The values of outstanding bonds change whenever the going rate of interest changes. In
general, short-term interest rates are more volatile than long-term interest rates. Therefore,
short-term bond prices are more sensitive to interest rate changes than are long-term bond
prices. Is that statement true or false? Explain. (Hint: Make up a “reasonable” example
based on a 1-year and a 20-year bond to help answer the question.)
The statement is true. Short-term bond prices are indeed more sensitive to interest rate changes compared to long-term bond prices.
To explain this, let's consider a hypothetical example with a 1-year bond and a 20-year bond. Assume the current interest rate is 4%.
If interest rates rise to 5%, the price of the 1-year bond will decrease more significantly compared to the 20-year bond. This is because the 1-year bond has a shorter duration and maturity, so its cash flows will be affected more by the increase in interest rates over a short period.
Let's suppose the 1-year bond has a face value of $100 and pays $4 in interest annually. If the interest rate rises to 5%, the bond's price will drop in order to provide a yield that matches the new interest rate. The new price of the 1-year bond would be calculated using the formula:
New price = $4 / (1 + 5%) = $3.81 (approximately)
On the other hand, the 20-year bond with a face value of $100 and an annual interest payment of $4 will be less impacted by the increase in interest rates. This is because its cash flows are spread out over a longer period, reducing the impact of short-term rate fluctuations.
The new price of the 20-year bond, using the same formula, would be:
New price = $4 / (1 + 5%)^20 = $2.41 (approximately)
From this example, it is clear that the short-term bond price (1-year bond) changed more significantly from $100 to $3.81, compared to the change in the long-term bond price (20-year bond) from $100 to $2.41. Therefore, short-term bond prices are more sensitive to changes in interest rates compared to long-term bond prices.
The statement is true. Short-term bond prices are indeed more sensitive to interest rate changes compared to long-term bond prices. Let's consider a reasonable example to understand why.
Suppose we have a 1-year bond and a 20-year bond with the same face value (e.g., $1000). The 1-year bond has a fixed interest rate of 3%, while the 20-year bond has a fixed interest rate of 5%.
Now, let's imagine that interest rates in the market suddenly increase by 1%. This means that the going rate of interest for new bonds becomes 4% for the 1-year bond and 6% for the 20-year bond.
To find out how the bond prices will be affected, we need to calculate the present value of future cash flows for each bond. The present value of a bond is determined by discounting its future cash flows by the market interest rate.
For the 1-year bond, the investor receives $1030 at maturity (face value + interest). To calculate the present value of this cash flow, we need to discount it by the new interest rate of 4%. Using a present value formula or financial software, we find that the present value of the 1-year bond is approximately $990.
For the 20-year bond, the investor receives $1000+$50 (interest) annually for 20 years, and $1000 at maturity. The interest rate used to discount these cash flows is now 6%. After performing the calculations, we find that the present value of the 20-year bond is approximately $748.
Comparing the initial prices of the two bonds ($1000 each) with their respective new present values, we can see that the 1-year bond decreased by $10, while the 20-year bond decreased by $252. This demonstrates that the short-term bond price is more sensitive to interest rate changes, as a 1% increase in interest rates resulted in a smaller decrease in the price of the 1-year bond compared to the 20-year bond.
Therefore, due to their shorter maturity, short-term bond prices are more responsive to changes in interest rates, making them generally more volatile than long-term bond prices.