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Your Revenue is My Expense
I saw a chart a few weeks ago, which someone sent me from The Daily Shot. It has been bothering me since then. Here’s the chart:
Well, it looks amazing and a great reason to invest in global equities, right? Global earnings are surging due to the AI revolution![1]
What bothers me is the simple phrase which is the title of this article. I completely understand that the leaders of the exploding AI industry are going to have drooling analysts projecting great earnings growth far into the future. That may even be correct. But if a company is making bank because their AI tools are tremendous, and their revenues are surging…it means that other companies are paying for that product and so revenues and expenses should net across the corporate landscape. This is not only true of AI, of course; big earnings of oil companies are offset by added costs for businesses and/or declining revenues for other companies selling to consumers with less ex-energy discretionary income.
That is probably the reason that, most years, forward estimates start out high because we can see the concentrated winners clearly but then decline gradually as the dispersed losers become plain. But that doesn’t seem to be happening this time. In fact, it seems like both sides are claiming gains from AI: the suppliers who are selling it, and the buyers who analysts think will show remarkable gains from using AI.
This is a great moment to review again Brad Cornell/Rob Arnott’s “The ‘Basic Speed Law’ for Capital Markets Returns“. I wrote about this most-recently in 2024, in “AI: Even a Big Deal is Smaller Than You Think.” The upshot of their ‘Basic Speed Law,’ which has held up remarkably well over time, is that real earnings cannot grow much faster (or slower) than the growth rate in real per capita GDP. So, unless we decide that AI is going to accelerate per capita GDP growth drastically – and as you can tell from the link to my prior article, I don’t buy that – we need to be skeptical about forecasts of huge earnings growth rates.
Now, a 100-year chart can hide a lot of deviations in the average. The basic speed law here is grounded by fundamental accounting identities. GDP is total expenditure on all goods and services, so it makes sense that total corporate revenues (and expenses) should be pretty highly correlated to that figure. So if the share of that expenditure that is profits increases – which is what the analysts are saying is going to happen – then something else needs to be true:
- Margins – and in this case global margins – need to expand as companies take more money from labor (if revenues minus costs go up, and revenues are constrained by GDP, costs need to go down and there’s only so much you can do with materials costs). But at least in the US, margins have been historically wide for some time. NIPA profits as a percentage of GDP are in the 12% range, which is already almost double of what it was pre-GFC. How much can this go up? Populism is already on the rise.
- Government spending can increase – this is another way to extract money from others, and that is to get the government to buy your stuff and sell debt to get the money to pay for it. Government deficits are part of the Kalecki equation. However, at least in the US the government deficit is shrinking. This might not be true this quarter since the US had to refund huge amounts of tariff revenues, but the general trend is towards better balancing of US trade and fiscal deficits.
- Consumers can spend a higher percentage of their income, and save less. This is also part of the Kalecki equation, and indeed personal savings have been declining. Over the last two years, the decline in personal savings has been the source of about 90% of the rise in corporate after-tax profits. See the chart below showing net corporate profits versus net savings (inverted, right scale). So…how much less can Americans save? Currently, savings is 2.72% of GDP. The last time it was lower (with the exception of right after COVID when people were spending their stimmy checks) was 2005-2008. And that was the all-time low of 1.5-2%. Before COVID, we were around 5%. Back in the early 1980s when interest rates were more attractive, savings was more like 7-8% of GDP.
- US companies can increase revenues and profits at the expense of non-US companies. That doesn’t really help us with the chart at the top of this article, which is global.
- Public companies can make hay at the expense of private companies. I totally believe in this one, since I manage a private company that is perpetually running into rule systems put into place to protect the big companies. But it doesn’t square with the AI promise, nor the fact that new business formation is robust and has been so for several years…and does not appear to be ebbing. These could all be profitless businesses – but now you have to explain why profitless businesses are exploding.
- Earnings per share could be increased by decreasing share count. That’s been the game for many a year, adding several percentage points to EPS growth by decreasing the “S”. There are some suspicions that that trend is reversing, with a lot of high-profile IPOs throwing a lot of shares onto the market. I don’t have good data on that. But I doubt that share buybacks are increasing.
- An increase in overall leverage, either financial leverage (debt/equity) or operating leverage (more fixed costs), could cause forward earnings growth to look better. It is instructive that over the last hundred years – looking at the ‘speed law’ chart – the gradual, pervasive increase in both forms of leverage has been associated with only a tiny acceleration in profits growth over time. I do think it has been a factor, but additional leverage is not freely available without bound. However, this might be part of the story – not because leverage is increasing broadly and suddenly, but because the composition of the indices is shifting to more high-margin and high-operating-leverage (but interestingly, very low-financial-leverage) businesses. Still, that doesn’t really explain the upward scoop in the global indices that cover a huge number of companies. Even accounting for the fact that those indices are generally market-cap-weighted, it seems far too large an effect to be mere substitution.
In short, while I think parts of these explanations have a kernel of truth to them…I think a lot of what we are looking at is analyst myopia. Analysts are focusing on the shiny objects of great worth, and are missing, for now, some of the offsetting effects on other companies. It may be possible for those earnings estimates to even be realized, if enough revenues are shifted temporally relative to costs (exciting companies realize the revenues now; boring companies capitalize the AI expenditures or defer the costs to later quarters). Sooner or later, though, it all must add up. Right now, in my mind it doesn’t seem to add up.
[1] As an aside, for much of the rest of this article I will refer to the US case. Not only is the US contribution to these earnings the largest by far but also – if the source of the surge is AI, then the US is where we would expect that surge to be sourced. I just mention this here because someone will noted the disconnect between this global chart, and the commentary based on US trends.
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 is the Season for an Inflation-Proof Currency?
By now readers will be well aware of USDi, the cryptocurrency whose price represents how many of today’s dollars you would need to buy a December 2024 dollar. (The answer at the time of this writing, according to https://usdicoin.com, is $1.044755). That construction means that USDi is inflation-proof, since as the price level increases so does its price. It is a ‘real’ dollar, always buying what a December 2024 dollar bought.
Now, I have recently pointed out that since recent NSA CPI prints were extremely high, USDi is accruing at a 12.6% rate in May and will accrue at a 10.2% rate in June. Buying a cash instrument with those yields is a no-brainer of course, and they won’t be sustained – as the energy price spike passes, future USDi yields will decline to become more normal.
But that’s a tactical call – compare USDi’s current return to 1-month TBills and allocate to whichever is higher. It’s fairly uninteresting grade school math and, anyway, not something you’d want to do with the whole nut, if you’re managing a $200mm stable portfolio. The more interesting question is about the longer-term strategic call. If you’re going to hold cash in your portfolio in some amount, and want to make an educated guess about the next year or two rather than actively move money in and out at hedge fund speeds – what’s the right ‘season’ for that? In what sorts of economic environments would you prefer to invest in an inflation-proof dollar, rather than in a dollar paying some simple nominal no-credit-risk interest rate?
The answer may surprise you, because of the recency effect. I am showing this most-recent period first for two reasons. (1) It will sync very nicely with people’s short-term memories of the last couple of years, when short-term interest rates have been above inflation, and (2) if I only show charts where USDi wins, any analyst worth his salt will assume I am hiding the bad chart. [N.b. – USDi was first launched in April 2025. But, since it is explicitly linked to the CPI index, we can easily and with complete confidence project its price backwards to any time there was a CPI index. So in these charts, I have labeled the return of “USDi” even though USDi did not exist at the time. Ergo, they are all charts about what returns would have been had USDi existed.]
The last few years have been a tale of great success for money-market investors. The Fed raised rates aggressively (finally) in 2022 and 2023, so that when we start this chart the Fed funds target rate was 5.25% and y/y CPI was 3.4%. Even though the Fed has subsequently eased rates a bit (despite inflation’s stubborn refusal to play along and fall to 2%), it was only recently that these lines started to move in parallel again as y/y CPI is 3.8% and 3-month Tbills are at 3.66%. Over the last few years, you would have lost roughly 5% holding an inflation-proof currency instead of rolling 3-month Treasury bills.
But whoa, let’s not forget the prior before that!
Here we see one solid reason to prefer an inflation-proof dollar, in that it adjusts automatically regardless of whether the central bank believes inflation to be ‘transitory.’ Ouch, this was a tough period for holders of cash. People for a long time leading up to this were holding lots of cash because precautionary cash balances are an option on future opportunities. The cost of that option – the time decay – is inflation, as I mentioned in an early podcast Ep. 18: Cash is an Option Whose Cost is Inflation. Holding cash through this period was painful: the price index (USDi) rose 18.2% versus Tbills at 6.6%, but it was really worse than that because the price level was up nearly 15% before the Fed did anything.
Speaking of the Fed, why don’t we go back to the Global Financial Crisis?
In 2005-2006, with growth strong the Fed was hiking rates. In 2007, Fed funds leveled off at 5.25% before stuff started coming unglued in the subprime mortgage market – but it was ‘contained’ – and the Fed started cutting rates. By late 2007 interest rates were at 3% but inflation was still rising. Then the bottom fell out, home prices declined, and oil prices dropped from $147/bbl to about $33/bbl. While core inflation never got below 0.6% y/y, the price index itself fell about 5% thanks to oil, leading to a lengthy period of deflation. Oh, wait…no, I guess it didn’t. As you can see from the green line, prices kept marching slowly higher – long after the Fed had collapsed interest rates to zero and were shoveling dirt on Lehman.
No need to cover every single year. But here are a couple of segments from the post-GFC period (aka ‘financial repression from the central bank’).
Inflation was low in the early ‘teens. But interest rates were even lower. The Fed felt they had a license to keep rates low, because inflation was low, and didn’t feel a need to impose positive real returns at the short end of the risk curve.
The same was true later in the decade, where the Fed responded to a growing economy by raising interest rates a little bit but still keeping them below the rate of inflation.
These periods cover lots of different economic environments, and for the last 20 years or so inflation has outperformed interest rates over a wide variety of them: the GFC collapse. Extended periods of low inflation in a period of Fed financial repression. Normal growth with a dovish central bank. The only time that it has not outperformed short rates is in a period like December 2023-March 2026, after inflation has already spiked and the Fed is belatedly trying to fix the problem by being hawkish.
Let’s back up even further. The chart below shows the annual return from rolling 3-month Treasury bills, compared with the inflation realized during that holding period, going back to 1969. [N.b. prior to 1983, the CPI’s shelter component incorporated home prices and mortgage rates, so that by construction CPI tended to be closer to interest rates.]
You can see, looking at the chart, that there are certainly periods when interest rates do outperform inflation. Not surprisingly, these include the epoch defined by Paul Volcker and the echo of Volcker maintained by his acolytes for years. Here are the annualized after-inflation returns of Tbills (approximately), by decade:
So in the inflationary 1970s and the disinflationary 2010s and so far since 2020, it paid to hold inflation (or it would have, if USDi had existed). I would argue that what those decades had in common was a Federal Reserve that leaned towards dovish. On the other hand, the 1980s and 1990s were a great time for bondholders – not to mention equityholders – as the Fed routinely held short rates above inflation and managed to squeeze inflation out of the system to lower rates. The 2000s were a period of transition between these two, and about a wash.
Therefore, in my opinion:
In order to bet against owning USDi in preference for Tbills or other credit-risk-free cash strategically rather than tactically, you need to believe one of the following:
- Kevin Warsh is the second coming of Paul Volcker, and he will tend to keep short-term interest rates above inflation. I do believe that Warsh is one of the more hawkish-by-construction Fed Chairs we have had in a while, but notably he is hawkish on the balance sheet and more dovish on rates themselves. So…this is difficult for me to believe. Inflation also started Volcker’s term quite high, so there was a long decline where rates could be lowered and still be above inflation. We aren’t in that situation right now.
- Or, you believe it’s a close call – maybe we are finally post-GFC-crisis and can return to the model of the 2000s – and you don’t care about the portfolio benefits of having a built-in hedge in your cash holdings. Because make no mistake, if it’s a coin flip on average then I want the Dec-2020 to Dec-2023 outcome where an inflation accident gives me a long-tail benefit rather than a long-tail cost!
The season for an inflation-proof currency is now.
Profiting From Zero Duration Inflation
One of the nice features of the USDi digital currency is that its path is known with certainty well in advance. The price of USDi is determined by the interpolated CPI index value compared with the value on the reference day (315.605). So, for example, we know that today’s[1] USDi value is 1.02681 because today’s CPI index value is 324.06614, and we know that because we know how to interpolate between the CPI prints from 3 months ago (324.122) and 2 months ago (324.054).
Importantly, those numbers we are interpolating between are the Non-seasonally-adjusted CPI figures from December (released in January) and January (released in February). And that interpolation methodology is exactly the methodology that TIPS use.[2]
You will notice that the CPI from 2 months ago is lower than the CPI from 3 months ago. That means that prices actually fell, before seasonal adjustment, which means that USDi actually declined slightly over the course of the month. It was even worse in January, because the November CPI was – as I have noted before – complete garbage due to the fact that BLS procedures led them to assume zero inflation for a lot of the missing October data. In the chart below, you can see the sharp correction during which USDi actually declined during January (and slightly further, in February).
Now, because we can ‘see the future’ due to the interpolation mechanism, we know exactly where USDi will trade each day in March. That’s also indicated on the chart. So we know that in March, USDi will rise at a 4.53% annualized pace. One-month t-bills are 3.6% right now. You do the math.
It gets better: the same BLS procedures that led to the terrible November number lead to self-correction, so the CPI Index will catch up over time. The biggest part of that catch-up is due to the rotation of the rent sample over 6 months, so while we do not know exactly what CPI will print at for February, March, April, and May, we have a good confidence that it will be above trend. We can see that from the CPI “fixings” market where those particular CPI prints trade. The market price is the market price, and sometimes wrong, but based on what trades in the market right now we can anticipate (orange line above) that USDi will climb at an annualized rate of 5.63% in April and 5.53% in May before slipping back to a still-better-than-bills 4.17% in June.
What does any of this have to do with duration?
Well, you may read this and say to yourself “I can get the same benefit if I just buy short TIPS bonds.” But no, you can’t. That’s because when you buy a TIPS bond, the principal amount rises with inflation but you still have to deal with price. It turns out that TIPS traders are very aware that their accretion (what we call the uplift in principal) is going to be higher than TBill rates over the next few months, and so the current price of TIPS bonds fully discount this. The July 2026 TIPS, which will mature at the CPI index value of July 15th (which is interpolated between April’s CPI and May’s CPI, so it includes all of those rebound months), trades at a price of 100-13…and remember, it matures at 100. So you’ll gain the accretion, but lose on price. I’ll save you the math: that price means the real yield of that bond is about -1%, which is convenient since the CPI between now and then is going to be something around 1% higher than the Tbill yield.
Every day that passes, as the principal value of the TIPS bond accretes, the price will decline. The only way you can profit versus fixed-rate Treasuries is if you are smarter than the market, and your forecast of CPI is better than what is already embedded in the price of the bond.
USDi has a price, but it is completely insensitive to yields which means you do not have to pay a premium to buy it now (nor did you get a discount back in December knowing the bad January numbers were coming). You can buy USDi today knowing that you will earn those exciting forthcoming CPI prints, without sacrificing principal.[3] You can buy USDi against USDC on Uniswap, or simply go to https://usdicoin.com/mint.
I’ve told you before how interesting USDi is since it’s the zero-duration instrument. Here is another concrete example.
[1] I say “today’s” because I am illustrating all of this with daily interpolation, but in practice USDi interpolates every block or “hash,” which is just a few seconds in length.
[2] …except for the fact that TIPS interpolate daily and USDi almost continuously.
[3] Of course, this is not investment advice. Although it sure sounds like it. Do your homework!
Modeling Shortfall Risk versus Inflation – What a Good Hedge Looks Like
When people ask me about hedging inflation, they aren’t always asking what they think they’re asking. There are two approaches to addressing inflation in your portfolio so that the portfolio grows in real terms. One of the approaches is to try to simply outrun inflation: “If inflation averages 3%, and I have an investment that averages 5%, I’ve succeeded.” This mode of thinking derives, I think, from the fact that all of our education has been in nominal space and in most financial modeling problems inflation is just assumed rather than modeled as a random variable. It turns out to be a lot harder than it sounds to find an asset class or collection of asset classes that dependably beat inflation over moderate (10+ year) periods, because there is significant (inverse) correlation between inflation and the performance of many asset classes. Most obvious here are stocks and bonds, so if you build a 60-40 portfolio that “should” return 5% over the long term and figure that will beat inflation, you’ll be right…as long as inflation stays low. If inflation goes up, you won’t only lose purchasing power but you’ll lose actual nominal value, since equities and bonds both tend to decline when inflation goes up. Let’s put that aside for a second but I will come back to it.
The other approach to addressing inflation is to try to hedge inflation: exceed inflation by a little bit, but all the time, so that your returns go up when inflation goes up and your returns go down when inflation goes down, but you always are experiencing some positive real return.
The difference between the first approach and the second approach can be summarized by thinking about shortfall risk. As an investor, you care about the upside (in real terms) but most of us are risk-averse meaning that we care more about the downside. Ask most people whether they’d risk a 25% loss in their portfolio purchasing power to have a similar risk of gaining 25%, and they will experience a strong preference to avoid that coin flip. Risk aversion isn’t linear, so investors treat small gains and losses differently from large gains and losses, and of course it matters whether you’re barely covering your goals or easily exceeding them so that you’re ‘playing with house money.’ Many things, in other words, affect risk preferences. But the bottom line is that if you are trying to ‘hedge’ inflation, you care about your shortfall risk over some horizon. What is the probability that you underperform inflation – that is, lose value in real terms – by some given amount between now and a stated horizon?
Now we are going to get a little mathy, but for those who aren’t so mathy I will try to explain in English as well.
If you want to evaluate the probability of asset B underperforming asset A by some given amount over some period, of course you need an estimate of the expected returns of A and B, or how they’re expected to drift relative to one another. That determines your jumping off point. Let’s suppose that A and B have the same expected return. The next thing that determines the frequency and severity of a shortfall of B versus A is the volatility of the spread between them, which is driven by (a) how correlated A and B are, and (b) how volatile each of them is. If they are highly correlated but B is far more volatile than A, you can have a large shortfall if B just has a bad day. If they aren’t very correlated, then when B happens to zig lower as A zags higher, you’ll get a shortfall even if they have similar volatilities. Essentially, we are valuing a spread or Margrabe option and like any option, we need a volatility parameter. In this case, it’s the volatility of the spread we care about, so we can evaluate “what’s the likelihood that the B-A spread is negative.”
If “SA” is the value of an inflation index (or an indexed token like USDi), and “SB” is the value of the hedging asset, then if distributions of A and B are approximately normal,[1] the option value is
C = SA N(d1) – SB N(d2), where
and
and, crucially, is the volatility of the ratio of A to B, which is a formula that will be familiar to travelers in traditional finance and depends on the individual asset volatilities and the correlation () between them:
For this ‘shortfall’ option to be as small as possible, assets A and B should have small volatilities () and a high correlation () between them.
In plain English terms: imagine two drunk guys walking down the boardwalk. What determines how far away they are from each other at any given time? Assuming no drift, it will depend on how much they’re weaving (volatility) and how much they’re weaving in the same pattern (correlation). If they’re holding hands (imposing high correlation), they’ll never get too far away from each other. And if neither one is very drunk (low volatility) they also won’t stray very far from each other. On the other hand, if both are wildly drunk and they don’t know each other, the spread between them will be wildly variable.
We aren’t trying to evaluate the spread between drunks, though. Let’s take this thought process and apply it to the inflation-hedging problem with an example. Suppose you are considering which of two assets is a better ‘hedge’ for inflation: the “INFL” ETF, or a mystery fund – let’s call it “EUSIT.”[2] Here is relevant data for these two assets, and for CPI. These are 3-year returns, volatilities, and month/month correlations, ending November 2025:
Using this data, we can see that the spread volatility (the result of the last formula listed above) for INFL versus CPI is 15.2%, while the spread volatility for EUSIT vs CPI is 1.1%. The Mystery Private Fund is the drunk holding hands with the other drunk, with neither of them that drunk; but INFL is really smashed (14.9% vol) and tending to zig when the CPI drunk zags (negative correlation).
Let’s extend this out one year, assume that INFL, EUSIT, and CPI all have the same expected returns, volatilities, and correlations. Practical question: What is the probability that your investment in INFL or EUSIT underperforms inflation?
For INFL: based on prior returns, it is expected to outperform CPI by 8.99% (11.97% – 2.98%). With a spread volatility of 15.2%, underperforming inflation (a spread of 0% or less) would mean an outcome that is 0.59 standard deviations below the mean. The probability of a draw from a normal distribution being 0.59 standard deviations below the mean is about 33.5%, which means that if you hedge your inflation exposure with INFL, you’ll underperform inflation about one year in three. Your chances of underperforming inflation by 10% or more in a given year is about 18%.
For EUSIT: based on prior returns, it is expected to outperform CPI by 3.15% (6.13% – 2.98%). With a spread volatility of 1.1%, underperforming inflation (a spread of 0% or less) would mean an outcome that is 2.86 standard deviations below the mean. The probability of a draw from a normal distribution being 2.86 standard deviations below the mean is about 0.66%, which means that if you hedge your inflation exposure with EUSIT, you’ll underperform inflation for a full year about once every 151 years. Your chances of underperforming inflation by 10%…even by 5% for that matter…is essentially zero.
Put a star by this paragraph: the assumptions here are key and I am making no claims about either of these strategies having those same characteristics going forward. This is only to illustrate the point that if you want an inflation hedge, meaning that you want to minimize shortfall risk, then it is very important to look at the volatility and correlation to CPI of your intended hedge. Having a better return is important, but less important than you think it is: at a 5-year horizon, the INFL ETF would be expected to outperform inflation (if we think 12% and 3% are decent long-term projections too) by about 60% compounded, but the spread standard deviation is now 15.2% times the square root of 5 years, so you’re only about 1.76 standard deviations above zero and thus you still have an 8% chance of underperforming inflation at the 5-year horizon! On the other hand, your chance of outperforming inflation by a huge amount, if you use the Mystery Fund, is also very small while that possibility exists if you use INFL. That’s what a hedge does: you give up the possibility of big outperformance to ‘buy back’ the chance of underperformance. If you are risk averse, that is a good trade because you’re giving up the less-salient part of your gains (big outperformance) to protect against the more-salient part (big underperformance).
So getting back to answering the question that we started with: what does a good inflation hedge look like?
- It has highly positive correlation to inflation at whatever horizon you’re focused on
- It has low volatility
- It outperforms, or at least doesn’t underperform, inflation over time
To this, I’ll add a fourth characteristic. It’s almost humorous, because hedges that fit those three characteristics are themselves quite rare. But the fourth one I would add is that it has convexity to higher inflation; that is, it does better at an increasing rate, the higher inflation gets. An inflation option, in other words.
Most of us should be happy with three! But at least now you’ll know how to evaluate whether you’re really getting a hedge, or something that will hopefully perform so well that you won’t care that it isn’t a hedge.
[1] I also conveniently wave away some complexities like the relative growth rates and the time value of money to make the math clearer with respect to volatility and correlation, which is my point here.
[2] Mystery fund is a private 3(c)1 fund available to verified accredited investors via a subscription agreement.
Why a 4.5% Nominal Rate is Roughly Equilibrium…Hmmm, Sounds Familiar…
I was planning to write today about why a 4.5%-5.0% nominal Treasury rate is not only not the end of the world, but actually sort of normal. Naturally, the reason I am even thinking about the topic is because of all of the apparent alarm because the current long bond recent peeked above 5% and the 10-year note at 4.50% continues to flirt with those levels. Because we haven’t seen the 10-year rate above 5% for a sustained period in about 18 years, it is natural that some of the young folks who were raised in an era of free money would think that this is the end of the world.
I’ve previously written about the return of some of the phenomena that we used to take for granted, such as the presence of optionality in the bond contract. After most of two decades of unhealthy interest rates produced unhealthy leverage habits among other unwelcome developments (including the leveraging of the government balance sheet because it was so cheap to borrow for one’s programs with no cost), I suppose it shouldn’t be surprising that there is so much wailing and gnashing of teeth, rending of garments, etc. But for those people who expect the Fed to lower rates significantly, because “after all 2% is the normal level of interest rates,” I am here to say that you probably don’t want the crack-up that would be necessary to make that plausible. The current level of interest rates is inconvenient for many organizations with a borrowing problem, but it is really quite normal.
Anyway, I’d intended to write a longer version of that, and as I started to write something bugged me and I looked back and noticed that I’d already written essentially the same thing a few years ago. At the time (June 2022) I was explaining “Why Roughly 2.25% is an Equilibrium Real Rate,” and of course if you add reasonable inflation expectations of 2.5%-3% you get to 4.75%-5.25% as an equilibrium nominal rate (and a bit higher than that for the 30-year, which also incorporates a modest additional risk premium). If you go and read that article directly, you can also get my screed on how models trained on the last 25 years of data leading up to the inflation spike only survived if they forecast a very strong reversion to the mean, and so *eureka* all of those models missed the entire inflation spike. But here is a reprinted snippet (reprinted by permission from myself) outlining the argument for why the current level of long-term real interest rates is about right.
Kashkari made a different error, in an essay posted on the Minneapolis Fed website on May 6th.[1] He claimed that the neutral long-term real interest rate is around 0.25%, which conveniently is where long-term real rates are now.
However, we can demonstrate that logic, reinforced by history, indicates that long-term real rates ought to be in the neighborhood of the economy’s long-term real growth rate potential.
I will use the classic economist’s expedient of a desert-island economy. Consider such an island, which has two coconut-milk producers and for mathematical convenience no inflation, so that real and nominal quantities are the same. These producers are able to expand production and profits by about 2% per year by deploying new machinery to extract the milk from the coconuts. Now, let’s suppose that one of the producers offers to sell his company to the other, and to finance the purchase by lending money at 5%. The proposal will fall on deaf ears, since paying 5% to expand production and profits by 2% makes no sense. At that interest rate, either producer would rather be a banker. Conversely, suppose one producer offers to sell his company to the other and to finance the purchase at a 0% rate of interest – the buyer can pay off the loan over time with no interest charged. Now the buyer will jump at the chance, because he can pay off the loan with the increased production and keep more money in the bargain. The leverage granted him by this loan is very attractive. In this circumstance, the only way the deal is struck is if the lender is not good at math. Clearly, the lender could increase his wealth by 2% per year by producing coconut milk, but is choosing instead to maintain his current level of wealth. Perhaps he likes playing golf more than cracking coconuts.
In this economy, a lender cannot charge more than the natural growth in production since a borrower will not intentionally reduce his real wealth by borrowing to buy an asset that returns less than the loan costs. And a lender will not intentionally reduce his real wealth by lending at a rate lower than he could expand his wealth by producing. Thus, the natural real rate of interest will tend to be in equilibrium at the natural real rate of economic growth. Lower real interest rates will induce leveraging of productive activities; higher real interest rates will result in deleveraging.
This isn’t only true of the coconut economy, although I would strongly caution that this isn’t exactly a trading model and only a natural tendency with a long history. The chart below shows (1) a naïve real 10-year yield created by taking the 10-year nominal Treasury yield and subtracting trailing 1-year inflation, in purple; (2) a real yield series derived from a research paper by Shanken & Kothari, in red; (3) the Enduring Investments real yield series, in green, and (4) 10y TIPS, in black.
The long-term averages for these four series are as follows:
- Naïve real: 2.34%
- Shanken/Kothari: 3.13%
- Enduring Investments: 2.34%
- 10y TIPS: 1.39%
- Shanken/Kothari thru 2007; 10y TIPS from 2007-present: 2.50%
It isn’t just a coincidence that calculating a long-term average of long-term real interest rates, no matter how you do it, ends up being about 2.3%-2.5%. That is also close to the long-term real growth rate of the economy. Using Commerce Department data, the compounded annual US growth rate from 1954-2021 was 2.95%.
It is generally conceded that the economy’s sustainable growth rate has fallen over the last 50 years, although some people place great stock (no pun intended) on the productivity enhancements which power the fantasies of tech sector investors. I believe that something like 2.25%-2.50% is the long-term growth rate that the US economy can sustain, although global demographic trends may be dampening that further. Which in turn implies that something like 2.00%-2.25% is where long-term real interest rates should be, in equilibrium.[2] Kashkari says “We do know that neutral rates have been falling in advanced economies around the world due to factors outside the influence of monetary policy, such as demographics, technology developments and trade.” Except that we don’t know anything of the sort, since there is a strong argument against each of these totems. Abbreviating, those counterarguments are (a) aging demographics is a supply shock which should decrease output and raise prices with the singular counterargument of Japan also happening to be the country with the lowest growth rate in money in the last three decades; (b) productivity has been improving since the Middle Ages, and there is no evidence that it is improving noticeably faster today – and if it did, that would raise the expected real growth rate and the demand for money; and (c) while trade certainly was a following wind for the last quarter century, every indication is that it is going to be the opposite sign for the next decade. It is time to retire these shibboleths. Real interest rates have been kept artificially too low for far too long, inducing excessive financial leverage. They will eventually return to equilibrium…but it will be a long and painful process.
At the time I wrote the passage above, 10-year TIPS yielded about 0.25%; today they yield 2.125%. It turned out that returning to equilibrium wasn’t at all a long process. But it certainly was painful!
Returning to the original point: just because 10-year rates are now approximately at equilibrium is not at all a prediction that they will remain at equilibrium. Indeed, if I made that prediction I would be making a very similar mistake to the one I criticized above. Mean reversion in rates is not a particularly powerful force, when set against an active central bank and a profligate legislature. But if it matters at all, it is very important to correctly identify the mean to which rates should revert.
And it’s not 2%.
[1] https://www.minneapolisfed.org/article/2022/policy-has-tightened-a-lot-is-it-enough
[2] The reason that real interest rates will be slightly lower than real growth rates is that real interest rates are typically computed using the Consumer Price Index, which is generally slightly higher than the GDP Deflator.
Illustrating the Cost of Leverage Effect on Returns
A couple of weeks ago, I presented a blog post called “The Effect of Crazy Time on Portfolio Allocations,” in which I pointed out that the effect of increasing volatility generally is to decrease the optimal portfolio allocations towards safer allocations. It was one of those posts where you initially say ‘well, duh’ but hopefully liked the fact that I ‘proved’ the intuition with the illustrations. While market volatility since then has been almost unbelievably low, it is hard for me to imagine that is sustained. It feels a little like a ‘deer in the headlights’ reaction from investors, as the Trump Train comes on so rapidly that all they can do is pull the shades.
I suspect that at some point, unless the Donald suddenly becomes a milquetoast business-as-usual kind of President, we will see those allocations shift.
But a few days ago I had another realization that called to mind the same old CFA-Level-I charts. I was explaining to someone who wanted me to leverage our really cool inflation-tracking strategy[1] that leveraging a mid-single-digits return makes a lot of sense when the cost of leverage is zero, but not so much sense when the cost of leverage was mid-single-digits. I’ve talked about this before – in October 2023 I published “Higher Rates’ Impact on Levered Strategies.”[2] I showed a table, but there’s a really simple way to illustrate the same thing.
I don’t really need the portfolio efficient frontier here. Maybe the optimizer spits out some share of the optimal portfolio that represents an investment in some hedge fund strategy you really like. Maybe it doesn’t. More likely, you don’t even use an optimizer. But if you really like that strategy, but want higher returns, you ask the manager ‘hey, can you lever that’? The manager says sure. But the manager can’t give you twice the returns for twice the risk – the leverage math doesn’t work that way. If the cost of leverage is 3% – which you can tell it is in this chart because that’s where the line hits the axis, at a risk-free rate of 3% – then your return for twice the risk is (2 x 4% – 1 x 3%) = 5%. So you pick up only 1% return for doubling the risk. And you can see that on the chart, because that’s the point the red line goes through: 5% return, 15% risk. For 3x risk, you get (3 x 4% – 2 x 3%) = 6%. And so on. The slope of the line is such that 7.5% additional risk gets you 1% additional return, no matter how many times you lever it.
So why do people ask for leverage? Well, because since 2008 the overnight rate was mostly at 0%.
If you can borrow at zero then levering simply multiplies risk and return simultaneously. At 2x leverage, your return is (2 x 4% – 1 x 0%) = 8%. You can see where this goes since 0 times anything drops out of the formula.
But this doesn’t work at higher costs of leverage. If the cost of leverage is equal to the expected return, then you just get more risk every turn of leverage you deploy. And if the cost of leverage is above the expected return, you make things worse every time you add leverage.
So it doesn’t make any sense to lever low-return strategies unless the cost of leverage is really low. And by the way, it doesn’t make much sense to lever high-return strategies unless they happen to be low risk. Because this math doesn’t just work with expected returns but also (and more importantly) with actual returns. Suppose you have a strategy that has a 6% expected return and a 15% risk. Say, an equity index. Now, you lever it 2x with the cost of leverage at 5% (by the way, if you use a levered ETF you’re not escaping the cost of leverage…but that’s for another day). Your expected return is now 7%, with 30% risk (check your understanding by doing the math).
Now, however, you get a 2-standard deviation outcome to the downside. Supposedly that happens only one year out of 40, but we know that there are fat tails in equity markets. But whatever the real probability, your unlevered return is now 6% – 2 x 15% = -24%. But now you’re riding the lightning and your return on the 2x leverage is (2 x -24% – 5%) = -53%. (Alternatively, you get to the same number if you just look at the new 7%ret/30%risk portfolio return as 7% – 2 x 30%).
Hedge fund managers understand this math…or should; if they don’t then get out…and it should change the numbers they report in forward-looking statements when interest rates are higher, for levered strategies. I will not comment on normal industry practice…
[1] To be clear, none of the red dots in this article represent the risk/return tradeoff for that strategy. I’m not trying to cagily present our fund’s performance because that would get me in trouble.
[2] This was a golden era for the blog. Right about the same time I also published one of my best posts in years, pointing out how the CME Bond Contract has shortened in duration and also has negative convexity again. “How Higher Rates Cause Big Changes in the Bond Contract.” How I loved that piece.
The Effect of Crazy Time on Portfolio Allocations
I am continually fascinated by how many second-order ‘understandings’ are missed, even by those people who have a really good first-order understanding of finance. For example, every financial advisor understands that bonds are less volatile than stocks. Most financial advisors understand that stocks and bonds in a portfolio together also benefit because they’re not correlated. Some financial advisors, and most CTAs, understand that diversifying a portfolio works because when you add uncorrelated assets together, the risk of the whole is less than the sum of the risks because of the offset from the correlation effects. Those are all coarse understandings that any financial professional should ‘get.’ However, it is fairly unusual for advisors or even CTAs to understand that the correlation of stocks and bonds undergoes a state shift when inflation get above about 2.5% for a few years, and become correlated, and that means more risk for the same combination of stocks and bonds. Here’s that chart I love to show, updated through the end of the year.
While that’s an example of a ‘second-order understanding’ that isn’t widely known, it isn’t what I want to write about today. Actually, for a change what I want to discuss is something that has nothing directly to do with inflation, and that is the effect of volatility on asset allocation.
This is an important discussion right now, because whether or not you have gotten the message yet that President Trump is going to be much more Machiavellian in his approach to the global world order than prior Presidents have been – and whether you think that’s a good thing or a bad thing – you surely must have noticed that the volatility of the markets under this regime is likely to be somewhat higher than under Sleepy Joe and also higher than it was during Trump’s first term. And that leads to the second-order understanding about what that implies for markets. Hang with me here; if you’re not a finance person this gets a little hairy.
The next chart shows Modern Portfolio Theory on one chart.
The blue line is the Markowitz efficient frontier: every point on the line represents a portfolio of assets that is the least-risky for that level of expected return. So, the highest vertical point is a portfolio of 100% in the asset with the highest expected return…you can’t get more return without leverage.[1] In this case, let’s assume that is equities. As you go down the curve, you allocate more to other less-risky assets and give up some portfolio return. Because assets are not 100% correlated, you can always get a portfolio that has at least as good (and usually better) returns for a unit of risk than any single asset – that’s the benefit of diversification. As you get to very low expected returns, you get to the part of the curve you’d have to be irrational to be on because you get higher risk and lower returns, and so we usually ignore that part of the curve that bends back.
The red line is popularly called the “Capital Asset Line.” Assuming there is some zero-risk instrument (that’s not already in the assets we’ve considered, so there’s some hand-waving here) and you can both borrow and invest at that rate, you can think of a portfolio that is the ‘best’ portfolio on the blue curve, either combined with the zero risk instrument (sliding down the red line to the left) or levered at the zero risk instrument (moving up the red line to the right). The ‘best’ portfolio here is defined as the place where the red curve is tangent to the blue curve.
A lot of times you’ll just see those two lines, but it doesn’t answer the question of which portfolio an actual investor prefers. It turns out that investors do not have linear risk preferences…that is, if I make my portfolio 10% more risky, perhaps I require 1% more return but if I make it another 10% risky, I’m going to need more than 1% additional return. I’m not only risk averse, but I get more risk averse the larger the potential risks. [Lots of experimental data on this. If I offer you a bet where you pay me $1 and on the basis of a coin flip I will either pay you $2 or $0, you are much more likely to take that bet than if I offer you a bet where you are risking $10,000 for the chance at $20,000…or zero]. So the purple dotted line is a hypothetical ‘investor indifference curve’. I just made up that term because I can’t remember what the theoreticians call it. The curve represents all of the combinations of risk and return that make the investor equally happy. So, the best portfolio for this investor is where the purple line – the highest purple line we can find, indicating the MOST happiness – touches the red line.
With me? Now consider the next chart. All I have done here is to increase the risk of every asset and shift the whole portfolio efficient frontier to the right.
What happens? The Capital Asset Line (red) now flattens out. And that means that the prior purple line no longer has a point of tangency. We have to go to a lower purple line, and since the purple line is concave upward the red line becomes tangent to the purple line at a point further to the left (the slope of the red line is flatter, and the flatter parts of the purple line are to the left). I’ve put the new ‘optimal portfolio’ as a dot in purple.
The implication is this: if overall risk in markets is perceived to have permanently increased, then rational investors will move from portfolios with more risky assets to portfolios with fewer risky assets.
You probably could have guessed that without all of the curves. If I am comfortable with a certain amount of risk, and the overall risk of things goes up, then it stands to reason that I’d work to reduce my overall risk. The second-order understanding here is, then, that if President Trump is perceived by investors to increase the overall volatility in markets and individual country and company outcomes, we should expect investors to lighten up on equities.
And that brings me to the final chart. This is the Baker, Bloom and Davis news-based Economic Policy Uncertainty Index, which counts the number of articles in US-based news sources that contain a set of predefined terms that indicate uncertainty about economic policy. The dotted lines below show weekly data; the heavy red line shows the 12-week moving average to get rid of the noise.
Notice the three prior spikes on the chart are during and immediately following the end of the internet/stock market bubble in the early 2000s, the end of the housing bubble and the Global Financial Crisis in 2008-09, and the COVID crisis. All three of those episodes were associated with significantly lower markets, although you could argue that harsh bear markets might trigger some policy uncertainty (that certainly happened after 2008). The jump on the right is the Trump jump, and it is already higher than any other period on this chart other than COVID.[2] Volatility we have. Uncertainty we have. And even if you like the President’s policies, the volatility means that we should not be surprised to see investors pull some chips off the table.
[1] If you take this best-returning asset and leverage it, you basically get a straight line going up and to the right forever; the slope of the line depends on the cost of leverage.
[2] Incidentally, the index goes back to about 1985 and although I didn’t show it there are two more bumps that are similar to the leftmost two on this chart: around the 1993 recession, and around the time of the stock market crash in 1987. They are all lower than the Trump jump.
Inflation Market Valuations and Tactics in the New Year
There is so much to talk about, since it has been such a long time since I posted, that it is a little hard to know where to begin. So let’s begin 2025 with a few quick notes about inflation markets and markets generally. I wouldn’t call this an outlook, per se…I am trying to resist making that year-end/year-beginning offering to the jinx gods…but an update with some observations. As an aside, later today I’m planning to post a new Inflation Guy Podcast (this is a Podbean link but it’s available anywhere you get your podcasts) with some comments on the trajectory of inflation (as opposed to markets), and how that may be affected by things such as the massive California wildfires.
I will begin with a content warning: this note is much denser than most of my columns. If you’re a retail investor and/or only interested in developments in inflation rather than inflation instruments, then you might skip this one. I’ll talk more about expectations for inflation, of course, in other posts. But that’s not today’s post.
Let’s start by looking at 10-year real yields. The blue line in the chart below is 10-year TIPS yields; the black line (because it’s topical) is 10-year UK Gilt linker (real) yields. TIPS yields are up to 2.25%. Normally, when they get to around 2% I think of them as roughly fair in an absolute sense, because long-term risk-free real yields ought to in principle look something like long-term real economic growth. Instructive in the chart below is that as far as nominal UK yields have risen, inflation-linked yields are still well below US real yields.[1]
That’s partly a clientele effect, since there are many forced holders of UK linkers. But still, while US real yields ran up from -1% to +2.25% once inflation started (that is, TIPS declined in a mark-to-market sense when inflation went up – very, very important to understand if you think of TIPS as an inflation hedge. They are, but only at maturity), Gilt real yields went from -3% to +1.19%. The selloff was 100bps worse. Yikes.
The next chart shows my quantitative measure of relative cheapness (negative indicates richness, because I’m a bond guy). I said before that TIPS are now roughly fair in an absolute sense; relative to nominal bonds, they’re also roughly fair to slightly cheap. That’s the blue line. You can see that TIPS for most of the past decade were pretty cheap relative to nominals (even while they were absolutely rich because of negative real yields), but since people started caring a bit about inflation they’ve gone back to being mostly fair. However, Gilt linkers have been massively rich for a long time – again, because of the forced-holders problem. But they are starting to get cheaper. That 100bps greater selloff I mentioned above happens to show up here as 100bps cheapening relative to nominals, and relative to TIPS!
Today’s column is supposed to be mostly about US markets, but I can’t help myself. I ought to also point out that breakeven inflation in the UK is roughly 100bps higher than it is in the US, even though core inflation in the UK is 3.6% and in the US it’s 3.5%. So, possibly, part of the relative richness of UK linkers – since I’m looking at each country’s linkers in relation to its own nominal bonds – is actually cheapness of UK nominals, compared to the actual inflation there. Or maybe it’s the richness of US nominals, compared to the actual inflation here. (This is why relative value trading is so useful and important – we don’t need to have an opinion about which of these two things is true. Are US nominals too rich, maybe because they can be financed cheaply in repo markets at ‘special’ rates? Or are UK nominals too cheap, maybe because the UK budget situation is perceived to be somehow even more precarious than our own? I don’t know.)
Sorry about the digression there to the UK. I just got excited. The inflation markets and inflation in Japan are also really interesting right now, especially as wage growth is surging and the yen is bordering on collapsing…yet 10-year inflation in Japan is quoted around 1.5%. If you can get someone to transact. Maybe I’ll talk about Japan another time.
US markets. First, note the weird shape of the US CPI swaps curve.
I have several issues here, with one of them being the overall optimism that inflation is definitely going back to be close to target, despite any real sign that is going to happen. It borders on religious conviction, frankly. But also, we have a weird implied path where inflation droops, then spikes near the 10-year point, and then declines. To be sure, I’m committing a chart crime here with the y-axis; if you stepped back this would look almost flat. But this is more than enough for a hedgie to be interested, usually. What is really happening is that if we had a core inflation swaps curve (I do, but you don’t) it would show a gentle decline out to 8 years. It’s steep on the CPI swaps curve because the energy curves imply that energy inflation will drag core inflation lower for years.
Of course, they won’t but you can hedge the energy. Out to about 5-8 years, probably. And that’s probably why we have that little dip in the CPI curve – it’s really an energy thing.
So I’ve said that 2.25% real yields on TIPS are fairly attractive. About as attractive as they’ve been for some time, actually. But be aware of a couple of things. One is that the bond market as a whole is under pressure and probably will stay under pressure for a bit as investors worry about financing the government in a world where the trade deficit is probably going to be coming down (implying that domestic savings will have to go up, and the only good way to make that happen is with higher yields). Real yields could go higher, and probably will at some point. But you should recognize that seasonality works in favor of the TIPS buyer right now.
Breakevens have a strong tendency to rise in the early part of the year. In 22 of the last 26 years, 10-year breakevens have risen in the 60 days following January 8th. To be sure, some of that is because TIPS bear flat-to-negative accretions in the early part of the year because CPI in December almost always declines on an NSA basis, so the rise in price/decline in real yields that helps widen breakevens is partly reflecting a change in the source of total return in TIPS during those months to being more price and less yield.[2] The point being that buying nominal bonds in the beginning of the year, up until about May, runs into difficult seasonal patterns but this is not true with TIPS. Indeed, it means that if you’re buying fixed income at all in Q1, it probably should be TIPS.
Finally, I really should say something about equities here. I think it’s always important to realize that TIPS yields are a direct competitor with equities. Nominal yields are not, necessarily, because 7% nominal yields in a world where prices (and earnings) are going up at 9% are much worse than 5% nominal yields in a world where prices (and earnings) are going up at 3%. Equity earnings do tend to rise with inflation (but stocks are a poor inflation hedge because multiples also tend to contract significantly when there is inflation, so you need to hold equities for a long, long time for them to be a good inflation hedge), and since they do it means that inflation-linked yields are a more-fair comparison. Real yields at 2.25% are neither rich nor cheap in the grand scheme of things. But equities are, once you discount expected earnings growth for expected inflation. I calculate the expected long-term S&P real return assuming that the current multiple of long-term average earnings (the Shiller PE) reverts 2/3 of the way to its mean over 10 years. By making it 10 years, and not demanding full reversion, I lessen the impact of apparent overvaluation on expected returns. But high returns do, historically, tend to precede low returns! In any event, you can debate my approach but below you can see my point.
This first chart shows 10-year TIPS yields set against my calculated expected 10-year annualized real returns from the S&P 500. Granted, the S&P 500 is cheaper outside of the Magnificent 7. But you can see that while stocks and TIPS cheapened together in the inflation spike of 2022, equities have ‘forgotten’ that they should be priced for higher real yields…resulting in the chart below, which I call the “Real Equity Risk Premium” of expected equity returns minus TIPS real yields.
Some of you will say “that’s a trend. Let’s get on that and buy stocks.” To me, that sounds like the fellow falling out a window on the 29th floor and declaring as he passes the 6th floor ‘so far, so good.’ The point of the chart is that when you buy stocks now, you should be expecting to lose money, in real terms, over the next decade. Maybe you’ll average 3% and inflation will be 4%, for example. But TIPS will guarantee you will make 2.25% after inflation. As this spread gets more and more tilted against stocks, it gets harder and harder to explain why anyone would choose equity risk over TIPS risk, other than as a diversifier.
[1] This is not wholly unique to the UK. US 10y inflation bonds have higher real yields than linkers in Australia, Italy, Israel, Canada, France, the UK, Germany, and Spain.
[2] This is wonky stuff. If the expected forward price level doesn’t change, then the breakeven needs to go up because we are starting from lower and lower current price levels due to the (short) lag between the reporting of CPI and its realization in the carry of TIPS. If you don’t understand this because you’re not a rates strategist, don’t worry about it and take my word for it.
Re-Blog: Volatility and Position Size
This is one of my favorites, and every few years I re-blog some portion of this article. The original, I wrote in 2010. The basic question is, what is the correct way to respond as an investor to increasing uncertainty? In the original blog and in various re-posting edits, I’ve applied a basic idea called the “Kelly Criterion” to explain why responding to market selloffs by trimming a position, rather than adding to it, is often the right strategy (in the sense of it being mathematically optimal, not in the sense of it always producing the best returns). The idea also applies to the question of what to do when the general level of uncertainty and volatility rises (or falls) in markets. With developing uncertainty in the Middle East and the US spiraling towards what looks to be a summer of crazy politics, it is rational – even optimal – to ‘take some chips off the table.’ Read on for why.
(“Kicking Tails” originally appeared February 12, 2018)
Like many people, I find that poker strategy is a good analogy for risk-taking in investing. Poker strategy isn’t as much about what cards you are dealt as it is about how you play the cards you are dealt. As it is with markets, you can’t control the flop – but you can still correctly play the cards that are out there.[1] Now, in poker we sometimes discover that someone at the table has amassed a large pile of chips by just being lucky and not because they actually understand poker strategy. Those are good people to play against, because luck is fickle. The people who started trading stocks in the last nine years, and have amassed a pile of chips by simply buying every dip, are these people.
All of this is prologue to the observation I have made from time to time about the optimal sizing of investment ‘bets’ under conditions of uncertainty. I wrote a column about this back in 2010 (here I link to the abbreviated re-blog of that column) called “Tales of Tails,” which talks about the Kelly Criterion and the sizing of optimal bets given the current “edge” and “odds” faced by the bettor. I like the column and look back at it myself with some regularity, but here is the two-sentence summary: lower prices imply putting more chips on the table, while higher volatility implies taking chips off of the table. In most cases, the lower edge implied by higher volatility outweighs the better odds from lower prices, which means that it isn’t cowardly to scale back bets on a pullback but correct to do so.
When you hear about trading desks having to cut back bets because the risk control officers are taking into account the higher VAR, they are doing half of this. They’re not really taking into account the better odds associated with lower prices, but they do understand that higher volatility implies that bets should be smaller.
In the current circumstance, the question merely boils down to this. How much have your odds improved with the recent 10% decline in equity prices? Probably, only a little bit. In the chart below, which is a copy of the chart in the article linked to above, you are moving in the direction from brown-to-purple-to-blue, but not very far. But the probability of winning is moving left.
Note that in this picture, a Kelly bet that is less than zero implies taking the other side of the bet, or eschewing a bet if that isn’t possible. If you think the chance that the market will go up (edge) is less than 50-50 you need better payoffs on a rally than on a selloff (odds). If not, then you’ll want to be short. (In the context of recent sports bets: prior to the game, the Patriots were given a better chance of winning so to take the Eagles at a negative edge, you needed solid odds in your favor).
Now if, on the other hand, you think the market selloff has taken us to “good support levels” so that there is little downside risk – and you think you can get out if the market breaks those support levels – and much more upside risk, then you are getting good odds and a positive edge and probably want to bet aggressively. But that is to some extent ignoring the message of higher implied volatility, which says that a much wider range of outcomes is possible (and higher implied volatility moves the delta of an in-the-money option closer to 0.5).
This is why sizing bets well in the first place, and adjusting position sizes quickly with changes in market conditions, is very important. Prior to the selloff, the market’s level suggested quite poor odds such that even the low volatility permitted limited bets – probably a lot more limited than many investors had in place, after many years of seeing bad bets pay off.
[1] I suspect that Bridge might be as good an analogy, or even better, but I don’t know how to play Bridge. Someday I should learn.
