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:
The breakeven inflation rate (blue) equals the fixed coupon bond yield (red) less the inflation-linked bond yield (green).
PIMCO's description is copied below:
To compare ILBs with nominal government bonds and determine their relative value, investors can look at the difference between nominal yields and real yields, called the breakeven inflation rate. The difference indicates the inflation expectations priced into the market; it is the rate differential at which the expected returns of ILBs and nominal bonds are equal. If the actual inflation rate over the life of the bond is higher than the breakeven inflation rate, investors would earn a higher return holding ILBs while having lower inflation risk.
If the actual inflation rate is lower than expectations, the nominal bond of the same maturity would garner a higher return, though with a higher inflation risk. For example, if a 10-year nominal UK gilt is yielding 2.5% and a 10-year UK inflation-linked bond is yielding 0.25%, then the breakeven inflation rate is 2.25%. If an investor believes the UK inflation rate will be above 2.25% for the next 10 years, then a then an Inflation-Linked Bond would be a more attractive investment.
Question 1023 monetary policy, inflation, breakeven inflation rate
If the breakeven inflation rate was far above the US Fed's long term 2% average inflation target, the Fed would be expected to:
When inflation expectations are too high above the US Federal Reserve's 2% pa inflation target, the Fed would be expected to raise the federal funds rate.
This is contractionary monetary policy would be expected to slow down future GDP growth and inflation, helping the Fed achieve its inflation target.
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:
The inflation-indexed principal is expected to grow by the 4% pa inflation rate compounding semi-annually to be $1485.94739598 (=1000*(1+0.04/2)^(10*2)) after 10 years (=20 semi-annual periods).
The 20th semi-annual coupon paid in 10 years is expected to be $18.574342 (=0.025/2*1485.94739598), which equals the semi-annual coupon rate of 1.25% (=2.5%/2) multiplied by the principal in 10 years.
###\begin{aligned} \text{Coupon}_\text{10 years, Semi-annual} &= \text{CouponRate}_\text{Semi-annual} \times \text{InflationIndexedPrincipal}_\text{10 years} \\ &= \text{CouponRate}_\text{Semi-annual} \times \text{Principal} \times \left( 1+\dfrac{r_\text{inflation, compounding semi-annually}}{2} \right)^{10 \times 2} \\ &= \dfrac{0.025}{2} \times 1000 \times \left( 1+\dfrac{0.04}{2} \right)^{10 \times 2} \\ &= 0.0125 \times 1000 \times \left( 1+0.02 \right)^{20} \\ &= 0.0125 \times 1485.94739598 \\ &= 18.574342 \\ \end{aligned}###