The longer the time to maturity the less the price increase from an increase in interest rates.
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If this is a True/False question, the answer is False.
Raising the prevailing interest rate in the bond market DECREASES the value of previously-issued fixed-rate bonds. The decrease in value is larger for longer-maturity bonds.
To understand why the longer the time to maturity, the less the price increase from an increase in interest rates, let's break it down step by step:
1. Bond prices and interest rates: Bond prices and interest rates have an inverse relationship, meaning when one goes up, the other goes down, and vice versa. This relationship exists because when interest rates rise, newly issued bonds offer higher coupon payments, making existing bonds with lower interest rates less attractive.
2. Coupon payments: Bonds typically pay periodic fixed interest payments called coupon payments to bondholders. These coupon payments are generally a percentage of the bond's face value, also known as the principal. For example, a bond with a face value of $1,000 and a coupon rate of 5% will pay $50 in coupon payments per year.
3. Price sensitivity to interest rate changes: The price of a bond is determined by discounting all the future cash flows (coupon payments and the final principal repayment) by a discount rate. This discount rate is generally tied to the prevailing interest rates. When interest rates increase, the discount rate used to calculate the present value of future cash flows also increases. Consequently, the bond price decreases because the future cash flows are worth less in today's dollars.
4. Time to maturity: The time to maturity of a bond refers to the number of years until the bond's principal is repaid. The longer the time to maturity, the more coupon payments are expected to be received. Longer-dated bonds have more cash flows to be discounted, making them more sensitive to changes in interest rates compared to shorter-dated bonds.
5. Impact of interest rate changes on longer-dated bonds: As longer-dated bonds have more coupon payments and a longer time horizon, any increase in interest rates has a more significant impact on their present value. This means that when interest rates rise, the price of longer-dated bonds falls more compared to shorter-dated bonds.
So, when you say that "the longer the time to maturity, the less the price increase from an increase in interest rates," it might be a misunderstanding. In reality, the longer the time to maturity, the larger the price decline is expected to be when interest rates increase. The increased sensitivity to interest rate changes makes longer-dated bonds riskier in terms of potential price fluctuations.