Chapter 2 - Bond Prices and Yields Formulas

Present value of a single cash flow

PV = FV / (1 + r)^t

Future value formula

Cn = C0(1 + r)^n

Bond pricing formula (general)

P0 = Σ CFt / (1 + r)^t

Coupon payment

Coupon = Coupon rate × Face value

Semi-annual coupon

C = (Coupon rate × Face value) / 2

Coupon bond price (semi-annual)

P0 = Σ C / (1 + y/2)^t + FV / (1 + y/2)^(2T)

Yield to maturity (YTM)

The discount rate that equates bond price to PV of cash flows (IRR of bond)

Current yield

Annual coupon / Bond price

Perpetuity price

P = C / r

Effective annual yield (EAY)

EAY = (1 + r/m)^m − 1

Continuous compounding (PV)

PV = Xe^(−rT)

Clean price

Bond price excluding accrued interest

Dirty price

Dirty price = Clean price + Accrued interest

Accrued interest formula

Accrued interest = Coupon × (Days since last coupon / Days in coupon period)

Bank discount rate (T-bills)

BDR = (FV − P) / FV × (360 / n)

Bond equivalent yield (BEY)

BEY = (FV − P) / P × (365 / n)

Spot rate (zero-coupon bond)

B(0,t) = 1 / (1 + st)^t

Par bond condition

Coupon rate = YTM → Bond price = Face value

Price–yield relationship

Interest rates ↑ → Bond prices ↓ (inverse relationship)