Fixed-Income Investments • Formulas CFA® Level 1

Need an all-in-one list with the Fixed-Income Investments formulas included in the CFA Level 1 Exam? We have compiled them for you here. The relevant formulas have been organized and presented by chapter. In this section, we will cover the following topics — Fixed-Income Securities and Fixed-Income Valuation.


1. Fixed-income Securities


Conversion ratio

Conversion~ratio = \frac {Par~value}{Conversion~price}

Conversion value

Conversion~value = Share~price \times Conversion~ratio

Conversion premium/discount

Conversion ~premium/discount=Convertible~bond~price - Conversion~value

2. Introduction to Fixed-income Valuation


Fixed-rate bonds

PV = \frac {PMT}{(1 + r)^1} + \frac {PMT}{(1 + r)^2}+…+ \frac {PMT+FV}{(1 + r)^N}

PV = Present value (price)
PMT = Coupon payment amount per period
r = Discount rate
N = Number of periods to maturity
FV = Face value/par value/future value

PV = \frac {PMT}{(1 + Z_1)^1} + \frac {PMT}{(1 + Z_2)^2}+…+ \frac {PMT+FV}{(1 + Z_N)^N}

PV = Present value (price)
PMT = Coupon payment amount per period
Z_n = Spot rate per period
N = Number of periods to maturity
FV = Face value/par value/future value

PVFlat = PVFull - AI
PVFull = \Bigg [\frac {PMT}{(1 + r)^{1-\frac {t}{T}}} + \frac {PMT}{(1 + r)^{2-\frac {t}{T}}}+…+ \frac {PMT}{(1 + r)^{N-\frac {t}{T}}} \Bigg ]
PVFull = PV \times (1 + r)^{\frac {t}{T}}
AI = \frac {t}{T} \times PMT

PVFull = Full price of a bond
PVFlat = Flat price of a bond
AI = Accrued interest
PMT = Coupon payment amount per period
N = Number of periods to maturity
T = Number of days within a coupon payment period
t = Number of days from the last coupon payment to the settlement date

Fixed-rate bonds

\bigg( 1+\frac {APR_m}{m}\bigg)^m=\bigg( 1+\frac {APR_n}{n}\bigg)^n

APRm = Annual percentage rate for m
m = Periodicity that you are converting from
APRn = Annual percentage rate for n
n = Periodicity that you are converting to

Current yield

Current~yield = \frac {Total~PMT~in~a~year}{Flat~Price}

Floating Rate Notes (FRNs)

PV=\frac { \frac {(Index + QM) \times FV}{m} }{ \Big(1+\frac {Index + DM}{m} \Big)^1} + \frac { \frac {(Index + QM) \times FV}{m} }{ \Big(1+\frac {Index + DM}{m} \Big)^2}+…+ \frac { \frac {(Index + QM) \times FV}{m}+FV }{ \Big(1+\frac {Index + DM}{m} \Big)^N}

PV = Present value (price) of a floating-rate note
Index = Reference rate (stated as an annual percentage rate)
QM = Quoted margin (stated as an annual percentage rate)
FV = Future value paid at maturity (par value)
m = Periodicity of the floating- rate note, or the number of payment periods per year
DM = Discount/required margin (stated as an annual percentage rate)
N = Number of evenly spaced periods to maturity

Money market instruments

PV = FV \times \bigg ( 1-\frac {Days}{Year} \times DR \bigg )
FV = PV + \bigg ( PV \times \frac {180}{365} \times AOR \bigg )

PV = Present value (price) of the money market instrument
FV = Future value (face/par value) of the money market instrument
Days = Number of days between settlement and maturity
Year = Number of days in the year
DR = Discount rate (stated as an annual percentage rate)
AOR = Add-on rate (stated as an annual percentage rate)

Forward rates

(1 + Z_A)^A \times (1 + IFR_{A,B-A})^{B-A} = (1 + Z_B)^B

Z_n = Spot rate
IFR = Implied forward rate


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