# Even at the break-even inflation rate, isn't the YTM of a TIPS greater than that of a normal treasury bond?

At a the break-even rate of inflation, the semi-annual interest payments from a TIPS and a normal government bond would be roughly equivalent. However, the principal amount originally invested in the TIPS continues to be compounded by the inflation rate while the principal amount invested in a normal government bond is nominally constant. Thus, assuming a positive break-even inflation rate throughout the holding period up till maturity (which includes both the semi-annual interest payments and the gains due to compounding of the principal by the annual inflation), the yield to maturity for a TIPS should be larger. Is my analysis correct?

The quoted market "breakeven inflation" is the spread between quoted yields. It is an approximation of the true economic breakeven from a total return perspective (possibly ignoring the par put on principal) to maturity, but under normal circumstances, it is not far off the economic breakeven. (Since the exact pattern of future CPI would matter, even the economic breakeven has technical calculation issues.)

Take an imaginary world with a 5% nominal par coupon, and a 3% inflation-linked par coupon (2% breakeven).

• The conventional bond pays a 5% coupon.
• The TIPS starts out with a 3% coupon, with the 3% of a par value that is expected to grow at 2% a year. It takes a long time for 3% to catch up to 5% at a 2% growth rate. (The principal future value increases by 2% per year, but that increase needs to be discounted by the nominal discount rate of 5%.)

The lower coupons are compensated by growth of the principal, keeping total returns equal.

(For an easier example, imagine a 2% nominal bond, and a 0% inflation-linked.)

• I see... Say if I have 100 dollars to begin with and after a year, the normal bond pays 5 dollars but the TIPS only pays 102*0.03 (i.e. slightly more than 3 dollars). However, my principal also grows by 2 dollars. So at break-even inflation, wouldn't my TIPS still give me slightly more than 5 dollars a year, more than the 5 dollars given by the normal bond? Aug 17 '20 at 14:05
• The TIPS pays \$3(1.02). The increase in the principal value needs to be discounted by the nominal discount rate, so the increase in the NPV is less than \$2. So long as you calculate the breakeven inflation rate correctly, they give the same total return - by definition. Yes, the quoted breakeven is a spread but it is not far off. For par coupons, the spread matches the economic breakeven. Aug 17 '20 at 14:16