What is the duration of a bond and how to determine it

What is the duration of a bond

When an investor buys a bond, he takes on risks. After all, securities are traded on the stock market, and their value can change depending on supply and demand, news and interest rates. To easily compare different bonds among themselves, investors use duration - the time for which investments will be returned, taking into account all payments, amortization (repayment of debt in installments) and other factors.

Why do you need the duration of a bond?

Duration helps to choose the most suitable bond and protect the investment portfolio from part of the risks. First of all from interest rates in economics: the longer the duration of a bond, the more the value of the security will change. The calculation also shows how the price and yield of certain bonds will rise or fall following interest rates.

Suppose an investor chooses between two fictitious bonds. They have the same denomination, yield and coupon size. The first bond is for three years, the second for five years. If the Central Bank raises the key rate by 1%, the price of bonds will decrease to compensate. In this case, a three-year bond looks less risky - it will also fall in price, but not as much as a five-year one.

If the key rate suddenly decreases, then everything works the other way around. The longer the duration, the stronger the bond grows. However, holding a lot of such securities in the portfolio is risky: everything can change quickly.

How to calculate the duration of a bond

It is not necessary for a private investor to dig into complex mathematics and use formulas. The Internet is full of portals where computers count everything for people. For example, in Russian there is Smart‑lab and Rusbonds, in English - Cbonds.

But in order to really understand what constitutes duration, and learn how to apply it, you should dig a little into the calculations. First at the level of the calculator, and then - formulas.

In the calculator on the website of the Moscow Exchange

Most of the bonds available to Russian private investors are traded on the Moscow Exchange. There are state, municipal and corporate securities. And the exchange itself helps to calculate the duration from market data. This is convenient if an investor chooses securities right now and needs calculations at the current price. And also calculator does not ask to register or buy a subscription, unlike some investment portals.

The details that an investor enters into the calculator are up to the individual. Perhaps the bonds are already in portfolio, and you need to calculate the duration based on other indicators. Or the investor is not going to hold the paper for four years and wants to choose a different end date.

The calculator will calculate everything for the investor. Duration by days and years will allow you to estimate how long the investments will pay off. And the modified duration will reflect interest rate risk, that is, probable price fluctuations.

According to the modified duration formula

Under what calculators easily show, a rather complex calculation is hidden. It consists of two parts: the Macaulay duration formula and the modified duration formula.

The first is the same average period for which the money will be returned. Let's calculate it manually OFZ‑PD 26211. Several indicators are needed:

• Price with accumulated coupon income (ACD): 1033.37 rubles.
• A coupon of 7% (34.9 rubles) is paid every six months.
• bond pay off in a year.
• The effective yield to maturity is 7.12% (for half a year it is 3.56%).

After that, you can deal with the modified duration and understand how the bond will react to a change in rates. Only the Macaulay duration and the effective yield of the bond itself will come in handy.

All these calculations will help the investor predict how the price and yield of bonds will change in the future. This is a legal form of providence that allows you to look into it.

For example, analysts orientedThe reduction follows: will the key rate be reduced in 2022 and to what level / Izvestia to cut the Central Bank rate by 75 basis points by the end of 2022 to 7.75%. Now you can estimate what will happen to the price of the bond.

All this means that if the rate is really lowered, then the bond could jump in price by almost seven percent. Provided that the investor buys it at the current price. Whether it will be possible to make money on this is a question, because analysts are sometimes mistaken, and other factors can affect the price more strongly.

According to the formula for a bond portfolio

People rarely buy a single bond issue and sit for years. Some investors make up a portfolio of bonds entirely, while others set aside some share for them. If interest rates are not taken into account, then fluctuations bonds can eat up part of the profit that the investor was counting on.

Therefore, there is a simple formula that will help you estimate the duration for the entire portfolio.

Let's say an investor has four bond issues:

1. OFZ‑PD 26211 with a duration of 354 days;
2. Yamalo-Nenets Autonomous Okrug with a duration of 418 days;
3. Sberbank with a duration of 1094 days;
4. «Rosneft» with a duration of 1487 days.

OFZ and Rosneft each account for 20% of the portfolio, the Yamalo-Nenets Autonomous Okrug - 15%, the remaining 45% go to Sberbank.

It's a little over 2.5 years. If an investor is not going to sell bonds earlier, his investments will return on average after this time.

How can an investor make money on understanding the duration of a bond?

A private investor can draw two main practical conclusions for himself: about risk and predicting the future.

The shorter the duration of a bond, the less risk the security carries and the lower the uncertainty. It will be useful for an investor to compare different bond issues with each other and look at his investment strategy. If the goal is to invest for a couple of years, and then sell everything and buy a car, then it is hardly worth looking at 10-, 15-, or 30-year bonds. It would be wiser to invest in shorter securities.

Professional analysts also help you figure out what to expect. Business publications and portals for investors publish consensus forecasts: assessments of many experts on changes in the key rate in the country. If specialists expect a rate cut, an investor can buy bonds with a long duration in advance - they are likely to rise in price. And if the regulator raises the rate, then bonds with a short duration will react weaker to this.

What is worth remembering

1. The duration of a bond is the time it takes an investor to return the money invested, taking into account all payments, amortization and other factors. Typically, the duration is less than the "life" of the bond.
2. Duration helps to look into the future. It shows how the cost can change and profitability bonds after changes in key rates in the economy. So, it allows you to predict what will happen with the money invested.
3. Duration formulas are not too simple, but calculators are available to all investors on the websites of stock exchanges and special portals.
4. The shorter the duration of the bond, the lower the risks and uncertainty - it is useful if the investment goal is close, on the horizon of several months or years. A long duration carries risks, but this is unimportant for an investor who plans for decades ahead.