What is bond duration in simple terms

When it comes to bonds, the most commonly mentioned parameters are yield and maturity.

But investors have another important tool to help them assess the risks and sensitivity of a security to changes in interest rates: duration.

At first glance, the term sounds complicated and is more suitable for academic finance textbooks.

However, when you get down to it, duration is simply a way to measure how quickly an investor will get their money back and how the bond's price will change if market rates rise or fall.

Definition of duration

Duration is the average weighted term for the return of funds invested in a bond, taking into account all future payments on it (coupon payments and par value repayment). Simply put, this number shows how many years it will take an investor "on average" to get their invested money back.

For example, if a bond without coupons (the so-called discount bond) matures in 3 years, then its duration is 3. If the paper has regular coupon payments, the investor receives part of the money earlier, and the duration will be less than the term until maturity - say, 2.4 years.

How to calculate bond duration

At first glance, the duration formula looks cumbersome, but if you explain it step by step, everything becomes clear.

The formula looks like this:

$$D = \frac{\sum (CF_t \times t / (1+r)^t)}{\sum (CF_t / (1+r)^t)}$$

Where:

• CF_t — cash flow at time t (coupon or par value redemption),

• t — year (or period) number,

• r is the discount rate (current market yield of the bond),

• D —duration in years.

In simple terms, we take all future payments on a bond, "weight" them over time to today's value, and then divide by the bond's price.

Step by step example

Let's imagine a bond with 1000 , a term of 3 years and a coupon of 10% per annum . This means that the investor receives:

• at the end of the 1st year: 100 ,

• at the end of the 2nd year: 100 ,

• at the end of the 3rd year: 100 + 1000 (return of the nominal value).

If the discount rate is the same as the coupon (10%), then the bond price = 1000. Now we calculate the duration:

1. We multiply each payment by the time it is received:

   • 100 × 1 = 100

   • 100 × 2 = 200

   • 1100 × 3 = 3300

2. We bring it to today's value (divide by (1+0.1)^t):

   • 100 / 1,1 ≈ 90,9

   • 200 / 1,1² ≈ 165,3

   • 3300 / 1,1³ ≈ 2478,9

3. Add up and divide by the bond price (1000):

   $$D ≈ (90.9 + 165.3 + 2478.9) / 1000 = 2.73 years$$

That is, the duration of this bond is approximately 2.7 years , which is less than its maturity (3 years), since part of the money is returned earlier through coupons.

What is the purpose of bond duration?

1. Assessing the risk of rate changes.

The main use of duration is to measure how much a bond's price will change when market interest rates change. A simple rule of thumb is that the higher the duration, the more sensitive the security is to changes in yield.

2. Comparison of different bonds.

Duration helps compare securities with different maturities and coupon payments. This is especially important if an investor is building a bond portfolio and wants to understand its sensitivity to rates.

3. Portfolio management.

Institutional investors (funds, banks) use duration to balance assets and liabilities. If, for example, a bank has liabilities for 5 years, it tries to select assets with similar duration to reduce risk.

A simple rule to remember

You can think of duration as a "sensitivity pendulum":

• A duration of 2 years means that if rates rise by 1%, the bond price will fall by about 2%.
• Duration of 7 years - a drop of about 7% with the same change in rates.

This is not an exact formula, but a simplified rule, but it helps a lot in everyday life.

Why does a private investor need this?

Many novice investors think that the main thing is to choose a bond with a good yield. But experienced players always look at duration. It shows how risky it is to hold a security given possible changes in the economy.

If you expect rates to rise, it is better to take securities with a short duration. If rates, on the contrary, will fall, a long duration will allow you to earn more on the price increase.

Bond duration is not a complicated formula for financiers, but a convenient tool that helps you understand when exactly your money will be returned and how much the price will change as rates fluctuate.

For an investor, this means: the higher the duration, the greater the risk and potential return; the lower the duration, the more stable the investment will be. Understanding this indicator makes investments in bonds more conscious and helps to avoid unpleasant surprises.