E-piphany

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.