But in a sense, this is still true of stocks, no? At the end of, say, the year, the stock will have returned some percentage. Your true return - i.e. your additional purchasing power as a result of that gain - is that amount minus inflation. In other words, when it comes to total return, inflation reduces every dollar to the same degree, regardless of how you made it, because it shows up on the spending side.

I figure I must be missing something, so I thought I'd look at this in a more quantitative way. Consider an investor who puts proportion

*p*of his assets in a stock index fund, and the rest (

*1-p*) in a bond index fund. The real return on the year, R, is

R = p*R_s + (1-p)*R_b - I

Where R_s is the nominal return to stocks, R_b is the nominal return to bonds, and I is inflation. These are all random variables: we don't know what they are going to be, and they vary every year. If one uses variance to measure volatility and risk (reader can insert the usual caveats here about equating risk with variance), then we get the following equation for variance in return, V(R):

V(R) = p^2*V(R_s) + (1-p)^2*V(R_b) + V(I) + 2p*(1-p)*C(R_s,R_b) - 2p*C(R_s,I) - 2(1-p)*C(R_b,I)

In this formula V() is a variance and C() is a covariance. (Follows from formula for variance of linear function of random variables.)

This is a little hard to read, but you can basically think of each term as follows (respectively): The total variance in real return is the sum of parts that are due to...

1. variance in stocks

2. variance in bonds

3. variance in inflation

4. covariance between stocks and bonds

5. negative covariance between inflation and stock return

6. negative covariance between inflation and bond return

The last term seems to be relevant to the topic at hand: it specifies how much of the volatility in your annual returns is due to the interaction of bonds and inflation. In short, if there is a positive correlation between annual bond returns and inflation, this reduces overall volatility: they tend to cancel each other out. If there is a negative correlation, it increases volatility: you tend to get a bad return precisely when your money loses most value. So, if investing in bonds increases inflation risk, perhaps I should expect the correlation between bonds and inflation to be negative.

Is that so? Well, using the annual inflation numbers from here:

https://www.usinflationcalculator.com/i ... 3-to-2008/

And the annual total bond returns to VBMFX from yahoo, I found that the correlation appears to be

**weakly positive**. Stocks even less so. I didn't bother to check if it's significant, because, in any case, the evidence does not suggest the negative correlation I expected.

Thoughts? Am I overthinking this? I guess what ultimately matters is this: what actionable advice is implied by the statement that bonds are subject to inflation risk? How does that affect how we invest?