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Question 1022  inflation linked bond, breakeven inflation rate, inflation, real and nominal returns and cash flows

Below is a graph of 10-year US treasury fixed coupon bond yields (red), inflation-indexed bond yields (green) and the 'breakeven' inflation rate (blue). Note that inflation-indexed bonds are also called treasury inflation protected securities (TIPS) in the US. In other countries they're called inflation-linked bonds (ILB's). For more information, see PIMCO's great article about inflation linked bonds here.

The 10 year breakeven inflation rate (blue) equals the:

Question 1024  inflation linked bond, bond pricing

PIMCO gives the following example of an Inflation Linked Bond (ILB), called Treasury Inflation Protected Securities (TIPS) in the US.

How do ILBs work?

An ILB’s explicit link to a nationally-recognized inflation measure means that any increase in price levels directly translates into higher principal values. As a hypothetical example, consider a $1,000 20-year U.S. TIPS with a 2.5% coupon (1.25% on semiannual basis), and an inflation rate of 4%. The principal on the TIPS note will adjust upward on a daily basis to account for the 4% inflation rate. At maturity, the principal value will be $2,208 (4% per year, compounded semiannually). Additionally, while the coupon rate remains fixed at 2.5%, the dollar value of each interest payment will rise, as the coupon will be paid on the inflation-adjusted principal value. The first semiannual coupon of 1.25% paid on the inflation-adjusted principal of $1,020 is $12.75, while the final semiannual interest payment will be 1.25% of $2,208, which is $27.60.

Forecast the semi-annual coupon paid in 10 years based on the bond details given above. The 20th semi-annual coupon, paid in 10 years, is expected to be: