# Maturity Premium

Maturity premium (also called maturity risk premium (MRP)) is the component of required return that accounts for the additional interest rate risk and reinvestment risk of an investment that results from longer time till maturity. Maturity risk premium increases with increase in the time to maturity. It can be estimated by comparing securities which are identical except for the difference in their time to maturity.

Price of an investment with longer maturity is subject to higher fluctuation due to changes in market interest rates. The risk of such price fluctuation is called interest rate risk and is represented by a bond’s duration. It can be illustrated by the fact that a bond’s value is determined as the present value of its coupon payments and redemption value. Over a longer period, discounting and compounding makes a bigger and bigger chunk of the investment return and any change is more pronounced.

An investment with longer maturity also has higher reinvestment risk, the risk that the cash flows received over the life of the investment can’t be reinvested at a good enough rate.

## Estimation Formula

Maturity premium varies with time, i.e. maturity premium over 10 years will be higher than maturity premium for 5 years. Hence, we must consider the maturity of investment for which we are determining the required return and add a maturity risk premium appropriate for the given maturity.

The following formula gives a general framework for estimation of maturity premium:

$$ Maturity\ Risk\ Premium={\rm Yield}_{n+m}-{\rm Yield}_n $$

Where **Yield _{n+m}** is the yield on a bond with (n+m) years to maturity and

**Yield**is the yield on a bond with n years till maturity and the bonds are otherwise identical, i.e. they have same default risk i.e. credit rating, liquidity risk i.e. bid-ask spread and both are either inflation-protected or not.

_{n}## Example

You are in situation where the risk-free rate is 2.5%, the default risk premium is 3%, the liquidity risk premium is 0.5% and you need to determine the required return on a 15-year bond. The risk-free rate is based on a 10-year Treasury bond and the difference between yield on 10-year Treasury bond and 10-year Treasury inflation-protected securities (TIPs) is 2.2%

To estimate the required return, we must add the inflation premium, default risk premium, liquidity premium and maturity premium to the real risk-free rate.

The risk-free rate on a Treasury bond is the nominal risk-free rate so we do not need to add the inflation premium (which equals the difference between yield on US Treasury bonds and TIPS, i.e. 2.2%). Further, since the risk-free rate is based on 10-years maturity, we need to add maturity premium that applies for the additional 5 years, which can be estimated as the yield difference between 15-year and 10-year Treasury bond, let’s say it is 1.5%.

Our required return would be 7.5%:

$$ Required\ Return=2.5\%+3\%+0.5\%+1.5\%=7.5\% $$