# How can TIPS have negative real yields?

In this Investopedia explainer about TIPS, it says:

The yields on TIPS are often negative. This is because after taking into account the effects of inflation, the real yield is negative. For instance, if standard two-year Treasuries yield 1% but inflation is 2%, then the real yield is -1%.

This makes no sense to me, since I thought that the principal in a TIPS is inflation-adjusted. So if the principal is P, then in the above example the yield after 1 year would be P * 1.02 * 0.01, i.e. 1% in real terms, not negative in real terms.

Am I missing something?

# The arithmetic

Writing out TIPS's math, as I've understood it, shows how TIPS' real returns are exactly the stated interest amount. If I've misunderstood how TIPS actually work below, please point out the lines that are wrong.

Let's say that I buy a 1-year TIPS bond from the Fed on Jan 1, and hold it to maturity. For simplicity, it pays coupons annually (in real life they're paid out twice a year).

• X is the original purchase price.
• y0 is the purchase year.
• y1 is the maturity year. y1 := y0 + 1.
• A is the inflation during y0.
• B is the interest.

Let A and B be defined as (1 + percentage/100). For example, if inflation is 2%, A is 1.02.

After a year, the original principal X becomes XA, and the coupon payed out in y1 is XAB. The returned principal at maturity is XA. So the total return is:

Cash at maturity / cash at purchase

= (XAB + XA) / X

= AB+A

= A(B+1)

This is the total return in y1 dollars. To get the real return, i.e. the return in y0 dollars, divide by inflation A:

real return = A(B+1) / A = B+1

This real return of B+1 is by definition positive. Which step(s) above were wrong?

• Inflation-Indexed securities can have a negative yield as a result of yields being below (expected) inflation. Commented Nov 11, 2023 at 17:26
• But they'll be less negative than non-protected might become. Basically, you're trading away part of the best range of (after-inflation) results to gain some protection from part of the worst range of those results. It's still not completely risk free, just less risk. Nothing can protect you from hyperinflation, for example, except not having money in that currency. Commented Nov 11, 2023 at 18:07
• I had thought that the principal gets adjusted upwards each year by that year's inflation rate, and the coupon payment is some fixed interest rate (1% above) of this adjusted principal. Are you saying that the coupon payments are all fixed at the original principal times the interest rate, and the adjusted principal is just what you get back at maturity? Commented Nov 12, 2023 at 13:14