Chapter 2 - Bond Prices and Yields

What is a bond?

A loan from an investor to a government or company that pays interest and repays principal at maturity.

Bond cash flows

Coupon payments during the life of the bond and face value at maturity.

Bond pricing steps

1) Identify cash flows 2) Discount cash flows to present value.

Bond pricing formula

P₀ = Σ CFₜ / (1 + r)ᵗ

What is the discount rate in bond pricing?

The interest rate used to discount future bond cash flows.

Yield to Maturity (YTM)

The single discount rate that equates the bond’s price to the present value of its cash flows.

YTM assumption

Assumes a flat yield curve and reinvestment of coupons at the same rate.

Is using one discount rate accurate?

It is a simplification; more accurate pricing uses different spot rates.

Most accurate bond pricing method

Discount each cash flow using its maturity-specific spot rate.

Term structure of interest rates

The relationship between interest rates and different maturities.

Time value of money

Money today is worth more than money in the future because it can earn interest.

Why do we discount cash flows?

Because future money is worth less than money today.

Coupon rate

Coupon payment divided by face value.

Coupon rate vs YTM

Coupon rate determines cash flows; YTM determines bond price.

Current yield

Annual coupon divided by the bond’s market price.

Interest rate and bond price relationship

Interest rates rise → bond prices fall; rates fall → prices rise.

Bond priced at par

Coupon rate equals YTM.

Bond priced below par

Coupon rate is less than YTM.

Bond priced above par

Coupon rate is greater than YTM.

Compounding frequency

How often interest is applied (annual, semi-annual, monthly).

More frequent compounding

Leads to a higher effective annual return.

Effective Annual Yield (EAY)

Annualized return with annual compounding.

Continuous compounding

PV = Xe⁻ʳᵀ

Perpetuity

A bond with no maturity that pays coupons forever.

Perpetuity pricing formula

P = C / r

Clean price

Bond price excluding accrued interest.

Dirty price

Clean price plus accrued interest.

Accrued interest

Interest earned since the last coupon payment.

T-bill

A zero-coupon government security sold at a discount.

Bank discount rate

The quoted rate on T-bills based on face value, not price paid.

Bond Equivalent Yield (BEY)

Adjusted yield that makes T-bills comparable to bonds.

Spot rate

The yield on a zero-coupon bond for a specific maturity.

Forward rate

Implied future interest rate derived from spot rates.