# What is bond duration: concept, formula, examples

When forming a bond portfolio, duration is one of the important risk indicators. In this article, we will tell you what duration is, how it works, and what it affects. The information will be useful to everyone who is interested in investing and earning on the stock exchange.

#### What is duration in simple words

Duration is the change in the price of the bond expressed in monetary units when the price expressed in yield to maturity changes.

For example, abstract paper is traded for 10% yield to maturity and today it is 1000 conventional units. The question arises: what will be the price in monetary units when the yield to maturity changes by 9% or, for example, by 11%? This question is answered by the duration indicator.

#### What the duration shows

In fact, simple duration shows:

- The time through which the bond will pay off.
- The price change in monetary units when the % yield to repayment changes.

The payback period of an investment is affected not only by its size, but also by the maturity date, yield and periodicity of coupon payments. Therefore, it is possible to draw conclusions:

- with a larger coupon size, the duration indicator will be lower, since you will be able to return your investments faster;
- with frequent payments, the duration is greater, which is explained by the spread of payments in time;
- with a high yield to maturity, the duration is low;
- with a long term until repayment, the duration indicator will be large.

Summarizing, let's say that, in fact, a low duration is a good indicator for an investor, because the invested capital will return faster, which means that the risks of investing are reduced.

*Read also: **What is trading*

#### How the duration of the bond is calculated: the formula

There are several formulas for calculating the duration:

- Macaulay duration;
- modified duration;
- effective duration.

Let's consider each option for calculating the duration in more detail.

##### Macaulay duration

Macaulay's duration is an indicator that indicates the period through which the investor will be able to return the funds invested in the bond.

**D**uration**=1 1001+0,1+2 100 (1+0,1)2+3 100 (1+0,1)3+4 100 (1+0,1)4+4 100 (1+0,1)41000= 3,486**

This example calculates a bond with a face value of 1,000, a one-time annual coupon of 10% (that is, 100) and a yield of 10%, purchased at a face value of 1,000 and 4 years to maturity.

Due to the presence of the coupon, the bond will "pay off" in 3,486 years, and the expected price change in the event of a price decrease/increase in % yield to maturity is 3,486%.

##### Modified duration

Modified duration is a modification of the result for the above-described Macaulay duration formula. It is calculated in order to more accurately reflect the change in the value of the bond in monetary units when the % of the price changes in yield to maturity:

**MD=D/(1+Y/n)**

where MD is the modified duration

D — Macaulay duration in years

Y — effective yield to maturity/offer, %

n — the frequency of coupon payments per hour.

Calculation of the duration according to this formula gives a more accurate result.

The usual duration shows the "payback" of the bond in years and roughly shows the change in price. And the modified duration is specially designed to calculate the change in value in money when the price changes in % yield to maturity.

*Read also: **How to start investing in Ukraine in 2023*

##### Effective duration

The effective duration is used for complex bonds in which the option is included. In Ukraine, there are no such instruments on the liquid market, but you will be interested to know how the duration is calculated according to this formula:

**Effective duration = (P (1) — P (2)) / (2 x P (0) x Y)**

P (0) = the initial price of the bond for 100 dollars of nominal value

P (1) = the price of the bond if the yield decreases by Y percent

P (2) = the price of the bond if the yield increases by Y percent

Y = estimated yield change used to calculate P (1) and P (2)

#### Bond portfolio duration: what an investor needs to know

Every investor should understand that duration is an indicator of bond risk. The longer the duration, the higher the risk of the bond.

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#### Frequently asked questions: bond portfolio duration

##### How is the duration measured

Usual duration is measured in years and other time values. The modified duration is measured in %.

##### What affects the duration

The duration is affected by the "length" of the paper — how much time until maturity: the longer the "length", the longer the duration. The size of the coupon yield also affects: the higher the coupon yield, the shorter the duration.