Overview
Understanding the relationship between bond prices and interest rates is crucial for investors and finance professionals, especially those preparing for the Canadian Securities Course (CSC) exam. This chapter delves into the fundamental inverse relationship that exists between bond prices and bond yields, which fluctuate with prevailing interest rates.
Inverse Relationship Between Bond Prices and Bond Yields
The cornerstone of bond pricing is the inverse relationship between bond prices and bond yields. When interest rates rise, bond yields also increase, leading to a decrease in bond prices. Conversely, when interest rates fall, bond yields decline, leading to an increase in bond prices. This inverse relationship can often be succinctly described using the following formula:
$$
(P_b = \frac{C}{Y})
$$
Where:
- \( P_b \): Bond price
- \( C \): Coupon payment
- \( Y \): Yield to maturity
Let’s take a closer look at the impact of interest rate changes on the price of a bond with examples.
Example and Calculation Breakdown
Scenario: Price of a 3% Five-Year Bond
The following table aims to provide clarity on how changes in interest rates affect the bond pricing process:
| % Yield |
% Change Yield |
Price |
Price Change |
% Price Change |
| 3% |
0 |
100.00 |
0 |
0 |
| 4% (1% Increase) |
+33.33* |
95.51 |
–4.49 |
–4.49 |
| 2% (1% Decrease) |
–33.33 |
104.74 |
+4.74 |
+4.74 |
defined as \(Change in Yield\): \( \frac{\text{Ending Value} - \text{Beginning Value}}{\text{Beginning Value}} \times 100; (0.04-0.03)/(0.03) \times 100 = 33.33%\)
Why Prices Change
The coupon rate of a bond remains constant over its lifetime regardless of price movements. However, when interest rates change, the bond’s yield must adjust accordingly. For yield to increase beyond the coupon rate when interest rates rise, the price of the bond must fall.
Conversely, for yield to decrease below the coupon rate when interest rates fall, the price of the bond must rise.
Key Takeaways
If a bond’s coupon rate remains constant, when interest rates rise, the bond price must decrease, prompting a rise in bond yields. Conversely, if interest rates fall, the bond price will need to increase to accommodate the fallen yield until bond maturity.
Frequently Asked Questions (FAQs)
Q1: What happens to bond prices when interest rates rise?
A1: When interest rates increase, bond prices generally decrease which in turn increases the yield.
Q2: Why is there an inverse relationship between bond prices and yields?
A2: This inverse relationship happens because the bond’s fixed coupon payments become more or less attractive compared to the new interest rates environment, forcing prices to adjust.
Glossary
Coupon Rate: The annual interest rate paid by the bond’s issuer to the bondholder.
Yield to Maturity (YTM): The total return anticipated on a bond if held until it matures.
References
For further reading on this topic, consider the official CSC Handbook or financial textbooks dealing with bond market strategies.
The next section covers the different fixed-income securities and their pricing mechanisms in more detail.
📚✨ Quiz Time! ✨📚
## What is the relationship between bond prices and interest rates?
- [ ] Direct relationship
- [x] Inverse relationship
- [ ] No relationship
- [ ] Exponential relationship
> **Explanation:** The relationship between bond prices and interest rates is inverse. As interest rates rise, bond prices fall, and as interest rates fall, bond prices rise.
## What happens to bond yields when interest rates increase?
- [ ] Bond yields decrease
- [x] Bond yields increase
- [ ] Bond prices increase
- [ ] Nothing happens to bond yields
> **Explanation:** When interest rates increase, bond yields increase to provide a higher rate of return equivalent to the new interest rate environment.
## How is the yield calculated when there is a change in interest rates?
- [ ] Current value minus initial value
- [ ] Yield difference divided by price
- [x] (Ending Value – Beginning Value) ÷ Beginning Value × 100
- [ ] Interest rate difference divided by bond price
> **Explanation:** Yield is calculated by considering the change in yield as a percentage of the original yield, given by the formula (Ending Value – Beginning Value) ÷ Beginning Value × 100.
## What is the effect on bond price when the interest rate decreases by 1%?
- [ ] Bond yield decreases by 33.33%
- [ ] Bond price decreases to 95.51
- [x] Bond price increases to 104.74
- [ ] No effect on bond price
> **Explanation:** When the interest rate decreases from 3% to 2%, the price of the bond increases from 100 to 104.74 to adjust the yield to 2%.
## If a bond’s coupon rate is 3% and the yield rises to 4%, what happens to the bond price?
- [x] Bond price drops to 95.51
- [ ] Bond price remains at 100
- [ ] Bond yield falls
- [ ] Bond price increases to 104.74
> **Explanation:** To achieve a yield of 4% on a 3% bond, the bond price must drop to 95.51. This adjustment compensates the yield rise in the market.
## Why doesn’t the coupon rate change over the life of the bond?
- [x] It is fixed at the time of issuance
- [ ] It changes with market interest rates
- [ ] It adjusts based on bond price
- [ ] It fluctuates daily
> **Explanation:** The coupon rate is fixed at the time of issuance and does not change, regardless of changes in bond prices or market interest rates.
## In the context of bond pricing, what does the term 'par' refer to?
- [ ] Current market price
- [ ] Discounted price
- [ ] Future price
- [x] Face value of the bond
> **Explanation:** 'Par' refers to the face value of the bond, which is the amount the bondholder will receive at maturity.
## How does a new buyer of a bond gain additional yield when market interest rates rise?
- [ ] By receiving higher coupon payments
- [x] By buying the bond at a lower price than par
- [ ] By selling the bond at a premium
- [ ] By holding the bond until maturity
> **Explanation:** When market interest rates rise, new buyers achieve additional yield by purchasing the bond at a price lower than its par value, which increases their yield to maturity.
## What happens to bond yields when bond prices increase?
- [x] Bond yields decrease
- [ ] Bond yields increase
- [ ] Bond yields remain unchanged
- [ ] Bond prices decrease
> **Explanation:** When bond prices increase, the yield decreases because the fixed coupon payment represents a smaller percentage of the higher purchase price.
## If a bond yield falls to 2%, how does the bond price adjust?
- [ ] Bond price decreases to 95.51
- [x] Bond price increases to 104.74
- [ ] Bond yield rises
- [ ] Bond coupon rate changes
> **Explanation:** When a bond yield falls to 2%, the bond price increases from 100 to 104.74 to adjust the overall yield to the new lower interest rate.