## Deflation and negative TIPS yields

In one of those classic understated TBI headlines, Vincent Fernando today says that “Actually You Should Panic” if TIPS yields go positive. His argument: “if TIPS yields hadn’t fallen to where they are now, then we’d truly have something to worry about — Deflation.”

The problem is, Fernando’s math doesn’t add up. Expected annualized inflation, over the next five years, is equal to the yield on 5-year government bonds, minus the yield on 5-year TIPS. (We’ll ignore things like the liquidity premium for on-the-run Treasuries.) The 5-year Treasury bond is currently yielding 1.47%, so if the 5-year TIPS yield is slightly negative, that puts expected inflation at about 1.5%. On the other hand, if the 5-year TIPS yield were up at 0.5%, then that would put expected inflation at 1%. Which does not count as Deflation, and is certainly nothing to Panic about.

Of course, it is a *bit* more complicated than that. For one thing, we’re talking about average inflation over five years, which given that inflation rates tend to bounce around a bit, might well mean a brief amount of time in negative territory. But that, again, isn’t the kind of deflation to panic about.

Meanwhile, deflation does provide one technical reason why negative TIPS yields aren’t necessarily as weird as they look. If we do have a brief bout of deflation, then TIPS coupons will be zero — which is actually positive in real terms. TIPS investors never need to give money back to Treasury. So it’s not necessarily true that you’re getting a negative real coupon: if there’s negative consumer price inflation for any length of time over the next five years, the zero bound on coupon payments might even things out. There’s also a lower bound of 100 on principal repayments, which may or may not come into play depending on the price/yield at which you buy your bonds.

So really, negative TIPS yields can be taken as a sign that the markets are beginning to price in some brief dip into negative-inflation territory. They’re *not* a sign that the markets are expecting no deflation.

Well, you’ve got the basic point right: a TIPS yield is not a good proxy for real yield when inflation is low because of the embedded option.

However, you’ve got the details wrong. All cashflows in the bond are multiplied by the growth of the price index I(t) from base date 0 to cashflow date t; in other words, by I(t)/I(0). When deflation occurs, this multiplier is less than one, but it stays positive because I is strictly positive. The multiplier is not adjusted for coupons, so the actual coupon paid can be less than the nominal rate, but never zero.

However, the ratio I(T)/I(0) is floored at 1 when applied to the principal; this is equivalent to a floor on the inflation rate at zero.

I think you have to view this one probabilistically. If you see the range of outcomes as being normally distributed around the mean expectation for inflation (presently 1.5%), then that implies a certain probability of higher inflation and a certain probability of deflation. The implied *risk* of deflation is surely greater when you have a 1.5% spread than when you have a 2.5% spread.

Otherwise, TIPS are just telling us the same thing that the rest of the bond market is telling us — investment returns are expected to be pretty crappy over the next five years.

“Expected annualized inflation, over the next five years, is equal to the yield on 5-year government bonds, minus the yield on 5-year TIPS. (We’ll ignore things like the liquidity premium for on-the-run Treasuries.) The 5-year Treasury bond is currently yielding 1.47%, so if the 5-year TIPS yield is slightly negative, that puts expected inflation at about 1.5%.”

You must still believe the market is rational and efficient. I see the treasury market as dominated by ‘automatic’ and irrational buying by sovereigns, and retirement funds and so forth, not to mention our own Fed. Even Pimco is a small fish in those waters and does not set prices.

I see treasury yields as a measure of demand by so many nations for treasuries, and nothing more.

I guess I should have said something else explicitly. It is practical to hedge, say, a 5Y inflation floor with a TIP (+ swap.) If, hypothetically, there was a net buy-side demand for inflation floors, this would be translated by broker-dealers into a demand for TIPS.

Regarding the modeling of inflation caps & floors, if you choose to model inflation rates directly, as per term sheets, then you need to use something like a normal model that allows negative rates. It is often convenient to model the price index instead, since that allows lognormal-type models. In a lognormal setup, you typically find that caps & floors trade with pronounced skews.

Efficient market types take prices from the market (which must be right, har har) and infer things about the real world. Like inflation.

Ok, so we learned that Internet stock prices don’t reflect their true value. We learned that house prices don’t reflect their true value. We learned that Greek bonds prices didn’t reflect their true value.

Yet somehow we keep believing that markets prices are rational. Prices are just prices.