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7.4.5 Duration As Measure Of Bond Price Volatility

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.

Duration as a Measure of Bond Price Volatility

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 two bonds with the same coupon rate and same yield, the bond with the longer term to maturity is usually more volatile in price than the bond with the shorter term to maturity.

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.

What is 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.

Example

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.

Impact of Interest Rate Changes on Bonds with Different Durations

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).

Key Takeaways

  • Duration is an essential measure for investors to gauge bond price volatility due to interest rate changes.
  • Bonds with higher duration are more sensitive to interest rate changes compared to bonds with lower duration.
  • Helpful examples and in-depth courses like IMT, PMT, and WME are recommended for further mastery of this concept.

Glossary

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.

Frequently Asked Questions (FAQs)

Why is duration an important measure for bond investors?

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.

How is duration different from maturity?

While maturity measures the time remaining until the bond’s principal is repaid, duration measures the bond’s price sensitivity to interest rate changes.

Is a higher duration always better?

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.


📚✨ CSC Exam Bank ✨📚

Welcome to the Knowledge Checkpoint! You'll find 10 carefully curated CSC exam practice questions designed to reinforce the key concepts covered. These questions will help you gauge your grasp of the material, identify areas that need further review, and ensure you're on the right track towards mastering the content for the Canadian Securities certification exams. Take your time, think critically, and use these quizzes as a tool to enhance your learning journey. 📘✨

Good luck!

## What is the primary concept that duration measures in the context of bonds? - [ ] The likelihood of a bond default - [ ] The bond's yield over its life - [x] The sensitivity of a bond’s price to changes in interest rates - [ ] The credit rating of the bond > **Explanation:** Duration measures how much a bond's price is expected to change with a 1% change in interest rates. This helps investors understand the interest rate risk of holding a bond. ## If two bonds have the same yield and term to maturity, which of the following statements is usually true? - [ ] The bond with the lower coupon rate is less volatile in price. - [ ] Both bonds will have the same price volatility. - [x] The bond with the higher coupon rate is less volatile in price. - [ ] Volatility does not depend on the coupon rate. > **Explanation:** Given the same yield and term to maturity, a bond with a higher coupon rate is typically less volatile in price compared to a bond with a lower coupon rate. ## How is the duration of a bond defined? - [ ] As the time remaining until the bond matures - [x] As the approximate percentage change in the price of the bond for a 1% change in interest rates - [ ] As the bond's yield to maturity - [ ] As the initial purchase price of the bond relative to its par value > **Explanation:** Duration is defined as the approximate percentage change in a bond’s price for a 1% change in interest rates, measuring interest rate risk. ## When are bonds with high duration most beneficial for investors? - [ ] When interest rates are stable - [ ] When the issuer's credit rating improves - [x] When interest rates are expected to decline - [ ] When inflation rates are high > **Explanation:** Bonds with high duration are most beneficial when interest rates are expected to decline because their prices will increase more significantly. ## What impact would a 1% increase in interest rates typically have on the price of a bond with a duration of 10? - [ ] An increase by 10% - [ ] No change - [x] A decrease by 10% - [ ] A decrease by 1% > **Explanation:** A bond with a duration of 10 would see its price decrease by approximately 10% with a 1% increase in interest rates. ## Which bond characteristic typically leads to greater price volatility? - [ ] Shorter term to maturity - [ ] Higher coupon rate - [x] Longer term to maturity - [ ] Lower credit rating > **Explanation:** A bond with a longer term to maturity is usually more volatile in price than one with a shorter term to maturity, assuming other factors are constant. ## You have a bond with a duration of 5. What happens to the bond’s price if interest rates fall by 0.50%? - [ ] The bond's price decreases by 2.5% - [x] The bond’s price increases by 2.5% - [ ] The bond’s price decreases by 5% - [ ] The bond's price increases by 5% > **Explanation:** If a bond has a duration of 5, a 0.50% drop in interest rates would cause its price to increase by 2.5% (5 * 0.50%). ## Given two bonds with the same coupon rate and yield, which one is more sensitive to interest rate changes? - [ ] The bond with more protective covenants - [x] The bond with the longer term to maturity - [ ] The bond with the shorter term to maturity - [ ] The bond with the higher yield > **Explanation:** Given the same coupon rate and yield, the bond with the longer term to maturity is generally more sensitive to interest rate changes. ## If you expect interest rates to rise, which type of bond should you invest in to reduce risk? - [ ] Bonds with high duration - [x] Bonds with low duration - [ ] Bonds with no duration - [ ] Bonds with variable interest rates > **Explanation:** When interest rates are expected to rise, it's safer to invest in bonds with low duration, as they are less sensitive to interest rate changes and thus experience smaller price declines. ## Why might an investor want to compare the duration of different bonds? - [ ] To determine the yield spread between bonds - [ ] To evaluate the liquidity of bonds - [x] To compare the interest rate risk and potential price volatility - [ ] To assess their tax implications > **Explanation:** Duration allows investors to compare the interest rate risk and potential price volatility of different bonds, helping them make more informed investment decisions.

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Tuesday, July 23, 2024