The U.S. Treasury just announced that its reissue of a 10-year TIPS auctioned with a record-low yield to maturity of -0.75%. This is CUSIP 912828TE0, which will mature on July 15, 2022.

The previous record low was for this same Treasury Inflation-Protected Security, when it was first auctioned in July with a yield of -0.637%.

**Breakeven rate. **The 10-year Treasury closed today with a yield of 1.80%, setting the inflation breakeven rate for this TIPS at 2.55%. This means that inflation will have to average 2.55% for the next 10 years for this TIPS to beat a traditional Treasury. This is a near record-high breakeven rate (I think the record isÂ 2.64%) for a 10-year TIPS, as shown in this chart from Michael Ashton’s E-piphany blog:

The higher the breakeven rate, the more expensive the TIPS. Buyers were paying a lot at today’s auction, that is clear. (And I should point out that this same TIPS, when it first auctioned in July, had a much more modest breakeven rate of 2.17%.)

**Reaction. **The Wall Street Journal cited ‘lukewarm‘ support for this auction, despite the record-low yield. The article notes:

TIPS shield owner from inflation because their payouts increase as the consumer price index rises. But without inflation, buying at a negative yield means the investor will get a smaller amount of money paid back than originally lent out.

Because of newfound inflation concerns, prices on TIPS have soared recently–but perhaps so much so that it made Thursday’s auction a bit too expensive, analysts say.

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Nice website on TIPS. Just wondering, how does the math work on today’s auction of 10 year TIPS. How does a -.75% yield and a .125% coupon work out to a price of around 108. My math is a bit rusty.

Technically, the (full) price equals the sum of the cash flows discounted by the yield to maturity. With TIPS, we do the math in real space so we can ignore the inflation accretion to date and not worry about what will accrue in the future. So you discount 20 coupons of 0.125% and a terminal payment of 100%, at a rate of (1 + -0.75%)^t . Note that since you’re discounting at a negative number, the coupon actually increases in value in real space! On Excel, it’s PRICE(SettlementDate,Maturity,Coupon,Yield,100,2,1), where in this case SettlementDate is 9/28/2012, MaturityDate is 7/15/2022, Coupon is 0.125%, and Yield is -0.75%.

Thank you Michael! I gave my lame and simplistic attempt at an answer, below. I am stuck with English, not Mathematics.

James, I was good at math … a long time ago. Anyway, I can get close to an answer. Since you will be getting 0.125% on this TIPS for 9 years, 10 months, but your actual yield to maturity is -0.75%, you had to pay for 0.875% yield upfront, over 10 years. It looks like you paid $108.52 for $100 of value, which might work out pretty close for 9 years, 10 months … you’ll get $8.52 in extra interest for every $100 invested? That’s my theory.

Thank you for the replies. Very informative. My Excel didn’t want to accept a negative yield but using .87% for the coupon and 0% for the yield brought me to the price.

Ha – Oops, my bad. Your method will get you pretty close, but I forgot that Excel has that glitch. I wrote my own function to handle the case of negative yields. If you want to, you can use it:

Function TIPSPricefromYield(Settlement As Date, Maturity As Date, Coupon As Double, Yield As Double)

Dim price As Double

If Yield > 0 Then ‘then we don’t need anything different!

price = WorksheetFunction.price(Settlement, Maturity, Coupon, Yield, 100, 2, 1)

GoTo done:

End If

accumulator = 0

firstcoup = WorksheetFunction.CoupPcd(Settlement, Maturity, 2, 1)

priorcoup = firstcoup

Do Until priorcoup = Maturity

nextcoup = WorksheetFunction.CoupNcd(priorcoup, Maturity, 2, 1)

If accumulator = 0 Then

x = (1 – AccrualFrac(priorcoup, nextcoup, 3, Settlement, 2)) / 2

Else

x = x + 0.5

End If

pvcashflow = Coupon * 100 / 2 / (1 + Yield / 2) ^ (2 * x)

accumulator = accumulator + pvcashflow

priorcoup = nextcoup

Loop

‘add maturity flow and last coupon

accumulator = accumulator + 100 / (1 + Yield / 2) ^ (2 * x)

‘subtract accrued int

price = accumulator – WorksheetFunction.AccrInt(firstcoup, WorksheetFunction.CoupNcd(firstcoup, Maturity, 2, 1), Settlement, Coupon, 100, 2, 1)

done:

TIPSPricefromYield = price

End Function

I do my estimated price calculations using an excel formula derived from the equations given in the Federal Register. It includes accrued interest, and handles reopenings after the first semi-annual interest payment. It is almost accurate, within about a penny per $1K par value. I’ve never tried tracking down exactly why it isn’t perfect, but I assume it has to do with excel not using enough precision in the calculations. Here’s the monster (formula is for row 53 of the worksheet):

H53*10*(G53/F53)*(J53/0.02+(J53/0.02)*(1-(1/(1+I53/2)^(INT((E53-C53+15)/182.5+0.9)-1)))/(I53/2)+(1/(1+I53/2)^(INT((E53-C53+15)/182.5+0.9)-1))*100)/(1+(IF(D53=C53,182,MOD(D53-C53,182))/182)*(I53/2))

C53 is the issue date, 9/29/2012

D53 is the dated date, 7/15/2012

E53 is the maturity date, 7/15/2022

F53 is ref CPI for the dated date, given in the offering announcement, 229.93606

G53 is ref CPI for the issue date, given in the offering announcement, 229.14140

H53 is the number of bonds, at 1,000 per bond

I53 is the auction rate, here -0.75%

J53 is the coupon rate, lately always 0.125%

result for this auction is $1085.46 per $1k par.

You can also just goal seek in excel to find a negative irr on the cash flows for the tips assuming zero inflation.

OK, then, you folks can keep discussing this, you lost me when you used that > sign. Still, Thanks Michael Ashton, for contributing, since I follow your every word. I highly recommend Michael’s blog …http://mikeashton.wordpress.com/

I’m honored and humbled. Thanks so much!

30 year TIPS next month, I wonder what the breakeven inflation rate will be, and what the real yield will be? I probably will wait for February because I feel I may be able to get a higher real yield, but I could be wrong.

Joe, as of today you are looking at a 30-year breakeven rate of 2.515%, with the TIPS that will be reissued yielding 0.435% and the traditional 30-year Treasury yielding 2.95%. When it was first issued on Feb. 16, this TIPS yielded 0.770%. On that date, the 30-year Treasury was 3.14%, creating a breakeven rate of 2.37%.

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