Need an all-in-one list with the **Equity 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 —** Market Organization and Structure, and Security Market Indexes**.

**1. Market Organization and Structure**

**Leverage ratio**

Leverage~ratio = \frac {1}{Initial~Margin~Requirement}

1 = 100%

Initial margin requirement = x%

**Margin call price**

Margin~call~price=P_0\bigg( \frac {1 - Initial~margin~requirement}{1 - Maintenance~margin~requirement} \bigg)

P0 = Initial purchase price

**2. Security Market Indexes**

**Value of price return index**

V_{PRI} =\frac {\textstyle\sum_{i=1}^N n_iP_i}{D}

V_{PRI} = Value of the price return index

n_i = Number of units of constituent security i held in the index portfolio

N = Number of constituent securities in the index

P_i = Unit price of constituent security i

D = Value of the divisor

**Price return of the index portfolio**

PR_I = \frac {V_{PRI1} - V_{PRI0}}{V_{PRI0}}= \displaystyle\sum_{i=1}^N w_iPR_i= \displaystyle\sum_{i=1}^Nw_ i\Bigg( \frac {P_{i1} - P_{i0}}{P_{i0}} \Bigg)

V_{PRI1} = Value of the price return index at the end of the period

V_{PRI0} = Value of the price return index at the beginning of the period

PR_i = Price return of constituent security i

N = Number of individual securities in the index

w_i = Weight of security i (the fraction of the index portfolio allocated to security i)

P_{i1} = Price of constituent security i at the end of the period

P_{i0} = Price of constituent security i at the beginning of the period

**Total return of an index**

TR_I = \frac {V_{PRI1} - V_{PRI0}+I}{V_{PRI0}}= \displaystyle\sum_{i=1}^N w_iTR_i= \displaystyle\sum_{i=1}^Nw_ i\Bigg( \frac {P_{1i} - P_{0i}+Inc_i}{P_{0i}} \Bigg)

TR_I = Total return of the index portfolio

V_{PRI1} = Value of the price return index at the end of the period

V_{PRI0} = Value of the price return index at the beginning of the period

Inc_i = Total income (dividends and/or interest) from all securities in the index held over the period

TR_i = Total return of constituent security i

w_i = Weight of security i (the fraction of the index portfolio allocated to security i)

N = Number of securities in the index

**Value of price return index** (Multiple periods)

V_{PRIT} = V_{PRI0} (1 + PR_{I1})(1 + PR_{I2}) … (1 + PR_{IT})

V_{PRI0} = Value of the price return index at inception

V_{PRIT} = Value of the price index at time t

PR_{IT} = Price return on the index over period t, t = *1, 2, …, T*

**Value of the total return index** (Multiple periods)

V_{TRIT} = V_{TRI0} (1 + TR_{I1})(1 + TR_{I2}) … (1 + TR_{IT})

V_{TRI0} = Value of the index at inception

V_{TRIT} = Value of the total return index at time t

TR_{IT} = Total return on the index over period t, t = *1, 2, …, T*

**Price weighting**

w_i^P= \frac {P_i}{\textstyle\sum_{i=1}^N P_i}

w_i = Weight of security i

P_i = Share price of security i

N = Number of securities in the index

**Equal weighting**

w_i^E= \frac {1}{N}

w_i = Weight of security i

N = Number of securities in the index

**Market-capitalization weighting**

w_i^M= \frac {Q_iP_i}{\textstyle\sum_{j=1}^N Q_jP_j}

w_i = Weight of security i

Q_i = Number of shares outstanding of security i

P_i = Share price of security i

N = Number of securities in the index

**Float-adjusted market-capitalization weighting**

w_i^M= \frac {f_iQ_iP_i}{\textstyle\sum_{j=1}^N f_iQ_jP_j}

f_i = Fraction of shares outstanding in the market float

w_i = Weight of security i

Q_i = Number of shares outstanding of security i

P_i = Share price of security i

N = Number of securities in the index

**Fundamental weighting**

w_i^F= \frac {F_i}{\textstyle\sum_{j=1}^N F_j}

w_i = Weight of security i

F_i = Fundamental size measure of company i

**3. 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

**4. 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

**Follow the links to find more formulas on Quantitative Methods, Economics, Corporate Finance, Alternative Investments, Financial Reporting and Analysis, Portfolio Management, Fixed-Income Investments, and Derivatives, included in the CFA® Level 1 Exam.**