Since the Treasury this week auctioned floating-rate notes (FRNs) for the first time, it seems that it is probably the right time for a brief discussion of whether FRNs protect against inflation.

The short answer is that FRNs protect against inflation slightly more than fixed-rate bonds, but not nearly as well as true TIPS-style bonds. This also goes, incidentally, for CPI-linked floaters that pay back par at maturity.

However, there are a number of advisors who advocate FRNs as an inflation hedge; my purpose here is to illustrate why this is **not** correct.

There are reasonable-sounding arguments to be made about the utility of FRNs as an inflation hedge. Where central bankers employ a Taylor-Rule-based approach, it is plausible to argue that short rates ought to be made to track inflation fairly explicitly, and even to outperform when inflation is rising as policymakers seek to establish positive real rates. And indeed, history shows this to be the case as LIBOR tracks CPI with some reasonable fidelity (the correlation between month-end 3m Libor and contemporaneous Y/Y CPI is 0.59 since 1985, see chart below, data sourced from Bloomberg).

It bears noting that the correlation of Libor with *forward-looking* inflation is not as strong, but these are still reasonable correlations for financial markets.

The correlation between inflation and T-Bills has a much longer history, and a higher correlation (0.69) as a result of tracking well through the '80s inflation (see chart below, source Bloomberg and Economagic.com).

And, of course, the contemporaneous correlation of CPI to itself, if we are thinking about CPI-linked bonds, is 1.0 although the more-relevant correlation, given the lags involved with the way CPI floaters are structured, of ** last** year's CPI to

**year's CPI is only 0.63.**

*next*Still, these are good correlations, and might lead you to argue that FRNs are likely good hedges for inflation. Simulations of LIBOR-based bonds compared to inflation outcomes also appear to support the conclusion that these bonds are suitable alternatives to inflation-linked bonds (ILBs) like TIPS. I simulated the performance of two 10-year bonds:

Bond 1: Pays 1y Libor+100, 10y swaps at 2.5%.

Bond 2: Pays an annual TIPS-style coupon of 1.5%, with expected inflation at 2.0%.

Note that both bonds have an *a priori* expected nominal return of 3.5%, and an *a priori* expected real return of 1.5%.

I generated 250 random paths for inflation and correlated LIBOR outcomes. I took normalized inflation volatility to be 1.0%, in line with current markets for 10-year caps, and normalized LIBOR volatility to be 1.0% (about 6.25bp/day but it doesn't make sense to be *less* than inflation, if LIBOR isn't pegged anyway) with a correlation of 0.7, with means of 2% for expected inflation and 2.5% for expected LIBOR and no memory. For each path, I calculated the IRR of both bonds, and the results of this simulation are shown in the chart below.

You can see that the simulation produced a chart that seems to suggest that the nominal internal rates of return of nominal bonds and of inflation-linked bonds (like TIPS) are highly correlated, with a mean of about 3.5% in each case and a correlation of about 0.7 (which is the same as an r-squared, indicated on the chart, of 0.49).

Plugged into a mean-variance optimization routine, the allocation to one or the other will be largely influenced by the correlation of the particular bond returns with other parts of the investor's portfolio. It should also be noted that the LIBOR-based bond may be more liquid in some cases than the TIPS-style bond, and that there may be opportunities for credit alpha if the analyst can select issuers that are trading at spreads which more than compensate for expected default losses.

The analysis so far certainly appears to validate the hypothesis that LIBOR bonds are nearly-equivalent inflation hedges, and perhaps even superior in certain ways, to explicitly indexed bonds. The simulation seems to suggest that LIBOR bonds should behave quite similarly to inflation-linked bonds. Since we know that inflation-linked bonds are good inflation hedges, it follows (or does it?) that FRNs are good inflation hedges, and so they are a reasonable substitute for TIPS. Right?

However, we are missing a crucial part of the story. Investors do not, in fact, seek to maximize nominal returns subject to limiting nominal risks, but rather seek to maximize **real** return subject to limiting **real** risks.[1]

If we run the same simulation, but this time calculate the **Real** IRRs, rather than the nominal IRRs, a very different picture emerges. It is summarized in the chart below.

The simulation produced the assumed equivalent average real returns of 1.5% for both the LIBOR bond and the TIPS-style bond. But the real story here is the relative variance. The TIPS-style bond had **zero** variance around the expected return, while the LIBOR bond had a non-zero variance. When *these* characteristics are fed into a mean-variance optimizer, the TIPS-style bond is likely to **completely dominate** the LIBOR bond as long as the investor isn't risk-seeking. This significantly raises the hurdle for the expected return required if an investor is going to include LIBOR-based bonds in an inflation-aware portfolio.

So what is happening here? The problem is that while the coupons in this case are both roughly inflation-protected, since LIBOR (it is assumed) is highly correlated to inflation, there is a serious difference in the value of the capital returned at the maturity of the bond. In one case, the principal is fully inflation-protected: if there has been 25% inflation, then the inflation-linked bond will return $125 on an initial $100 investment. But the LIBOR-based bond in this case, and in all other cases, returns only $100. That $100 is worth, in real terms, a widely varying amount (I should note that the only reason the real IRR of the LIBOR-based bond is as constrained as it appears to be in this simulation is because I gave the process no memory - that is, I can't get a 5% compounded inflation rate, but will usually get something close to the 2% assumed figure. So, in reality, the performance in real terms of a LIBOR bond is going to be even more variable than this simulation suggests.

The resolution of the conundrum is, therefore, this: if you have a floating rate *annuity*, with no terminal value, then *that* is passably decent protection for an inflation-linked annuity. But as soon as you add the principal paid at maturity, the TIPS-style bond dominates a similar LIBOR bond. "Hooray! I got a 15% coupon! Boo! That means my principal is worth 15% less!"

The moral of the story is that if your advisor doesn't understand this nuance, they don't understand how inflation operates on nominal values in an investor's portfolio. I am sorry if that sounds harsh, but what is even worse than the fact that so many advisors don't know this is that many of *those* advisors don't know that they don't know it!

[1] N.b. Of course, they seek to maximize *after-tax* real returns and risks, but since the tax treatments of ILBs and Libor floaters are essentially identical we can abstract from this detail.

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