Price and Interest Rate Relationship

With bond pricing and yields covered, you can now understand the most fundamental concept in fixed income: the inverse relationship between bond prices and interest rates.

The Inverse Relationship

• When interest rates rise, bond prices fall
• When interest rates fall, bond prices rise
• This is a mathematical certainty, not a market tendency

Why does this happen? When new bonds are issued at higher rates, existing bonds with lower coupons become less attractive. Their prices must drop so that their effective yield matches the new, higher market rate. The reverse happens when rates fall.

Example:

• You own a bond paying 4% interest
• New bonds are issued paying 5%
• Nobody wants your 4% bond at full price, so its price drops until its yield matches 5%

Memory Aid: See-Saw

Picture a see-saw with rates on one end and bond prices on the other. When rates go up, prices go down. When rates go down, prices go up. The two ends always move in opposite directions.

Exam Tip: Gotchas

• Bond prices and interest rates move in OPPOSITE directions. This is a mathematical certainty, not a market tendency.

What Affects Price Sensitivity?

Not all bonds react equally to interest rate changes. Two factors determine how much a bond's price will move:

Maturity Effect

• Longer-maturity bonds are more sensitive to interest rate changes
• A 30-year bond will move much more in price than a 2-year note for the same rate change
• Reason: the longer you're locked into an old rate, the greater the opportunity cost

Coupon Effect

• Lower-coupon bonds are more sensitive to interest rate changes
• A bond paying 2% will move more than a bond paying 8% for the same rate change
• A higher coupon provides more cash flow sooner, reducing effective duration

Think of it this way: A bond paying 8% gives you large cash payments along the way, so you are less dependent on the final payout at maturity. A bond paying 2% gives you very little along the way, so almost all of your return rides on that maturity value, making its price more sensitive to rate shifts.

Zero-Coupon Bonds: Maximum Sensitivity

• Zero-coupon bonds have the highest interest rate risk of all bonds
• They provide no periodic cash flow, so the investor's entire return depends on the maturity value
• All the price sensitivity is concentrated in a single future payment
• This makes zero-coupon bonds (like Separate Trading of Registered Interest and Principal of Securities (STRIPS) and T-Bills) the most volatile when rates change

Exam Tip: Gotchas

• Zero-coupon bonds have the HIGHEST interest rate risk of all bonds, not the lowest. No periodic cash flow means maximum price sensitivity.
• A bond's coupon rate never changes when market rates change. Only the bond's price adjusts to bring its yield in line with current rates.
• Longer maturity = MORE price sensitivity (not less). The longer you are locked into an old rate, the greater the opportunity cost.
• Lower coupon = MORE price sensitivity (not less). Higher coupons return cash sooner, which cushions price swings.