Understand duration as a measure of bond price volatility, and how it can help investors make informed decisions. Delve into bond value changes, interest rate impacts, coupon rates, and time to maturity factors. Includes examples, table analyses, and further reading references.
So far in this chapter, we discussed the following relationships:
The value of a bond changes in the opposite direction to a change in interest rates: as interest rates rise, bond prices fall; as interest rates fall, bond prices rise.
Given two bonds with the same term to maturity and the same yield, the bond with the higher coupon is usually less volatile in price than the bond with the lower coupon.
Given these relationships, it is fairly easy to compare bonds with the same term to maturity or the same coupon.
However, how do we compare bonds with different coupon rates and different terms to maturity? For example, how can we determine whether a bond with a high coupon and a long term will be more or less volatile than a bond with a lower coupon and a shorter term?
A change in interest rates affects the price of different bonds differently, depending on features such as coupons, maturities, and protective covenants. In fact, a change in interest rates is one of the main risks faced by investors holding fixed-income securities. To make sound investment decisions, you must be able to determine the impact of interest rate changes on the prices of different types of bonds.
The calculation that combines the impact of both the coupon rate and the term to maturity is called duration.
Duration is a measure of the sensitivity of a bond’s price to changes in interest rates. It is defined as the approximate percentage change in the price or value of a bond for a 1% change in interest rates. The higher the duration of the bond, the more it will react to a change in interest rates.
When duration is known, that value helps investors determine the bond’s, or the bond fund’s, volatility—the amount of change in price as interest rates change. In this way, a single duration figure for each bond can be compared directly with the duration of every other bond.
You are interested in buying a DEC Corp. bond priced at 105 with 12 years left to maturity, but you are concerned that interest rates are going to rise by 1% over the next year. The duration of the bond is 10, which means that its price will change by approximately 10% for each 1% change in interest rates. You determine that the price of the bond could drop from 105 to 94.50, if your expectations about the interest rate change are correct. This figure is calculated as follows:
$$ 105 - (0.10 imes 105) = 94.50 $$
A higher duration translates into a higher percentage price change for a given change in yield. To earn the greatest return, you should therefore invest in bonds with a higher duration when you expect interest rates to decline.
Conversely, when interest rates are expected to rise, you should invest in bonds with low duration to protect a bond portfolio from a dramatic decline.
| Bond Duration | Current Price | Price When Interest Rates Rise by 1% | Price When Interest Rates Fall by 0.5% |
|---|---|---|---|
| Bond A: Duration 10 | $1,000 | $900 (-10%) | $1,050 (+5%) |
| Bond B: Duration 5 | $1,000 | $950 (-5%) | $1,025 (+2.5%) |
Note: The price changes for any range of interest rate changes can be estimated as long as the bond duration is known. For example, the price change for Bond B with a duration of 5 and a 0.50% interest rate drop is 2.5% (calculated as 5 × 0.50).
Calculating a bond’s duration is a complicated process, and the value can also change over longer holding periods and larger interest rate swings. Therefore, we do not show the formula for calculating duration in this course. However, the concept is elaborated significantly in three CSI courses: Investment Management Techniques (IMT), Portfolio Management Techniques (PMT), and Wealth Management Essentials (WME).
Duration: A measure of the sensitivity of a bond’s price to changes in interest rates, representing the approximate percentage change in price for a 1% change in interest rates.
Coupon Rate: The annual interest rate paid on a bond, expressed as a percentage of the face value.
Term to Maturity: The time remaining until the bond’s principal amount is repaid.
Volatility: The degree of variation of a bond’s trading price, often measured by standard deviation.
Interest Rate Risk: The potential for investment losses due to changes in interest rates.
Duration helps investors understand the potential impact of interest rate movements on bond prices, allowing them to make more informed investment decisions based on expected interest rate changes.
While maturity measures the time remaining until the bond’s principal is repaid, duration measures the bond’s price sensitivity to interest rate changes.
Not necessarily. A higher duration means greater sensitivity to interest rate changes, which can translate into higher gains when rates fall but also larger losses when rates rise. Your investment strategy should align with your interest rate outlook.
This comprehensive guide provides clarity on bond duration and its role in managing bond investment risks. Continue exploring advanced topics in courses like IMT, PMT, and WME for deeper understanding and risk management strategies.