# Inflation Premium

Inflation premium is the component of a required return that represents compensation for inflation risk. It is the chunk of interest rate which investors demand in addition to real risk-free rate due to risk of decrease in purchasing power of money. It can be estimated as the difference between the yield on Treasury inflation-protected securities (TIPS) and Treasury bonds of the same maturity.

A required return i.e. interest rate on a bank loan, yield on a bond or the required return on equity can be estimated by starting with a real risk-free rate and adding premiums for each additional risk taken such as inflation risk, default risk, etc. Inflation premium is the allowance i.e. the additional chunk of interest rate that represents the risk of expected inflation. Inflation premium must not be added if we use the nominal risk-free rate.

## Formula

To estimate inflation risk premium, we must compare the yield on bonds which are otherwise identical but only one of them carries inflation risk. Majority of government and corporate bonds carry inflation risk. However, there are some government bonds which are inflation-protected, i.e. their coupon payments and face value are adjusted based on change in some price index such CPI. Hence, they do not carry inflation risk. The following formula can be used to estimate inflation premium:

$$ Inflation\ Premium={\rm Yield}_{TB}-{\rm Yield}_{IP} $$

Where **Yield _{TB}** is the yield on a Treasury bond and

**Yield**is the yield on Treasury inflation-protected security of the same coupon rate, redemption value, maturity, etc.

_{IP}If we already have a nominal rate and a real rate, we can isolate inflation risk premium using the following equation:

$$ Inflation\ Premium=\frac{1\ +\ nominal\ rate}{1\ +\ real\ rate}-1 $$

## Example

On 01 February 2018, US Treasury Yield Curve Rate for 5, 10 and 20-year maturity is 2.56%, 2.78% and 2.90% respectively and US Treasury Real Yield Curve Rates for 5, 10 and 20-year maturity are 0.63%, 0.67% and 0.78% respectively. Find out the inflation premium appropriate for a bond with 10 years maturity.

For an interest rate for 10 years the difference between US nominal and real rates for 10-year maturity is relevant. The inflation premium estimate is 2.11% (=2.78% - 0.67%).