Bond Duration

When investing in bonds, understanding the concept of "duration" is essential. It plays a key role in assessing interest rate risk and anticipating how bond prices move.

Bonds

A bond is a financial instrument representing a debt issued by a company, a government, or a financial institution. The investor who buys a bond is essentially lending money to the issuer in exchange for repayment of the principal at maturity, along with a premium or regular interest payments (known as coupons). There are several types of bonds, including:

• Zero-coupon bonds, which pay no coupon but are issued at a discount to their face value (meaning you receive more at maturity than you originally lent, with no interest payments in between),
• Fixed-rate bonds, which pay regular fixed coupons until maturity,
• Floating-rate bonds, whose coupon rate varies based on a reference index such as Euribor or €STR.

Interest Rate Risk

Most bonds are issued at a fixed rate or as zero-coupon instruments. As a result, the yield on a bond is locked in at the time of issuance. The holder knows exactly how much they will be repaid, when, and on what schedule.

Between issuance and maturity, however, market interest rates can move.

• If the holder keeps the bond until maturity, those moves are irrelevant, the bond's rate is fixed.
• But if they decide to sell before maturity, the price they can achieve will depend on how interest rates have shifted, which can work either for or against them.

An Example

Take this example: suppose Alice buys ten French government bonds, each priced at €96.15, for a total investment of €961.50. In one year, at maturity, each bond will be redeemed at €100, for a total of €1,000. Her yield to maturity is therefore (1,000 / 961.50) − 1 = 4%.

Now suppose interest rates shift immediately after Alice's purchase:

• Rates fall: the following day, interest rates unexpectedly drop from 4% to 3%. Alice's bonds still pay out €100 in a year — that's fixed. But a new investor targeting a 3% return would now be willing to pay 100 / (1 + 3%) ≈ €97.09 per bond. If Alice sells immediately, she pockets a gain of around €0.94 per bond, or €9.40 across her portfolio. If she holds to maturity, she still receives €1,000 in a year, completely unaffected by the rate move.
• Rates rise: now suppose rates climb from 4% to 5%. Alice's bonds still redeem at €100, but a buyer seeking a 5% return would only pay 100 / (1 + 5%) ≈ €95.24 per bond. Selling now means a loss of around €0.91 per bond, or €9.10 across the portfolio. Holding to maturity, she still receives €1,000 in a year, regardless of what rates do.

Defining Duration

In this context, duration represents the weighted average time required to recover all of a bond's cash flows, coupons and principal repayment combined.

The key takeaway is this: the longer a bond's duration, the more sensitive it is to changes in interest rates. More precisely, the relationship is expressed as:

Change in bond price≈−Change in interest rate×Bond duration

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Conclusion

Duration is a critical concept for bond investors because it provides a direct measure of exposure to interest rate movements.

• The higher the duration, the more sensitive the bond is to rate changes. A rise in rates will cause a sharper drop in price.
• Conversely, a bond with a short duration will be far less affected by those swings.

For any saver or treasurer looking to minimize interest rate exposure, the logical approach is to favor bonds with the shortest possible duration, in practice, very short-term debt instruments known as money market instruments, or funds invested in such assets: money market funds.

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