TIPS Index Ratio: How the Reference CPI Is Worked Out

The TIPS index ratio is the multiplier that turns a Treasury Inflation-Protected Security’s par amount into its inflation-adjusted principal on a given date. You find it by putting that date’s reference CPI over the reference CPI from the bond’s dated date, then rounding to five decimals. Multiply par by it and you get the adjusted principal. Apply it to a real price plus real accrued interest and you get what a trade in the bond costs.

The division is simple. The work is in the reference CPI.

Where the reference CPI comes from

Treasury builds it from the non-seasonally-adjusted CPI-U, the consumer price index for all urban consumers, and it does so with a lag.

On the first day of a month, the reference CPI is simply the CPI-U for the third preceding month. On any other day it sits on a straight line between the CPI-U of the third preceding month and that of the second preceding month, moving a fraction of the way each day.

Take a date in June. M-3 is March and M-2 is April.

On June 1 the reference CPI is March’s figure. By the middle of the month it has climbed halfway toward April’s, and on July 1 it lands on April’s figure exactly, because for a July date April becomes the third preceding month and the climb starts again toward May.

So the reference CPI for any date in June is drawn from March and April data, and nothing published later in June or July changes it.

One date worked through

All the CPI values here are hypothetical. Say the CPI-U was 300.000 for March and 301.200 for April. June has 30 days, and the date is June 16. The bond’s reference CPI on its dated date was a hypothetical 250.000.

Shift the date and only the fraction changes.

Between June 16 and June 21 the ratio rose from 1.20240 to 1.20320. Each day in this hypothetical month adds 1.200 / 30 = 0.04 to the reference CPI.

What the ratio does to the bond

Adjusted principal is par times the index ratio. Coupons are paid at the real coupon rate on that adjusted principal, so as the ratio rises the dollar coupon rises with it, and if the ratio falls the coupon falls too.

There is a floor. It applies at maturity only, when Treasury pays the greater of the adjusted principal and par.

Before maturity the floor does nothing, so in that hypothetical any coupon paid while the ratio sat at 0.99200 would be figured on 9,920.00 of adjusted principal, and anyone pricing a sale on that date would scale the real price and accrued interest by 0.99200 as well, which leaves the protection concentrated in a single payment at the very end of the bond’s life.

Trades use the ratio as well. A purchase or sale is invoiced at the real price plus real accrued interest, scaled to par and multiplied by the ratio for the settlement date, which is the question taken apart in does a TIPS trade settle on the settle-date factor. The real coupon and real yield leave inflation out, since the ratio carries it, and how real returns line up against nominal ones is set out in real interest rates explained.

What goes wrong

The easiest error to make is using the newest CPI release. A trader sees an inflation print in the morning and expects the factor to jump. It won’t. The reference CPI for today was fixed by figures from months earlier, and the new print only starts to feed in when its month becomes the second preceding month of some later date.

Forgetting the accrued interest is the next one. The ratio multiplies real accrued interest exactly as it multiplies the real price, and an invoice rebuilt without that step will not match the confirmation.

Then there’s tax. Inside a taxable account, each year’s inflation adjustment to principal is taxed, so a rising ratio can create a tax bill on a bond you have not sold. Ask a tax professional how it is reported on your return.

Small things trip people as well:

• Using a seasonally adjusted CPI figure.
• Using the day of the month where the formula wants day minus 1.
• Rounding the share of the month before multiplying.
• Dividing by the wrong bond’s dated-date CPI.

How to check it on your own account

Treasury publishes the daily reference CPI and index ratio for each TIPS, and TreasuryDirect’s TIPS CPI data lets you look them up by CUSIP. Find your bond, find the date, and read the ratio straight off the table.

To test your own arithmetic, pick a date from that table, take the two monthly CPI-U figures the formula calls for, and run it. Your answer should match Treasury’s to five decimals.

Your broker’s trade confirmation should show either the index ratio used or the adjusted principal. If it shows the adjusted principal, divide by par.

Compare that with Treasury’s figure for the settlement date shown on the confirmation. If the two agree, the invoice was built on the right day’s factor, and you can rebuild the rest of the amount from the real price and accrued interest with the steps above. If they disagree by a few days’ movement, check whether the confirmation used the trade date, and ask your broker why.