The TIPS Index Ratio and Auction Mechanics

A regular Treasury bond pays a fixed coupon on a fixed $1,000 (or similar) face value until maturity. A TIPS does something different: its principal amount itself grows (or occasionally shrinks) with the Consumer Price Index, and the coupon rate, though fixed, is paid on that adjusted principal, not the original issue amount. The running multiplier that tracks how much the original principal has grown since issuance is the index ratio, and it's the number that turns a TIPS's fixed real coupon rate into an actual cash payment.

How the ratio is built

The index ratio on any given date is the reference CPI for that date divided by the reference CPI on the bond's original dated date (its first accrual date, not necessarily its issue date). The reference CPI itself is interpolated daily between the CPI figures published (with roughly a two-and-a-half month lag) for the first of each month, so a TIPS's inflation adjustment updates smoothly every day rather than jumping only on CPI release days.

$$\text{Index ratio}_t = \frac{\text{Reference CPI}_t}{\text{Reference CPI}_{\text{dated date}}}$$

In words: divide today's (interpolated) reference CPI level by the CPI level on the day the bond started accruing — the result tells you how many dollars of adjusted principal exist today for every original dollar of face value.

Worked example

A 10-year TIPS is issued with a dated date reference CPI of 290.000. Three years later, the reference CPI for today's settlement date is 307.700. The index ratio is $307.700 / 290.000 = 1.06103$. On $100,000 of original face value, the adjusted principal is now 100{,}000 \times 1.06103 = \106{,}103$. If the bond's fixed real coupon rate is 1.75$106{,}103 \times 0.0175 / 2 \approx $928.40$, not the$875 you'd get from the unadjusted $100,000 face — the coupon itself scales with the index ratio because it's paid on adjusted principal.

Worked example: a reopening auction

The Treasury periodically reopens existing TIPS issues (auctioning more of an already-outstanding bond) rather than only issuing brand-new ones. A reopening auction of the bond above, settling when the index ratio is 1.06103, means a buyer bidding on $100,000 of face value actually pays for $106,103 of adjusted principal at the auction's clearing real yield, plus accrued interest calculated on that adjusted principal. The settlement amount explicitly multiplies the auctioned face amount by the index ratio on the settlement date, so two investors buying the "same" bond at different reopening auctions months apart pay for different amounts of adjusted principal per $100,000 of face, purely because the index ratio has moved between auctions.

What this means in practice

Every TIPS quote convention (clean price quoted per $100 of original face, then multiplied by the index ratio to get the actual invoice amount) exists so dealers can quote a real-yield-consistent price without re-deriving CPI history every time; the index ratio is the bridge back to actual settlement dollars. Investors comparing TIPS across different dated dates need the index ratio to know how much inflation compensation is already embedded versus how much remains to accrue.