**The Formula for Inventory Turnover Calculation (Table of Contents)**

## What is Modified Duration Formula?

Modified duration is a formula that provides the change in the price of a bond with respect to the change in the interest/coupon rates. The concept of modified duration states that the price of the bond is inversely proportional to the change in the interest rates. Since the bond market is complex as compared to the equity market, understanding the modified duration of a bond is very crucial in making investment decisions.

The calculation of the modified duration formula is as follows,

Where,

**Macaulay Duration =**Duration of a bond after considering the time-weighted present value of the principal and interest cash flow (Calculated as per the formula is given above).**YTM =**Yield to maturity is the total return an investor will earn when the bond is held until its maturity.**n =**Number of coupons per year.

### Examples of Modified Duration Formula (with Excel Template)

Let’s see some simple to advanced practical examples of the modified duration equation to understand it better.

#### Modified Duration Formula – Example #1

**In the illustration, we are given that a bond is being floated in the market whose YTM will is 8%, the time period being 3 years, Coupon is paid annually and the Macaulay duration is 2.70. we are required to calculate the Modified duration.**

**Solution**

Here since the coupon is paid annually n would be 1, After application of the formula we will get

- = 2.70/(1 + 0.08/1)

**Modified Duration will be –**

**Modified Duration = 2.50**

This shows that every 1 % or 100 bases point movement in the interest rate of the bond with show an inverse movement in price by 2.5 %

- i.e. if interest rate increase by 1 % the bond price will reduce by 2.5 % and
- if the interest rate decreased by 1 % the bond price will increase by 2.5%.

#### Modified Duration Formula – Example #2

** In this illustration, we will calculate both the Macaulay duration and the modified duration of the bond, the details of the bond in consideration is as follows,**

**Time period = 5 years**

**Face value = Rs. 1000**

**Annual Coupon = 6 %**

**Current interest rate = 7 %**

**Solution**

Use below given data for the calculation of the modified duration formula.

- Macaulay Duration = 4269.74/959

**Macaulay Duration will be –**

**Macaulay Duration = 4.45 years**

Calculation of modified duration can be done as follows-

- = 4.45/(1 + 0.07/1)

**Modified Duration will be –**

**Modified Duration = 4.16**

This shows that every 1 % or 100 bases point movement in the interest rate of the bond with show an inverse movement in price by 4.16 %

- i.e. if interest rate increase by 1 % the bond price will reduce by 4.16 % and
- if the interest rate decreased by 1 % the bond price will increase by 4.16 %.

#### Modified Duration Formula – Example #3

**In the illustration, we are given that a bond is being floated in the market whose YTM will is 7 %, the time period being 4 years, Coupon is paid annually and the Macaulay duration is 3.60. we are required to calculate the Modified duration.**

**Solution**

Here since the coupon is paid annually n would be 1, After application of the formula we will get,

- = 3.60 / (1 + 0.07/1)

**Modified Duration will be –**

**Modified duration = 3.36**

This shows that every 1 % or 100 bases point movement in the interest rate of the bond with show an inverse movement in price by 3.36 %

- i.e. if interest rate increase by 1 % the bond price will reduce by 3.36 % and
- if the interest rate decreased by 1 % the bond price will increase by 3.36 %.

### Calculator

You can use these modified duration formula calculator

Macaulay Duration | |

YTM | |

n | |

Modified Duration Formula | |

Modified Duration Formula = | Macaulay Duration / (1 +YTM/n) | |

0 / (1 +0/0) = | 0 |

### Relevance and Use of Modified Duration Formula

- Since the change in the interest rate is inversely proportional to the change in the price of the bond, the investor can calculate the change in the price of a bond easily whenever there is a change in the interest rate.
- It also measures the risk of the bond with the change in yield of the price of the bond
- As the bond market is more complex than the equity market modified duration work as a tool for decision making
- Since the duration of the bond is directly proportional to the bond prices, we can understand that the increase in the duration of the bond will lead to an increase in the price of the bond.

### Recommended Articles

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