# How duration affects the price of your bonds

If you are invested in bonds or bond funds, there is a ratio that you should know: Duration. It helps estimate how much the price of your bond investment will fluctuate as interest rates go up or down. The higher the duration, the more sensitive a bond investment is to changes in interest rates.

Many factors influence the prices of bonds, one of which is interest rates. Whether interest rate movements are caused by central bank measures, economic indicators or fears of inflation, the effects on a bond are usually always the same: as interest rates rise, bond prices fall; bond prices rise as interest rates fall. But why are bond prices and interest rates heading in the opposite direction?

Bonds are fixed income securities and are used for investment purposes. Usually, a bond pays a fixed interest rate for a fixed term. The term of the bond expresses the length of time until the capital must be repaid. For example, for a ten year bond, interest is paid annually for 10 years from the issue date. At maturity, the bondholder receives the principal while the interest payments cease. Assuming that you have subscribed a bond for CHF 10 000 with a fixed interest coupon of 4 percent and a term of 10 years, you will receive interest at CHF 400 per year and at maturity or at maturity the nominal value (EUR 10 000) Francs) back.

However, when market rates suddenly rise, a newly issued bond, very similar to the original bond, could carry a coupon of 5 percent and pay interest at a rate of 500 francs a year. Your bond is thus less attractive compared to the newly issued bond. The reason for this is that the interest coupon on your bond is now below the market rate. So, the market value of your bond drops to bring it in line with the yield of the 5 percent coupon bond.

### Some bonds are more sensitive to interest rates than others.

The bond yield is the total return if you buy the bond today and hold it to maturity. It takes into account not only the coupons, but also the expected price gains or losses. With rising interest rates, the prices of bonds fall. The expected price gains from their low levels until maturity offset the disadvantage that the coupon is now below market interest rates. The same is true in the reverse case – with the difference that if interest rates fall, your bond becomes more attractive and the price therefore rises.

Bonds with the same credit are, however, not identical, and some bonds are more sensitive to interest rates than others. For example, a ten-year bond is subject to a higher interest rate risk than a five-year bond, since the capital is tied up over a longer period of time. Long-term bonds usually offer a higher yield than short-term bonds with the same credit rating to compensate for the interest rate risk.

But how can one measure how sensitive a bond investment reacts to interest rate movements? Here the duration comes into play. This measure combines several bond characteristics (such as expiration date, coupon payments, and so on) into a single number.

In contrast to the term of a bond, the duration of a bond is an abstract term. The simple duration expresses the period of time that an investor (on average) must wait to receive returns from the investment. The duration is shorter than the remaining term of a bond, for the reason that the amortization period is shortened by interim interest payments on the invested capital. In the case of so-called zero-coupon bonds (zero bonds), however, the duration corresponds to the maturity, as the interest payments are only made at the end of the term.

Duration is especially important for investors who want to sell their bonds before maturity. If you buy a ten-year bond with a fixed coupon of 4 per cent for 10 000 francs, you will receive 400 francs interest a year and ten years later you will get back the 10 000 francs invested – regardless of what happens to interest rates. However, if you sell this bond before maturity, the price of your bonds will be affected by changes in interest rates.

The so-called Macaulay Duration represents the average remaining term of all cash flows of a bond investment. This key figure shows how long the capital is tied on average. Your unit of measure is years. The Macaulay duration indicates the period during which the price effect and the coupon effect (reinvestment of distributions at changed market interest rates) balance each other as interest rates change. If the duration corresponds to the investment horizon, you are hedged against interest rate changes. It is therefore important that the investor equates the duration with the investment horizon.

### The higher the duration of a bond or a bond fund, the more the value falls when interest rates rise – and vice versa.

The modified duration, which is derived from the Macaulay duration, measures the elasticity of the bond price from the market interest rate. The modified duration is an approximate concept based on simplifying assumptions concerning the flat rate structure and the change (parallel offset). From a technical point of view, this indicator expresses the interest rate risk of a bond investment. It shows how sensitively the price of a bond or a bond fund reacts to an interest rate change of 1 percentage point.

In general, the price of a bond changes by about 1 percentage point in the opposite direction for each year of the bond, with an interest rate move of 1 percentage point (see the text box below). For example, if the interest rate rose by 1 percentage point, a bond or bond fund with an average maturity of five years would probably lose about 5 percent of its value. As a rule of thumb, you can remember that the higher the duration of a bond or a bond fund, the more the value falls when interest rates rise – and vice versa.

Let’s illustrate this with an example: Let’s say you have a bond with a remaining maturity of five years and a coupon of 4 percent. Market interest rates meanwhile amount to 5 percent. Thus, every year you are missing one percentage point of the market return. To make up for this, you would need to gain 5 percentage points. The price of the bond should therefore be 95 percent.

### Just because the duration of a bond or a bond fund is low does not mean that the investment is risk-free.

Long-dated bonds and low coupons have the longest duration. Such bonds are most sensitive to changes in market rates, and are volatile in a changing interest rate environment. Conversely, bonds with shorter maturities or higher coupons have a shorter duration. Bonds with shorter maturities are less sensitive to changes in interest rates and are therefore less volatile in a changing interest rate environment.

Duration is thus a very useful tool for building bond portfolios and risk management. For example, if a portfolio manager’s interest rate outlook changes, he can adjust the portfolio’s average duration by changing portfolio holdings to his interest rate forecast. These adjustments can be made either for the entire portfolio or for a specific segment within the portfolio. When a fund manager expects interest rates to rise, it makes sense to focus more on shorter-dated (ie, lower interest-rate) bonds. On the other hand, if he expects interest rates to fall during the life of the bond, longer dated bonds would be attractive, as the value of bonds would rise more sharply than comparable bonds with shorter maturities.

Just because the duration of a bond fund is low does not mean that the investment is risk-free. In addition to the duration risk, bonds and bond funds are subject to inflation risk, default risk and other risk factors. The duration of a bond portfolio or a bond fund also changes permanently, as the remaining term of the bonds held is shortened daily, bonds mature and interest rates fluctuate. Risk diversification and rebalancing are very important for long-term investment performance, but not so easy. The fund professionals of Migros Bank will gladly do that for you in our investment solutions.