# Duration vs. Modified Duration

## What's the Difference?

Duration and Modified Duration are both measures used in finance to assess the sensitivity of a bond's price to changes in interest rates. However, there are some key differences between the two. Duration measures the weighted average time it takes for an investor to receive the bond's cash flows, including both coupon payments and the principal repayment. It provides an estimate of the bond's price volatility in response to interest rate changes. On the other hand, Modified Duration is a modified version of duration that takes into account the bond's yield. It is a more accurate measure of price sensitivity as it adjusts for the bond's yield, making it suitable for comparing bonds with different coupon rates and maturities.

## Comparison

Attribute | Duration | Modified Duration |
---|---|---|

Definition | The measure of the average time it takes to receive the cash flows from an investment. | The measure of the sensitivity of a bond's price to changes in interest rates. |

Calculation | Weighted average of the time until each cash flow is received, considering the present value of each cash flow. | Duration multiplied by (1 + yield to maturity). |

Units | Time (years) | Time (years) |

Interpretation | Higher duration indicates higher interest rate risk and higher price volatility. | Modified duration provides an estimate of the percentage change in price for a given change in yield. |

Use | Used to assess the risk and price sensitivity of fixed-income securities. | Used to estimate the impact of interest rate changes on bond prices. |

## Further Detail

### Introduction

When it comes to fixed-income investments, understanding the concept of duration is crucial for investors. Duration is a measure of the sensitivity of a bond's price to changes in interest rates. It helps investors assess the potential impact of interest rate fluctuations on their bond portfolios. However, there are different types of duration measures, with two of the most commonly used being duration and modified duration. In this article, we will explore the attributes of duration and modified duration, highlighting their similarities and differences.

### Duration

Duration is a measure of the weighted average time it takes to receive the cash flows from a bond, including both coupon payments and the return of principal at maturity. It provides an estimate of the bond's price sensitivity to changes in interest rates. The higher the duration, the more sensitive the bond's price is to interest rate movements.

Duration takes into account the timing and magnitude of all cash flows, making it a comprehensive measure of a bond's interest rate risk. It considers both the coupon payments received over the bond's life and the final principal repayment. By calculating the present value of each cash flow and weighting it by the proportion of the bond's price it represents, duration provides a single number that summarizes the bond's interest rate risk.

For example, if a bond has a duration of 5 years, it means that a 1% increase in interest rates would lead to an approximate 5% decrease in the bond's price. Conversely, a 1% decrease in interest rates would result in a 5% increase in the bond's price.

### Modified Duration

Modified duration is a modified version of duration that adjusts for the bond's yield. It is a more commonly used measure as it provides a better approximation of the bond's price sensitivity to interest rate changes when compared to duration.

Modified duration is calculated by dividing the duration by 1 plus the bond's yield to maturity. By incorporating the yield, it accounts for the fact that as interest rates change, the bond's yield will also change. This adjustment makes modified duration a more accurate measure of price sensitivity.

Similar to duration, a higher modified duration indicates a greater price sensitivity to interest rate movements. For example, if a bond has a modified duration of 4 years, a 1% increase in interest rates would lead to an approximate 4% decrease in the bond's price. Conversely, a 1% decrease in interest rates would result in a 4% increase in the bond's price.

### Key Similarities

Both duration and modified duration are measures of a bond's price sensitivity to changes in interest rates. They provide investors with an understanding of how much a bond's price is likely to change in response to interest rate movements. Additionally, both measures take into account the timing and magnitude of all cash flows, including coupon payments and principal repayment.

Furthermore, duration and modified duration are expressed in years, making them easily comparable across different bonds. This allows investors to assess the interest rate risk of various bonds and make informed investment decisions.

### Key Differences

While duration and modified duration share similarities, there are some important differences between the two measures.

One key difference is that duration is an absolute measure, while modified duration is a relative measure. Duration provides the actual time it takes to recover the bond's price through cash flows, while modified duration adjusts for the bond's yield. This adjustment allows investors to compare the price sensitivity of bonds with different yields.

Another difference is that duration is more suitable for bonds with fixed cash flows, such as zero-coupon bonds, while modified duration is better suited for bonds with variable cash flows, such as coupon-paying bonds. Modified duration takes into account the changing yield of the bond, making it a more accurate measure for bonds with varying coupon payments.

Additionally, duration is a more comprehensive measure that considers all cash flows, including the final principal repayment, while modified duration focuses primarily on the bond's coupon payments. This difference makes modified duration more appropriate for bonds with shorter maturities, where the principal repayment is a smaller portion of the bond's price.

### Conclusion

Duration and modified duration are both important measures for assessing the interest rate risk of fixed-income investments. While duration provides a comprehensive measure of a bond's price sensitivity to interest rate changes, modified duration adjusts for the bond's yield, making it a more accurate measure in most cases. Understanding the attributes of duration and modified duration can help investors make informed decisions when managing their bond portfolios and navigating the ever-changing interest rate environment.

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