## DURATION Function

The duration function in Excel is a financial tool that calculates the length of time required for an investment to double in value, assuming a fixed annual interest rate and periodic compounding. This function is often used to compare the relative value of investments with different interest rates and to determine the impact of interest rate changes on an investment’s future value.

To use the duration function in Excel, you need to input four arguments: the settlement date, the maturity date, the yield, and the redemption value. The settlement date is the date on which the investment is made, and the maturity date is the date on which the investment reaches its full value. The yield is the annual interest rate, expressed as a percentage, that is earned on the investment, and the redemption value is the amount of money that will be received at the end of the investment period.

To calculate the duration of an investment, Excel uses the following formula:

Duration = (1 + Yield/N)^(-N*T) – 1

Where N is the number of compounding periods per year and T is the number of years between the settlement date and the maturity date.

For example, suppose you want to calculate the duration of a 10-year bond with a 5% annual interest rate that is compounded quarterly. To do this, you would input the following values into the duration function:

Settlement date: 1/1/2021 Maturity date: 1/1/2031 Yield: 5% Redemption value: \$1000

With these inputs, the duration function would return a value of 9.5 years. This means that, based on the inputted interest rate and compounding frequency, it will take approximately 9.5 years for the investment to double in value.

One important thing to note is that the duration function calculates the duration of an investment based on the assumption that the yield remains constant throughout the investment period. In reality, interest rates may fluctuate over time, which can impact the value of an investment. For this reason, it is important to consider the potential impact of changing interest rates when using the duration function.

To illustrate this point, let’s consider the same 10-year bond with a 5% annual interest rate, but this time we will assume that interest rates rise to 7% halfway through the investment period. Using the duration function, we would calculate the duration of the investment as 9.5 years based on the initial 5% interest rate. However, if we recalculate the duration using the 7% interest rate for the second half of the investment period, we would get a different result.

To more accurately reflect the impact of changing interest rates on an investment, we can use a modified duration function, which adjusts the calculation to account for the impact of changing interest rates. The modified duration function is calculated as follows:

Modified duration = (1 + Yield/N)^(-N*T) – 1 / (1 + Yield/N)

Using the modified duration function, we can recalculate the duration of our 10-year bond assuming a 7% interest rate for the second half of the investment period. In this case, the modified duration would be 8.7 years, which is lower than the original duration calculated using the constant 5% interest rate. This illustrates the impact of changing interest rates on an investment’s duration.