Bond Price-Yield Relationship

A bond’s price is what investors pay for it in the secondary market, while its market yield is the return implied by that price and its future payments. For a conventional fixed-rate bond, the coupon and redemption amount are fixed; therefore, price must fall when the required yield rises, and vice versa.

Present-value mechanism

A bond’s price equals the present value of its future coupons and principal: P = Σ[C/(1+y)^t] + F/(1+y)^n. When the discount rate y rises, the present value of every fixed payment falls, producing the inverse relationship.

• The yield to maturity is the discount rate that equates the bond’s market price with the present value of its promised payments, assuming payments occur as scheduled.
• For a bond redeemable at face value, a yield above its coupon rate implies a discount price; an equal yield implies par; a lower yield implies a premium.

Adjustment in the secondary market

If prevailing interest rates rise, newly issued bonds offer higher returns, making older fixed-coupon bonds less attractive. Their prices fall until their implied yields become competitive; when prevailing rates fall, demand for older higher-coupon bonds raises their prices and lowers their yields.

• Changes in inflation expectations, credit risk, liquidity and demand for bonds can also alter investors’ required yield.
• The inverse relationship is a valuation identity for fixed cash flows, although the market forces changing the required yield may differ.

Magnitude of the price response

The price response is not identical across bonds. Duration measures the approximate sensitivity of price to a change in yield.

• Longer-maturity bonds generally have greater interest-rate risk because more payments are discounted over longer periods.
• Lower-coupon bonds generally show greater price sensitivity than higher-coupon bonds of the same maturity and yield.
• For an option-free bond, convexity makes the price gain from a given yield fall generally larger than the price loss from an equal yield rise.

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