflation expectations rise). So, in periods where inflation is low and stable, the growth factor dominates and stocks and bonds move in different directions; in periods where asset markets perceive inflation risk, stocks and bonds tend to move together more often.
By the way, this shifting of correlations isn’t only true with stocks and bonds. The entire correlation matrix between many asset classes experiences a shift when the inflation-state changes. But since portfolios tend to be most heavily weighted in stocks and bonds, and because the math gets quite a bit uglier when we add more assets, we tend to focus this sort of discussion on stocks and bonds.
Again, the point of this is that portfolio optimization routines – which tend to be built on covariance matrices built from some recent window of historical data – will tend to completely miss this shift unless portfolio managers intervene, and portfolio managers are loathe to mess with the models.
How much does it matter?
Let me introduce another concept. A ‘risk parity’ portfolio is one in which the assets are weighted in such a way that they each contribute the same amount to the overall variance of the portfolio. So, since bonds are lots less volatile than stocks in general, a risk-parity allocation means that you’ll tend to hold a lot more weight in bonds.[1] Suppose stocks have over time a 15% standard deviation and bonds have a 7.5% standard deviation (which isn’t that far off, actually). Then the weight in stocks, ignoring the stock/bond covariance for now, is 7.5% / (15%+7.5%) = 33.33%; the weight in bonds is 15%/(15%+7.5%) = 66.67%. The 2/3 of your portfolio that is in bonds will contribute 66.67% x 7.5% = 5% to your portfolio risk, and the 1/3 that is in stocks will contribute 33.33% x 15% = 5% to your portfolio risk. That’s the ‘parity’ in risk parity.
Now, true risk parity is done with variances, not standard deviations, and also takes into account the correlation between the assets – and here’s where it gets interesting. If I assume stocks and bonds have a correlation of -0.3, then my weight in stocks is more like 26% and my weight in bonds 74%. But, if the stock/bond correlation is +0.3, the weight of stocks drops to 10.5% and bonds go to 89.5%. So that correlation shift should cause you to cut your holdings of stocks by 60%, from 26% of your portfolio to 10.5% of your portfolio!
[“Heck,” you say. “I gotta hold more stocks than that! I can handle the risk!” That’s fine. The risk parity proposition is merely that you get better returns per unit of risk if you equate the marginal contribution of risk. With stocks, since 1948 you’ve earned 11.74% annualized through the end of April (relax, we are ending this accounting in the middle of a bubble so of course it looks stupid), on annual risk of 14.85%. So every 1% of risk got you 0.79% return. On the other hand, the naïve risk parity got you 7.47% return on 7.15% risk, so you got 1.04% return per unit of risk. And that’s where the risk parity firms will lever up that portfolio so you get similar to equity risk or at least 60/40 risk.]
Again, my point though is not to argue for risk parity. My point is that shifting the correlation between stocks and bonds given even basic approaches to portfolio construction implies a significant reduction in equity risk is in order in an inflationary environment – and that doesn’t even consider the fact that inflation tends to lower market-clearing equity multiples so that prospective equity returns are lower in that kind of environment. So if the new higher-inflation era (and it appears ever more difficult to refute the notion that we are in one) means that investors either need to accept higher levels of portfolio risk or to shed equity risk…where is the stock market selloff?
Your guess is as good as mine. Either (a) investors still don’t believe that inflation is going to be persistent (although the flip in correlations suggests they do), or (b) investors are willing at least for now to hold more portfolio risk in order to harvest the fruits of the AI valuation explosion, or (c) portfolio managers are loathe to cut equity exposures because they don’t want to lose performance to their peers (since actual customers tend to look at returns, not risk-adjusted returns!). I think the answer is some combination of (b) and (c). But both of those reasons are ephemeral, and depend on continued momentum. Given the valuation levels in the equity market, a prudent manager will be at least trimming risks opportunistically these days.
[1] Since over time, stocks have better returns than bonds, people tend to hold more stocks than bonds and firms who deploy risk-parity portfolios typically employ leverage so that they aren’t sacrificing stock allocations so much as adding levered bonds. Anyway, a mean-variance optimization done correctly makes more sense than risk parity, but I’m just using risk parity as a way to illustrate the size of the effect a correlation shift can have on a portfolio.
What Risk-Parity Paring Could Mean for Equities
The stock market, the bond market, the commodities markets (to a lesser extent), FX markets – they are all experiencing a marked increase in volatility.
Some observers want to call this bearish for equities, mainly because they already are bearish. This is a very bad reason. While really bad equity returns almost always occur coincident with a rise in volatility – the old maxim is that stocks go ‘up on the staircase and down on the escalator’ – that does not mean that volatility causes bad returns. Or, put another way, there are also periods of increased volatility that do not precede and are not coincident with bad returns.
However, there actually is a reason that increased volatility might lead to poor short- to medium-term returns, that isn’t based on technical analysis or spurious correlations. Moreover, a relatively new phenomenon (the rise of so-called ‘risk-parity’ strategies) is starting to institutionalize what was already a somewhat natural response to volatility.
In ‘risk-parity’ strategies, the weight of an asset class (or a security within an asset class, sometimes) is inversely proportional to the risk it adds to the portfolio. Generally speaking, “risk” here is defined as variance, because it is easy to estimate and there are markets where symmetrical variance trades – i.e., options markets. But what this means is that when volatility (sometimes realized volatility, and sometimes option “implied” volatility) rises in stocks, then risk parity strategies tend to be shedding equities because they look riskier, and vice-versa. Right now, risk parity strategies are likely to be overweight equities because of the long period of low realized and implied volatility (even though the valuation measures imply quite high risk in the sense most of us mean it, in terms of the probability of return shortfall). Risk parity strategies are probably superior to ‘return-chasing’ methodologies, but by being ‘risk-chasing’ they end up doing something fairly similar when they are all operating together.
Note that while risk-parity strategies are comparatively new – well, not exactly because it is an oldish idea, but they have only recently become a big fad – this general phenomenon is not. The natural response to greater equity market volatility is to pare back exposure; when your broker statement starts to swing around wildly it makes you nervous and so you may start to take some profits. This is also true of other asset classes but it seems to me to be especially true in equities. Nobody who gets involved in commodities is surprised at volatility: the asset class suffers from a midguided belief that it is terribly volatile even though commodity indices are just about exactly as volatile as equity indices over time. But equity investors, contrariwise, seem perennially surprised at 2% moves.
So, while the recent volatility doesn’t mean that a move lower in equities is assured, it increases the probability of such because risk-parity strategies (and other investors reacting nervously to overweights in their equity exposure) will begin to scale back positions in the asset class in favor of positions in other asset classes, probably mostly bonds and commodities. At this point it would be good for me to point out that only the very short-term volatility measures have moved up dramatically; the VIX is well off its bottom but only up to 18.8 and it has been there numerous times in the last few years (see chart, source Bloomberg). But the longer the volatility continues like we have seen it for the last week or two, the bigger the chances that the asset-allocation boxes start to make important shifts (and the quant hedge fund boxes will probably move a bit before those asset allocation boxes do).
As an aside, the tendency for asset allocation shifts to follow volatility shifts is not the reason that the VIX displays a strong inverse directionality. Neither is the main reason for this inverse directionality because the VIX is a “fear gauge.” The main reason is that the VIX weights near-the-money options more heavily than out-of-the-money options. Because options skews almost always imply more downside volatility for stocks than upside volatility[1], when the market declines it tends to bring more “high volatility” strikes into play and so part of the VIX increase in a down market is simply mechanical.
I am not calling for a sharp decline in stocks, nor for an extended decline in stocks. My position and view is as it has long been, that the prospect for attractive real returns from equities over the next 5-10 years is quite small and beaten handily by commodities’ prospective returns at that end of the risk spectrum. I don’t think that most investors (me included!) should swing asset allocations around frequently in response to technical indicators or such things as “momentum”, but rather should focus on evaluating expected long-term returns (which are somewhat predictable) and invest for value. And I must admit I also think that “risk-parity” is a clever marketing gimmick but a pretty absurd way to assemble a portfolio for almost everyone. My point here is to highlight one little-considered aspect of herd behavior, and how that herd behavior may have become more institutionalized as late, and to consider the risks that herd behavior may create.
[1] This in turn is not due so much from the tendency of markets to have more downside volatility than upside volatility, but from the fact that buying protective puts and selling “covered” calls are both considered “conservative” options strategies. So, out-of-the-money puts tend to be too expensive and out-of-the-money calls too rich.
