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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 “S_A” is the value of an inflation index (or an indexed token like USDi), and “S_B” is the value of the hedging asset, then if distributions of A and B are approximately normal,[1] the option value is

C = S_A N(d₁) – S_B 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.

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