THE IMPACT OF MATURITY
The duration or maturity of a bond significantly affects its price volatility. It is crucial to understand that longer-term bonds are generally more volatile in price compared to shorter-term bonds. This section illustrates this concept using the comparison of two bonds—a five-year bond and a 10-year bond both with a 3% coupon rate.
To explicate this relationship, Table 7.3 below shows the effect of interest rate changes on the two types of bonds:
Table 7.3 | The Effect of Interest Rate Changes on Bonds of Different Terms:
| Bond Type |
Interest Rate (Yield) |
% Change Yield |
Price |
Price Change |
% Price Change |
| 3% Five-Year Bond |
3% |
0 |
100.00 |
0 |
0 |
|
4% |
+33.33 |
95.51 |
–4.49 |
–4.49 |
|
2% |
–33.33 |
104.74 |
+4.74 |
+4.74 |
| 3% Ten-Year Bond |
3% |
0 |
100.00 |
0 |
0 |
|
4% |
+33.33 |
91.82 |
–8.18 |
–8.18 |
|
2% |
–33.33 |
109.02 |
+9.02 |
+9.02 |
Note: The price change percentage is calculated using the formula:
$$
\text{Percentage Price Change} = \left(\frac{\text{Ending Value} - \text{Beginning Value}}{\text{Beginning Value}}\right) \times 100
$$
Example Calculation for the 10-Year Bond during the Interest Rate increase to 4%:
$$
(91.82 - 100) ÷ 100 × 100 = -8.18
$$
Interpretation of Results
When interest rates increase from 3% to 4%, both the five-year and 10-year bonds experience a price drop, but not to the same extent. The five-year bond decreases by 4.49%, and the 10-year bond drops even more significantly by 8.18%.
Similarly, when interest rates decrease to 2%, the five-year bond price rises by 4.74%, whereas the 10-year bond price jumps by 9.02%. This greater sensitivity of the 10-year bond illustrates its higher volatility.
Why Longer-Term Bonds are More Volatile
Longer-term bonds are more volatile because of the increasing uncertainty associated with forecasting interest rates further into the future. As bonds approach their maturity dates, their remaining term to maturity shortens, and thus, they behave more like short-term bonds, becoming less susceptible to interest-rate changes.
Key Takeaways
- Longer-term bonds exhibit higher price volatility compared to shorter-term bonds due to the increased uncertainty over longer time horizons.
- As market interest rates change, longer-term bonds react more severely than shorter-term bonds.
- A bond initially issued with a long maturity will become less volatile as it nears its maturity date, starting to trade more like a short-term bond.
Frequently Asked Questions (FAQs)
1. Why do longer-term bonds react more to interest rate changes?
Longer-term bonds are more exposed to changes in interest rates due to the longer time over which investors are fixed to a specific interest rate, increasing the uncertainty and potential impact of such changes.
2. How does the approach of a bond to its maturity reduce its volatility?
As a bond approaches maturity, it has fewer remaining scheduled payments, meaning that interest rate changes affect its present value to a lesser extent.
3. Can a bond’s volatility move from being long-term to short-term?
Yes, a bond originally issued with a long maturity will progressively lose its volatility as it nears maturity, mediaǯ. This happens because the bond’s remaining term shortens over time.
These interpretations and illustrations should help solidify the understanding of the impact of bond maturity on price volatility, a critical concept for anyone pursuing the Canadian Securities Course.
📚✨ Quiz Time! ✨📚
## Which of the following statements best describes the relationship between bond maturity and price volatility?
- [ ] Shorter-term bonds are more volatile than longer-term bonds.
- [x] Longer-term bonds are more volatile than shorter-term bonds.
- [ ] Bonds of all maturities have the same price volatility.
- [ ] Volatility is not influenced by bond maturity.
> **Explanation:** Longer-term bonds are more volatile in price than shorter-term bonds due to the increased uncertainty about future markets and interest rates further into the future.
## If interest rates increase by 1%, what is the approximate price change for a 3%, five-year bond?
- [ ] 0
- [ ] -4.49%
- [x] -4.49%
- [ ] -8.18%
> **Explanation:** The price of a 3%, five-year bond will drop by approximately 4.49% if the interest rates increase by 1%.
## How much does a 3%, 10-year bond increase in price if interest rates decrease to 2%?
- [x] 9.02%
- [ ] 8.18%
- [ ] 4.49%
- [ ] 5.53%
> **Explanation:** The price of a 3%, 10-year bond will increase by approximately 9.02% if the interest rates decrease to 2%.
## Why do longer-term bonds tend to be more volatile in their prices compared to shorter-term bonds?
- [ ] Longer-term bonds have higher coupon rates.
- [x] Uncertainty about the markets and interest rates increases as we forecast farther into the future.
- [ ] Longer-term bonds have lower yields.
- [ ] Shorter-term bonds have less demand.
> **Explanation:** The longer the term of the bond, the more uncertainty exists about future market conditions and interest rates, making longer-term bonds more volatile in price.
## What happens to the volatility of a bond's price as it approaches maturity?
- [ ] It increases.
- [x] It decreases.
- [ ] It remains the same.
- [ ] It fluctuates randomly.
> **Explanation:** As bonds approach maturity, they become less volatile because they have a shorter duration to maturity and less uncertainty about future interest rates.
## When analyzing the price change of a bond due to a yield increase of 1%, how do the results vary between a five-year bond and a 10-year bond?
- [x] The 10-year bond will drop more in price than the five-year bond.
- [ ] The five-year bond will drop more in price than the 10-year bond.
- [ ] Both bonds will drop the same amount in price.
- [ ] The 10-year bond will drop less in price than the five-year bond.
> **Explanation:** The price of a 10-year bond will drop more significantly (8.18%) compared to a five-year bond (4.49%) when yields increase by 1%.
## Over time, how does the maturity of a bond originally issued as a 10-year bond change after seven years?
- [ ] It remains a 10-year bond.
- [ ] It becomes a zero-coupon bond.
- [ ] It converts to a variable-rate bond.
- [x] It becomes a three-year bond.
> **Explanation:** A bond originally issued with a 10-year maturity will have a remaining term of three years after seven years, making it effectively a three-year bond at that time.
## What is the percentage price change of a 3%, 10-year bond if yields rise to 4%?
- [x] -8.18%
- [ ] -9.02%
- [ ] -4.74%
- [ ] -5.53%
> **Explanation:** If yields rise to 4%, the price of a 3%, 10-year bond will drop by approximately 8.18%.
## How is the price change of a bond calculated when interest rates change?
- [ ] By using the bond’s initial coupon rate.
- [x] By calculating the percentage change in yield and applying it to the bond’s price.
- [ ] By using the bond's face value.
- [ ] By adjusting the bond’s duration.
> **Explanation:** The price change of a bond is calculated by taking the percentage change in yield and applying it to the bond's price.
## What factor primarily causes longer-term bonds to react more sharply to interest rate changes compared to shorter-term bonds?
- [ ] The face value of the bond
- [ ] The initial coupon rate
- [x] The extended period of uncertainty regarding interest rate forecasts
- [ ] The credit rating of the issuer
> **Explanation:** The longer-term bonds are more susceptible to sharp reactions because of the extended period of uncertainty regarding future interest rates.
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