Bond prices are inversely related to interest rates:
Essentially, the incomes (coupons and face value at maturity) are fixed – hence they’re called fixed income securities. Thus, for yield to maturity of a bond to match the prevailing market interest, its price must change. To get higher YTM to match higher interest rates, we need price to fall. To get lower YTM to match lower interest rates, we need price to rise.
Basic Bond Pricing Example
Suppose we have bond that pays 1000 bond).
Case 1 – Market interest rates rise to 6%:
- New bonds are being issued that pay $60/year
- Our bond only pays $50, which is less attractive to buyers
- Thus, to sell it, we would need to drop the price so that our bond’s total return (coupon + face value at maturity) matches the 6% interest rate
- Price falls → YTM rises to match market rate
Case 2 – Market interest rates drop to 4%
- New bonds only pay $40/year
- Our bond pays $50, which is better, so people are willing to pay more for it
- Price rises until our bond’s yield falls to 4%, aligning with the new market rate
- Price rises –> YTM falls to match market rate
Example: Suppose an 8% semi-annual coupon US treasury bond was just sold at par at issuance. However, the Federal Reserve Bank’s fed fund rate suddenly rises to 9%.
- What will be the rate of return on the bond now? The current YTM of the bond must be the same as the current interest rate in the market, i.e. 9%.
- What will be the current price of the bond? The current price will equal the present value of the future cash flows discounted at the going market rate.
Bond Pricing Principle
Bond pricing is based on the basic principle on valuing the PV of known cash flows.
- A change in market interest rate causes a change in the opposite direction in the market values of fixed income securities.
- Inverse relationship between $P and r%
Implications:
- Because interest rates are unpredictable, prices of fixed income securities are uncertain up to the time they mature.
- Bonds do not “guarantee” a fixed return
- Fixed income does not mean fixed return!
Why do bond prices change? The level of market interest has changed, but the promised future cash flows from the bond do not. A higher YTM implies a higher discount rate for a bond’s remaining cash flows, reducing their PV and hence the bond’s price. Thus, the price will fall to the point where it equals the PV of future values discounted at the prevailing interest rate.
- Bond prices subject to the effects of both the passage of time and changes in interest rate.
- Capital gain/loss yield = .
