CFA® Program
Level I
FORMULA SHEET (2024) Version 1.0
Prepared by: Fabian Moa, CFA, FRM, CTP, FMVA, AFM, FSA Credential
FOR REFERENCE ONLY
(Note: Formula Sheet is not provided in the CFA exam)
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NOESIS EXED SDN BHD
Block VO2, Level 5, Unit 8, Lingkaran SV, Sunway Velocity, 55100 Kuala Lumpur, Malaysia
Website: www.noesis.edu.sg
CFA Institute does not endorse, promote, or warrant the accuracy or quality of the products or services offered by Noesis Exed. CFA
Institute, CFA® and Chartered Financial Analyst® are trademarks owned by CFA Institute.
CFA Level 1 (2024) Formula Sheet – Noesis Exed
CFA Level 1 – Formula Sheet (2024)
Setting Up the Texas BA II Plus Financial Calculator
Video: https://youtu.be/0MS8d8QOFmc
Using Texas BA II Plus Financial Calculator
Video: https://youtu.be/LWmTTiZz8BU
Video (Requires Login to Facebook): https://fb.watch/nci5V7Dwtj/
QUANTITATIVE METHODS
ed
Learning Module 1: Rates and Returns
Determinants of Interest Rates
Ex
Interest rate, = Real risk-free rate + Inflation premium + Default risk premium
+ Liquidity premium + Maturity premium
s
(1 + Nominal risk-free rate) = (1 + Real risk-free rate) × (1 + Inflation premium)
si
Nominal risk-free rate = Real risk-free rate + Inflation premium
N
oe
Maturity premium = Interest rate on longer-maturity, liquid Treasury debt
– Interest rate on short-term Treasury debt
Holding Period Return
=
where:
= Price at the beginning of the period
= Price at the end of the period
= Income
If given holding period returns ,
= 1+
−
+
, …,
over the holding period:
× 1+
× …× 1 +
−1
2
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Arithmetic Return
=
1
=
1
+
+ ⋯+
Geometric Mean Return
=
1+
Harmonic Mean
−1=
=
∑#
1+
× 1+
× …× 1+
%&
1⁄
−1
>0
ed
Relationship between Arithmetic Mean, Geometric Mean, and Harmonic Mean
)*&+*, -. +*/
= 0 -,ℎ+*,-. +*/ × 2/ +& -. +*/
34
1 + 56
=0
s
Ex
Money-Weighted Return (MWR)
oe
si
Time-Weighted Return (TWR)
Given the holding period returns for each sub-period,
If T > 1 year, then
0 7/8-9*: 6 = ; 1 +
If
= 1 year, then
0 7/8-9*: 6 = 1 +
N
If
× 1+
< 1 year, then
6 %& ℎ&8:- > ?* -&: = 1 +
Non-Annual Compounding
,
× …× 1 +
× 1+
× 1+
@ = 4@A B1 +
where:
+ = Number of compounding periods per year
G = Quoted annual interest rate
H = Number of years
3
C
+
, …,
D
× …× 1 +
EFA
< ⁄ −1
× …× 1+
−1
−1
CFA Level 1 (2024) Formula Sheet – Noesis Exed
−1
R
MNNOKP Q
I##JIK = L1 +
I##JIK = L1 +
MNNOKP = L1 +
FS# TKP Q − 1
R
−1
UI KP Q
R
UI KP Q − 1
assuming 252 trading days per year
assuming 5 trading days per week
Continuously Compounded Returns
,
=
,
+
,
,
=
* VW,
= ln B D
+ ⋯+
Real Returns
E , E
+
E ,
ed
I##JIK = L1 +
Annualizing Returns
Pre-Tax and After-Tax Nominal Return
Ex
(1 + real return) = (1 + real risk-free rate) × (1 + risk premium)
*- /\ &+- /8 *,7 × 1 − /\ /,* <
−1
1 + %8/,-& ? *+-7+
si
;1 +
N
Leveraged Return
=
oe
0%,* -,/\ */8 *,7
s
After-tax nominal return = Pre-tax nominal return × (1 – Tax rate)
Return on a leveraged portfolio
] =
^ +
@_
@`
^− a
where:
^ = Return on the investment portfolio (unleveraged)
a = Cost of debt
@_ = Debt/borrowed funds
@` = Equity of the portfolio
4
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Learning Module 2: The Time Value of Money in Finance
4@ = @ 1 +
@=
where:
4@ = Future value at time ,
@ = Present value
= Discount rate per period
, = Number of compounding periods
4@
1+
As compounding frequency becomes very large (i.e., continuous compounding)
4@ = @* V
@ = 4@ * EV
Present Value of Zero-Coupon Bond
4@
1+
ed
@ b-c.&7 , d& : =
Ex
where:
4@ = Principal (or Face Value)
= Market discount rate per period
, = Maturity of bond
s
4@ ⁄
−1
D
@
oe
si
=B
Present Value of Coupon Bond
N
@ 3&7?& d& : =
where:
@ = Bond’s price
5 = Periodic coupon payment
4@ = Face value
H = Number of periods
= Market discount rate per period
5
1+
+
Present Value of a Perpetual Bond (Perpetuity)
@
5
1+
* ?*,7/8 d& : =
5
+⋯+
5
5 + 4@
1+ A
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Annuity Instruments (e.g., Mortgage)
0=
@
1− 1+
E
where:
0 = Periodic cash flow
= Market interest rate per period
@ = Present value or principal amount of loan/bond
, = Number of payment periods
Price of a Preferred Share
@ =
ed
where:
b = Fixed periodic dividend
= Expected rate of return
b
Ex
Price of a Common Share
Constant Dividend Growth Rate into Perpetuity
b 1+>
be
=
−>
−>
N
oe
si
where:
b = Common dividend at time ,
> = Constant growth rate
= Expected rate of return
s
@ =
where:
f = Earnings per share for period ,
^gh
`h
^gh
= Trailing price-to-earnings ratio
`hij
=
be
+>
@
@
be
fe
=
−>
b
@
f × 1+>
=
f
−>
fe
= Forward price-to-earnings ratio
6
>>
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Two-stage Dividend Discount Model
@ =
b 1 + >G
1+
+
1+
1+
−1
where:
>G = Higher short-term dividend growth rate
>] = Lower long-term dividend growth rate
= Initial growth phase
f k e# = Stock value in periods (Terminal value)
b e#e
=
− >]
Forward Rate
4, =
f k e#
1+ #
ed
#
Ex
where:
4 , = One-year forward rate one year from now
= Discount rate on one-year risk-free discount bond
= Discount rate on two-year risk-free discount bond
si
s
Learning Module 3: Statistical Measures of Asset Returns
Measures of Central Tendency
oe
k/+?8* 5*/ ,
N
where:
= Observation - (- = 1, 2, 3, … , )
Median
Position of median =
Quantiles
where: q = First quartile
qr = Third quartile
=
1
#
AJFnNV So SnGNVpI S#Ge
Interquartile range = qr − q
7
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Box and Whisker Plot
s??* %* .* = qr + 1.5 × q
v&w* %* .* = q − 1.5 × q
Measures of Dispersion
Range = Maximum value – Minimum value
c =
Sample Standard Deviation
∑#
−
−1
∑#
−
−1
si
s
c=y
− |
ed
Sample Variance
50b =
∑# |
Ex
Mean Absolute Deviation (MAD)
c IVzN = y
oe
Sample Target Semideviation
∑#{| }_
−1
N
where:
d = target
= total number of sample observations
−d
Coefficient of Variation
Sample Skewness
Sample Excess Kurtosis
3@ =
c
1 ∑#
k~*w *cc ≈ B D
1 ∑#
€` ≈ B D
c•
8
−
cr
−
•
−3
r
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Sample Covariance
1
−1
c{‚ =
Sample Correlation Coefficient
#
−
{‚ =
ƒ −ƒ
c{‚
c{ c‚
Learning Module 4: Probability Trees and Conditional Expectations
#
Expected Value of a Discrete Random Variable
„
= f; − f
=
#
<
; −f
<
Ex
Variance of a Random Variable
=
ed
f
Conditional Expected Value of a Random Variable
|k
|k
f |k =
+
si
s
+ ⋯+
oe
Conditional Variance of a Random Variable
|k =
|k ; − f |k < +
„
+
# |k ; # − f
|k ;
# |k <
# |k
−f
|k
Bayes’ Formula
d|0
× 0
d
%& +/,-& |f…* ,
×
%& +/,-&
N
Total Probability Rule for Expected Value
f
= f |k
k +f
k
+ ⋯+ f
where: k , k , …, k# are mutually exclusive and exhaustive events.
0|d =
f…* ,| %& +/,-&
=
|k#
#
|k < + ⋯
k#
f…* ,
Video (Bayes’ Formula and Total Probability Rule): https://youtu.be/9_h0EzssPZ4
9
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Learning Module 5: Portfolio Mathematics
assets in a portfolio
Expected return on portfolio
f ^ =w f
Variance on portfolio
Requires
„
variances and
# #E
^
+w f
=
#
†
#
w w† 3&…L ,
1
−1
†Q
−f
#
L
,
Q ˆ † − fL † Q‰Š
−
QL †, −
Ex
=
,
ׄ
ׄ
si
=‹
oe
,
s
For a two-asset ( = 2) portfolio:
„
^ = w „ + w „ + 2w w 3&…
where: 3&…
#
distinct covariances to estimate portfolio variance.
3&…L , † Q = f ‡L
Covariance
+ ⋯ + w# f
ed
For
†Q
,
Video: https://youtu.be/lUwulZ9ONC0
N
For a three-asset ( = 3) portfolio:
„
,
^ = w „ + w „ + wr „r + 2w w 3&…
+2w wr 3&… , r + 2w wr 3&…
,
r
Covariance Given a Joint Probability Function
3&…
Œ,
_
=
†
If X and Y are uncorrelated, then f
If X and Y are independent, then
L Œ, ,
_,† Q × • Œ,
ƒ =f
f ƒ
,ƒ =
ƒ
10
−f
Œ Ž × • _,† − f
_ Ž
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Safety-First Optimal Portfolio
Safety-First Ratio
k4 /,-& =
kℎ& ,%/88 -c~ = Pr;f
f
<
^
where:
] = Investor’s threshold level
f ^ = Expected portfolio return
„^ = Portfolio standard deviation
^
−
„^
]
] < = H& +/8 −k4
/,-&
ed
Video: https://youtu.be/S3x5JrGIOUA
Learning Module 6: Simulation Methods
Ex
Lognormal Distribution
s
Mean of a lognormal random variable
‘] = exp ‘ + 0.50„
oe
si
Variance of a lognormal random variable
„] = exp 2‘ + „
− 1<
N
where:
‘ = Mean of the normal random variable
„ = Variance of the normal random variable
× ;exp „
Continuously Compounded Rates of Return
=
expL
where:
= Current asset price
= Asset price at time
, = Continuously compounded return from 0 to
, Q
If returns are independently and identically distributed (i.i.d.), then
, = , + , + ⋯+
E , E +
E ,
11
CFA Level 1 (2024) Formula Sheet – Noesis Exed
If the one-period continuously compounded returns are i.i.d. random variables with mean ‘
and „ , then
fL
,
„ L
„L
,
Q=‘
, Q= „
Q = „√
Learning Module 7: Estimation and Inference
kℎ/ ?* /,-& =
„^
–
ed
where:
^ = Portfolio return
– = Risk-free rate
„^ = Portfolio standard deviation of return
^−
Ex
„
@/ -/ .* &% ,ℎ* c/+?8- > :-c, -—7,-&
=
&% ,ℎ* c/+?8* +*/ c
oe
si
where:
„ = Population standard deviation
= Sample size
s
„
k,/ :/ : * & &%
=
,ℎ* c/+?8* +*/
√
N
Note: If „ is not known, use c, the sample standard deviation.
Bootstrap Resampling
c{ =
1
d−1
n
_
L˜™n − ˜̅Q
where:
c{ = Estimate of the standard error of the sample mean
d = Number of resamples drawn from the original sample
˜™n = Mean of a resample
˜̅ = Mean across all the resample means
12
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Learning Module 8: Hypothesis Testing
Confidence level = 1 − ›
Power of the test = 1 − œ
where:
› = Significance level (Probability of Type I error)
œ = Probability of Type II error
Test statistic
1 − › % 3& %-:* .*
−1
c
+ 3 -,-./8 …/87* × B D
√
,* …/8 =
si
s
Test of the Difference in Means
c ⁄√
Ex
Degrees of freedom =
−‘
,=
ed
Test of a Single Mean
Test statistic
U
N
oe
,=
Degrees of freedom =
U
+
U
cž =
−2
U
−
U
− ‘U − ‘U
c
c
y ž + ž
U
− 1 cU + U − 1 cU
U + U −2
Test of the Mean of Differences
Test statistic
Degrees of freedom =
−1
U
,=
:̅ − ‘U
cU
13
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Test of a Single Variance
Test statistic
Degrees of freedom =
−1 c
„
Ÿ =
−1
Test of the Difference in Variances
Degrees of freedom =
− 1,
−1
4=
c_NoSVN
cŒo NV
ed
Test statistic
Ex
Test of a Correlation
Test statistic
√ −2
s
√1 −
si
−2
oe
Degrees of freedom =
,=
Test statistic
N
Test of Independence (Categorical Data)
Degrees of freedom =
Ÿ =
F
L
−1 .−1
† − f †Q
f†
where:
+ = Number of cells in the table
† = Number of observations in each cell of row - and column ¡
f † = Expected number of observations in each cell of row - and column ¡
14
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Learning Module 9: Parametric and Non-Parametric Tests of Independence
Test of a Correlation
Degrees of freedom =
,=
−2
√ −2
√1 −
{‚ =
Pearson Correlation (or Bivariate Correlation)
Spearman Rank Correlation Coefficient
C =1−
where:
6 ∑# :
−1
Ex
: = Difference in ranks
c{‚
c{ c‚
ed
Test statistic
si
s
Test of Independence (Categorical Data)
Test statistic
oe
Ÿ =
L
−1 .−1
N
Degrees of freedom =
F
† − f †Q
f†
where:
+ = Number of cells in the table
† = Number of observations in each cell of row - and column ¡
f † = Expected number of observations in each cell of row - and column ¡
&,/8 &w - × &,/8 .&87+ ¡
=
…* /88 ,&,/8
Standardized Residual (or Pearson Residual)
k,/ :/ :-9*: *c-:7/8 =
15
† −f†
f†
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Learning Module 10: Simple Linear Regression
ƒ =— +—
+ ⋯ + —# # + £ , - = 1, 2, … ,
where:
ƒ = Dependent variable
= Independent variable
— = Intercept
— = Slope coefficient, - = 1, 2, … ,
£ = Error term
— , — , … , —# = Regression coefficients
Ī = Ѫ + Ѫ
+*
3&…/ -/ .* &% / : ƒ ∑# ƒ − ƒ
=
@/ -/ .* &%
∑#
−
s
—™ =
Ex
ed
where:
Ī = Estimated value on the regression line for the ith observation
—™ = Intercept
—™ = Slope
* = Residual for the ith observation
oe
si
—™ = ƒ − —™
−
Sum of Squares Total, kk = ∑#
ƒ −ƒ
= kk + kkf
N
Sum of Squares Regression, kk = ∑# Lƒ™ − ƒQ
Sum of Squares Error, kkf = ∑# Lƒ − ƒ™ Q = ∑# *
Coefficient of Determination
kk
kkf
=1−
kk
kk
3&…/ -/ .* &% / : ƒ
k,/ :/ : :*…-/,-& &%
k,/ :/ : :*…-/,-& &% ƒ
Correlation coefficient
=
=
Note: (Correlation coefficient)2 = Coefficient of determination
16
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Sample standard deviation of X
Sample standard deviation of Y
k{ = y
−
−1
∑#
ƒ −ƒ
−1
k‚ = y
f £
Homoskedasticity
∑#
= „¤ ,
- = 1, 2, … ,
Mean square regression (MSR)
Ex
kkf
−~−1
s
5kf =
oe
F-distributed test statistic
kk
~
4=
5k
5kf
si
Mean square error (MSE)
5k =
ed
ANOVA F-Test
N
where:
= Number of observations
~ = Number of independent variables
Standard error of estimate
cN = √5kf = y
17
∑# Lƒ − ƒ™ Q
−~−1
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Hypothesis Test of the Slope Coefficient
Degrees of freedom, :% =
−~−1
,=
—™ − d
cn™j
where:
d = Hypothesized population slope
cn™j = Standard error of the slope coefficient
cN
=
¥∑#
−
Standard error of the intercept, cn™W
, # NV¦Nž =
Ex
1
cn™W = y +
—™ − d
cn™W
ed
Hypothesis Test of the Intercept
s
∑#
oe
where: Īo = Ѫ + Ѫ
ƒ™o ± ,¨⁄ × co
si
Prediction Intervals
−
N
o
Variance of the prediction error of Y, given X
1
Standard error of the forecast
1
co = cN ©1 +
co = cN y1 +
+
L o− Q
ª
− 1 c{
+
L o− Q
− 1 c{
18
CFA Level 1 (2024) Formula Sheet – Noesis Exed
ln ƒ = — + —
The Log-Lin Model
ƒ = — + — ln
The Lin-Log Model
ln ƒ = — + — ln
The Log-Log Model
Learning Module 11: Introduction to Big Data Techniques
N
oe
si
s
Ex
ed
No formula.
19
CFA Level 1 (2024) Formula Sheet – Noesis Exed
ECONOMICS
Learning Module 1: Firms and Market Structures
Total profit = Total revenue – Total cost
Economic profit = Total revenue – Total economic costs
Accounting profit = Total revenue – Total accounting costs
Δ 3
Δq
0…* />* …/ -/—8* .&c, =
0…* />* %-\*: .&c, =
&,/8 …/ -/—8* .&c,
q7/ ,-,«
&,/8 %-\*: .&c,
q7/ ,-,«
Ex
5/ >- /8 .&c, =
&,/8 *…* 7*
q7/ ,-,«
s
0…* />* *…* 7* =
×q
ed
-.* × q7/ ,-,« =
si
&,/8 *…* 7* =
oe
Total cost = Total fixed cost + Total variable cost
N
Average total cost = Average fixed cost + Average variable cost
Concentration Ratio
3& .* , /,-&
Herfindahl-Hirschman Index (HHI)
22 =
/,-& =
#
#
5/ ~*, cℎ/ *
5/ ~*, cℎ/ *
Learning Module 2: Understanding Business Cycles
No formula
20
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Learning Module 3: Fiscal Policy
d7:>*, c7 ?87c⁄ :*%-.-, = ) −
where:
) = Government spending
= Taxes
d = Payments of transfer benefits
where:
, = Net tax rate
H = Net taxes = Taxes – Transfers
,ƒ = Total tax revenue
4-c./8 +78,-?8-* =
1
1−. 1−,
Ex
The Fiscal Multiplier
ed
ƒb = ƒ − H = 1 − , ƒ
Disposable Income
si
s
where:
. = Marginal propensity to consume
, = Tax rate
Learning Module 4: Monetary Policy
%8/,-& ,/ >*,
oe
* : > &w,ℎ +
N
H*7, /8 /,* =
+d
Learning Module 5: Introduction to Geopolitics
No formula
Learning Module 6: International Trade
No formula
21
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Learning Module 7: Capital Flows and the FX Market
*/8 *\.ℎ/ >* /,*U⁄o = kU⁄o ×
% 3ℎ/ >* -
o
U
L1 + %Δ o Q
−1
1 + %Δ U
≈ %ΔkU⁄o + %Δ o − %Δ U
*/8 *\.ℎ/ >* /,* = L1 + %ΔkU⁄o Q ×
Percentage change in base currency % (vs currency :)
fLkU⁄o Q − kU⁄o
kU⁄o
Ex
ed
where:
kU⁄o = Spot exchange rate
o = General price level of goods indexed in currency %
U = General price level of goods indexed in currency :
Learning Module 8: Exchange Rate Calculations
0 0 3
= ×
d 3 b
N
Forward Rate
oe
si
s
Cross-Rate
4Œ⁄_ = kŒ⁄_ × -
1+ Œ×
®
1+ _×
4& w/ : ?&- ,c = 4Œ⁄_ − kŒ⁄_
= kŒ⁄_ B
where:
kŒ⁄_ = Spot exchange rate
4Œ⁄_ = Forward exchange rate
= Time to maturity
22
Œ− _
1+ _
D
CFA Level 1 (2024) Formula Sheet – Noesis Exed
CORPORATE ISSUERS
Learning Module 1: Organizational Forms, Corporate Issuer Features, and Ownership
No formula
Learning Module 2: Investors and Other Stakeholders
No formula
Learning Module 3: Working Capital and Liquidity
No formula
ed
Learning Module 4: Corporate Governance: Conflicts, Mechanisms, Risks, and Benefits
Ex
3/cℎ
b/«c c/8*c
b/«c ?/«/—8*c
b/«c &% - …* ,& «
.& …* c-& =
+
−
&7,c,/ :- >
&7,c,/ :- >
&
ℎ/
:
.«.8*
aIPG # ‚NIV
s
^IPFN# ^NV SUEa G¦SJ# ^NV SU
b-c.&7 ,%
f0 &% k7??8-*
= B1 +
−1
D
4- / .- >
100% − b-c.&7 ,%
si
&,/8 w& ~- > ./?-,/8 = 37 * , /cc*,c − 37 * , v-/—-8-,-*c
N
oe
H*, w& ~- >
= 37 * , /cc*,c *\.87:- > ./cℎ / : +/ ~*,/—8* c*.7 -,-*c
./?-,/8
−37 * , v-/—-8-,-*c *\.87:- > cℎ& ,-,* + / : .7 * , :*—,
Cash flow from operations
= Cash received from customers
+ Interest and dividends received on financial investments
− Cash paid to employees and suppliers
− Taxes paid to governments
− Interest paid to lenders
Free cash flow = Cash flow from operations – Investments in long-term assets
37 * , /,-& =
37 * , /cc*,c
37 * , 8-/—-8-,-*c
23
CFA Level 1 (2024) Formula Sheet – Noesis Exed
q7-.~ /,-& =
3/cℎ + kℎ& ,-,* + +/ ~*,/—8* - c, 7+* ,c + *.*-…/—8*c
37 * , 8-/—-8-,-*c
3/cℎ /,-& =
3/cℎ + kℎ& ,-,* + +/ ~*,/—8* - c, 7+* ,c
37 * , 8-/—-8-,-*c
Learning Module 5: Capital Investments and Capital Allocation
H @ = 34 +
34
1+
where:
34 = After-tax cash flow at time ,
= Required rate of return
34 = Initial outlay
+
34
1+
+ ⋯+
34
1+
=
34
1+
=0
Ex
Internal Rate of Return
34
1+
ed
Net Present Value
si
s
Video: https://youtu.be/bzck7QLhICw
3=
N
oe
Return on Invested Capital
0%,* -,/\ &?* /,- > ? &%-,
3=
0…* />* - …*c,*: ./?-,/8
?* /,- > ? &%-, × 1 − /\ /,*
=
0…* />* ,&,/8 8& >-,* + 8-/—-8-,-*c / : *¯7-,« E ,
0%,* -,/\ &?* /,- > ? &%-,
k/8*c
×
k/8*c
0…* />* - …*c,*: ./?-,/8
Real Options in Capital Budgeting
&¡*., H @
&¡*., H @
=
w-,ℎ &?,-&
w-,ℎ&7, &?,-&
24
− ?,-& .&c, + ?,-& …/87*
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Learning Module 6: Capital Structure
Weighted Average Cost of Capital
6033 = wU U 1 − , + wN N
wU = Target weight of debt in capital structure = ae`
a
where:
wN = Target weight of common stock in capital structure = ae`
`
U = Before-tax marginal cost of debt
Operating Leverage
4-\*: .&c,c
&,/8 .&c,c
Ex
&%-, —*%& * - ,* *c, / : ,/\*c
,* *c, *\?* c*
,* *c, .&…* />* =
s
Interest Coverage
?* /,- > 8*…* />* =
ed
, = Marginal tax rate
U 1 − , = After-tax marginal cost of debt
N = Marginal cost of common stock
Modigliani-Miller Capital Structure Propositions
si
@] = @° + ,b
N
oe
N =
f=
+
− U 1−,
34N − U b 1 − ,
@] =
N
34N 1 − ,
±Œ²²
where:
@] = Value of levered firm
@° = Value of unlevered firm
, = Marginal tax rate
N = Cost of equity
U = Cost of debt
= Cost of capital (for a 100% equity-financed company)
b = Market value of debt
f = Market value of equity
34N = After-tax cash flows to shareholders
U b = Interest expense on debt
25
b
f
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Static Trade-off Theory of Capital Structure
@] = @° + ,b − @ 3&c,c &% 4- / .-/8 b-c, *cc
Learning Module 7: Business Models
N
oe
si
s
Ex
ed
No formula
26
CFA Level 1 (2024) Formula Sheet – Noesis Exed
FINANCIAL STATEMENT ANALYSIS
VOLUME 2
Learning Module 1: Introduction to Financial Statement Analysis
No formula
Learning Module 2: Analyzing Income Statements
Gross profit = Revenue – Cost of Goods Sold
Operating income = Gross margin – Selling, General, and Administrative Expense
Taxable income = Operating income – Interest expense
ed
Net income = Taxable income − Taxes
Ex
Ending shareholders’ equity = Beginning shareholders’ equity + Net income
+ Other comprehensive income
− Dividends
+ Net capital contributions from shareholders
si
s
Ending retained earnings = Beginning retained earnings + Net income – Dividends
Net Profit Margin
Basic EPS
H*, - .&+*
0…* />* cℎ/ *ℎ&8:* c ³ *¯7-,«
oe
N
Return on Equity
d/c-. f k =
f=
H*, ? &%-, +/ >- =
H*, - .&+* − *%* *: :-…-:* :c
6*->ℎ,*: /…* />* 7+—* &% cℎ/ *c &7,c,/ :- >
H*, - .&+*
6*->ℎ,*: /…* />* 7+—*
H*w .&++& cℎ/ *c ,ℎ/, w&78:
+
&% cℎ/ *c &7,c,/ :- >
ℎ/…* —** -cc7*: /, .& …* c-&
Diluted EPS (for convertible preferred stock)
b-87,*: f k =
H*, - .&+*
*…* 7*
27
CFA Level 1 (2024) Formula Sheet – Noesis Exed
0%,* ,/\ - ,* *c, *\?* c*
& .& …* ,-—8* :*—,
b-87,*: f k =
6*->ℎ,*: /…* />* 7+—*
H*w .&++& cℎ/ *c ,ℎ/, w&78:
+
&% cℎ/ *c &7,c,/ :- >
ℎ/…* —** -cc7*: /, .& …* c-&
Diluted EPS (for convertible debt)
H*, - .&+* −
Diluted EPS (for options)
b-87,*: f k =
*%* *: :-…-:* :c +
H*, - .&+* −
*%* *: :-…-:* :c
0::-,-& /8 .&++&
6*->ℎ,*: /…* />* 7+—*
+ cℎ/ *c -cc7*: 7?&
&% cℎ/ *c &7,c,/ :- >
.& …* c-&
&?& ,-& &% «*/
kℎ/ *c *?7 .ℎ/c*:
H*w cℎ/ *c
0::-,-& /8 .&++&
-cc7*:
/,
:7
- > wℎ-.ℎ &?,-& c
w-,ℎ
./cℎ
*.*-…*:
=
−
×
´
µ
cℎ/ *c -cc7*: 7?&
&?,-&
*\*
.-c*
%
&+
&?,-&
*\*
.-c*:
w* * &7,c,/ :- >
.& …* c-&
Treasury stock method
ed
Video (Basic & Diluted EPS): https://youtu.be/2C-mwVqO2SQ
Learning Module 3: Analyzing Balance Sheets
Ex
6& ~- > ./?-,/8 = 37 * , /cc*,c − 37 * , 8-/—-8-,-*c
37 * , /,-& =
37 * , /cc*,c
37 * , 8-/—-8-,-*c
/,-& =
3/cℎ + 5/ ~*,/—8* c*.7 -,-*c + *.*-…/—8*c
37 * , 8-/—-8-,-*c
oe
q7-.~ /.-: ,*c,
si
s
Liquidity Ratios
N
3/cℎ /,-& =
Solvency Ratios
3/cℎ + 5/ ~*,/—8* c*.7 -,-*c
37 * , 8-/—-8-,-*c
v& >-,* + :*—,-,&-*¯7-,« =
b*—,-,&-*¯7-,« =
&,/8 :*—, =
&,/8 :*—,
&,/8 *¯7-,«
&,/8 :*—,
&,/8 /cc*,c
4- / .-/8 8*…* />* =
28
v& >-,* + :*—,
&,/8 *¯7-,«
&,/8 /cc*,c
&,/8 *¯7-,«
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Learning Module 4: Analyzing Statements of Cash Flows I
3/cℎ %8&w
3/cℎ %8&w
3/cℎ %8&w
f :- > d*>- - >
=
+ % &+ &?* /,- > + % &+ - …*c,- > + % &+ %- / .- >
./cℎ
./cℎ
/.,-…-,-*c
/.,-…-,-*c
/.,-…-,-*c
3/cℎ .&88*.,*:
f :- > /..&7 ,c d*>- - > /..&7 ,c
=
+ *…* 7* −
% &+ .7c,&+* c
*.*-…/—8*
*.*-…/—8*
d*>- - >
3&c, &%
f :- >
=
+ 7 .ℎ/c*c −
- …* ,& « - …* ,& «
>&&:c c&8:
f :- > /..&7 ,c d*>- - > /..&7 ,c
3/cℎ ?/-:
=
+ 7 .ℎ/c*c −
?/«/—8*
?/«/—8*
,& c7??8-* c
ed
f :- > w/>*c d*>- - > w/>*c 6/>*c
3/cℎ ?/-:
=
+
−
*\?*
c*
?/«/—8*
?/«/—8*
,& *+?8&«**c
Ex
f :- > - ,* *c, d*>- - > - ,* *c,
3/cℎ ?/-:
,* *c,
=
+
−
*\?* c* %& - ,* *c,
?/«/—8*
?/«/—8*
f :- > - .&+* d*>- - > - .&+*
3/cℎ ?/-:
.&+* ,/\
=
+
−
*\?* c*
,/\ ?/«/—8*
,/\ ?/«/—8*
%& - .&+* ,/\*c
- >
f¯7-?+* , f¯7-?+* ,
−
?7 .ℎ/c*:
c&8:
s
&f = d*>-
&f +
si
f :- >
N
oe
0..7+78/,*:
f :- > /..7+78/,*: d*>- - > /..7+78/,*: b*? *.-/,-&
=
+
− :*? *.-/,-& &
*\?* c*
:*? *.-/,-&
:*? *.-/,-&
*¯7-?+* , c&8:
Note:
3/cℎ *.*-…*: % &+
d&&~ …/87* &%
)/- & c/8*
=
−
&% *¯7-?+* ,
c/8* &% *¯7-?+* ,
*¯7-?+* , c&8:
f :- > *,/- *: d*>- - > *,/- *:
H*,
=
+
− b-…-:* :c
*/ - >c
*/ - >c
- .&+*
29
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Learning Module 5: Analyzing Statements of Cash Flows II
Free Cash Flow To Firm (FCFF)
4344 = H + H33 + , 1 − /\ /,* − 43 … − 63 …
= 34 + , 1 − /\ /,* − 43 …
where:
H = Net income
H33 = Non-cash charges (e.g., depreciation and amortization)
, = Interest expense
43 … = Capital expenditures
63 … = Working capital expenditures
34 = Cash flow from operating activities = H + H33 − 63 …
Performance Ratios
s
34
0…* />* ,&,/8 /cc*,c
oe
3/cℎ *,7
& /cc*,c =
& *¯7-,« =
34
0…* />* cℎ/ *ℎ&8:* c *¯7-,«
N
3/cℎ *,7
34
*…* 7*
si
3/cℎ %8&w ,& *…* 7* =
Ex
where:
H*, d& &w- > = b*—, -cc7*: − b*—, *?/-:
ed
Free Cash Flow to Equity (FCFE)
434f = 34 − 43 … + H*, d& &w- >
3/cℎ ,& - .&+* =
34
?* /,- > - .&+*
3/cℎ %8&w ?* cℎ/ * =
Coverage Ratios
b*—, .&…* />* /,-& =
34 − *%* *: :-…-:* :c
H7+—* &% .&++& cℎ/ *c &7,c,/ :- >
34
&,/8 :*—,
30
CFA Level 1 (2024) Formula Sheet – Noesis Exed
,* *c, .&…* />* /,-& =
b*—, ?/«+* , /,-& =
,* *c, ?/-: + /\*c ?/-:
,* *c, ?/-:
34
3/cℎ ?/-: %& 8& > ,* + /cc*,c
34
3/cℎ ?/-: %& 8& > ,* + :*—, *?/«+* ,
b-…-:* : ?/«+* , /,-& =
34
b-…-:* :c ?/-:
…*c,- > / : %- / .- > /,-& =
34
3/cℎ %8&w %& - …*c,- > / :
%- / .- > /.,-…-,-*c
ed
*- …*c,+* , /,-& =
34 +
Learning Module 6: Analysis of Inventories
Ex
IFRS
…* ,& -*c = v&w* &% 3&c, / : H*, */8-9/—8* @/87* H @
si
s
H @ = Estimated selling price less estimated costs of completion and costs necessary to
complete the sale
oe
US GAAP
…* ,& -*c = v&w* &% 3&c, / : H @
N
For last-in, first-out (LIFO) method or retail inventory methods
…* ,& -*c = v&w* &% 3&c, / : 5/ ~*, @/87*
5/ ~*, …/87* = 37 * , *?8/.*+* , .&c, c7—¡*., ,& 8&w* / : 7??* 8-+-,c
Lower limit = H @ − H& +/8 ? &%-, +/ >Upper limit = H @
Video: https://youtu.be/V8C31msIBzs
…* ,& « ,7
&…*
/,-& =
3&c, &% c/8*c
0…* />* - …* ,& «
b/«c &% - …* ,& « & ℎ/ : =
H7+—* &% :/«c - ?* -&:
…* ,& « ,7 &…* /,-&
31
CFA Level 1 (2024) Formula Sheet – Noesis Exed
f :- > - …* ,& « 4 4
3 )k 4 4
= f :- > - …* ,& « v 4
= 3 )k v 4
− 3ℎ/ >* - v 4
+v 4
*c* …*
*c* …*
Learning Module 7: Analysis of Long-Term Assets
H*, —&&~ …/87* = 2-c,& -./8 .&c, − 0..7+78/,*: :*? *.-/,-&
)/- & c/8* &% /cc*, = k/8* ? &.**:c − H*, —&&~ …/87*
fc,-+/,*: ,&,/8 fc,-+/,*: />*
fc,-+/,*:
=
+
7c*%78 8-%*
*+/- - > 8-%*
&% *¯7-?+* ,
) &cc &f
7/8 :*? *.-/,-& *\?* c*
fc,-+/,*:
=
*+/- - > 8-%* 0
H*, &f
7/8 :*? *.-/,-& *\?* c*
s
Ex
0..7+78/,*: :*? *.-/,-&
fc,-+/,*: />*
=
&% *¯7-?+* ,
0 7/8 :*? *.-/,-& *\?* c*
Straight-line Depreciation
2-c,& -./8 .&c, − k/8…/>* …/87*
fc,-+/,*: 7c*%78 8-%*
si
7/8 :*? *.-/,-& *\?* c* =
oe
0
ed
fc,-+/,*: ,&,/8
=
7c*%78 8-%*
0
4-\*: /cc*, ,7
N
Fixed Asset Turnover
&…* =
*…* 7*
0…* />* *, &f
Impairment of Long-Lived Assets
IFRS
Impairment = Carrying amount – Recoverable amount
where:
Recoverable amount = max(Fair value less costs to sell, Value in use)
US GAAP
If asset’s carrying amount > undiscounted expected future cash flows:
Impairment = Carrying amount – Fair value
32
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Learning Module 8: Topics in Long-Term Liabilities and Equity
Lessee Accounting – Finance Lease (IFRS)
,* *c, *\?* c*
= +?8-*: - ,* *c, /,* × d*>& 8*/c*
- .-?/8 *?/«+* , = v*/c* ?/«+* , −
f :- > 8*/c* d*>- - > 8*/c*
=
+
8-/—-8-,«
8-/—-8-,«
- > 8*/c* 8-/—-8-,«
,* *c, *\?* c*
,* *c, *\?* c* − v*/c* ?/«+* ,
s
−
0+& ,-9/,-&
*\?* c*
Ex
f :- >
s d*>- - >
=
/cc*,
/cc*,
ed
If ROU asset is amortized on a straight-line basis:
-,-/8
s /cc*, …/87* − k/8…/>* …/87*
0+& ,-9/,-&
=
*\?* c*
v*/c* ,* +
Lessee Accounting – Operating Lease (US GAAP)
s
−
0+& ,-9/,-&
*\?* c*
si
f :- >
s d*>- - >
=
/cc*,
/cc*,
,* *c, *\?* c*
s
0+& ,-9/,-&
= v*/c* ?/«+* , −
*\?* c*
N
oe
f :- > 8*/c* d*>- - > 8*/c* 0+& ,-9/,-&
=
−
*\?* c*
8-/—-8-,«
8-/—-8-,«
Stock Options
3&+?* c/,-& *\?* c* =
4/- …/87* &% &?,-& c > / ,*:
@*c,- > ?* -&:
33
CFA Level 1 (2024) Formula Sheet – Noesis Exed
VOLUME 3
Learning Module 1: Analysis of Income Taxes
Deferred Tax Asset/Liability
For Assets:
b*%* *: ,/\
3/ «- > /+&7 ,
/\ —/c*
= /\ /,* × B
−
D
&% /cc*,
&% /cc*,
8-/—-8-,«⁄ /cc*,
For Liabilities:
b*%* *: ,/\
3/ «- > /+&7 ,
/\ —/c*
= /\ /,* × B
−
D
&% 8-/—-8-,«
&% 8-/—-8-,«
8-/—-8-,«⁄ /cc*,
f%%*.,-…* ,/\ /,* =
.&+* ,/\ *\?* c*
*-,/\ - .&+*
3/cℎ ,/\
*-,/\ - .&+*
3ℎ/ >*c - :*%* *: ,/\
/cc*,c / : 8-/—-8-,-*c
Ex
3/cℎ ,/\ /,* =
.&+* ,/\ ?/«/—8* +
ed
.&+* ,/\ *\?* c* =
si
s
Learning Module 2: Financial Reporting Quality
Adjusted EBITDA
k&%,w/ *
&c,/ : &b + b*? *.-/,-& + cℎ/ *-—/c*:
/+& ,-9/,-&
/+& ,-9/,-&
N
oe
0:¡7c,*: 0:¡7c,*:
=
+
fd b0
fd
Straight-line method of depreciation
b*? *.-/,-& *\?* c* =
2
× 3&c, − 0..7+78/,*: :*? *.-/,-&
sc*%78 8-%*
Double-Declining Balance method
b*? *.-/,& *\?* c* =
3&c, − k/8…/>* …/87*
sc*%78 8-%*
Video: https://youtu.be/6RskYAxdAFk
Units-of-Production method
b*? *.-/,-& *\?* c* =
s -,c ? &:7.*:
× 3&c, − k/8…/>* …/87*
&,/8 7 -,c &…* 7c*%78 8-%*
34
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Learning Module 3: Financial Analysis Techniques
Activity Ratios
…* ,& « ,7
&…* =
3&c, &% c/8*c
0…* />* - …* ,& «
b/«c &% - …* ,& « & ℎ/ : =
H7+—* &% :/«c - ,ℎ* ?* -&:
…* ,& « ,7 &…*
b/«c &% c/8*c &7,c,/ :- > =
H7+—* &% :/«c - ,ℎ* ?* -&:
*.*-…/—8*c ,7 &…*
7 .ℎ/c*c
0…* />* ?/«/—8*c
H7+—* &% :/«c &% ?/«/—8*c =
&…* =
H7+—* &% :/«c - ,ℎ* ?* -&:
/«/—8*c ,7 &…*
*…* 7*
0…* />* w& ~- > ./?-,/8
si
6& ~- > ./?-,/8 ,7
ed
&…* =
*…* 7*
0…* />* *.*-…/—8*c
Ex
/«/—8*c ,7
&…* =
s
*.*-…/—8*c ,7
*…* 7*
0…* />* *, %-\*: /cc*,c
*…* 7*
&…* =
0…* />* ,&,/8 /cc*,c
&…* =
oe
4-\*: /cc*, ,7
N
&,/8 /cc*, ,7
Liquidity Ratios
37 * , /,-& =
q7-.~ /,-& =
3/cℎ /,-& =
37 * , /cc*,c
37 * , 8-/—-8-,-*c
3/cℎ + kℎ& , ,* + +/ ~*,/—8* - …*c,+* ,c + *.*-…/—8*c
37 * , 8-/—-8-,-*c
3/cℎ + kℎ& , ,* + +/ ~*,/—8* - …*c,+* ,c
37 * , 8-/—-8-,-*c
b*%* c-…* - ,* …/8 3/cℎ + kℎ& , ,* + +/ ~*,/—8* - …*c,+* ,c + *.*-…/—8*c
=
/,-&
b/-8« ./cℎ *\?* :-,7 *c
35
CFA Level 1 (2024) Formula Sheet – Noesis Exed
3/cℎ .& …* c-&
b/«c &% - …* ,& « b/«c &% c/8*c H7+—* &% :/«c
=
+
−
.«.8*
&7,c,/ :- >
&% ?/«/—8*c
& ℎ/ :
Video (Cash Conversion Cycle): https://youtu.be/IFsI9c4wUD4
Solvency Ratios
&,/8 :*—,
b*—,-,&-/cc*,c /,-&
=
"Total debt ratio"
&,/8 /cc*,c
&,/8 :*—,
&,/8 :*—, + &,/8 *¯7-,«
&,/8 :*—,
&,/8 *¯7-,«
4- / .-/8 8*…* />* /,-& =
&,/8 & *, :*—,
fd b0
s
b*—,-,&-fd b0 /,-& =
0…* />* ,&,/8 /cc*,c
0…* />* ,&,/8 *¯7-,«
Ex
b*—,-,&-*¯7-,« /,-& =
fd
,* *c, ?/«+* ,c
oe
,* *c, .&…* />* /,-& =
si
Coverage Ratios
N
4-\*: .ℎ/ >* .&…* />* /,-& =
Profitability Ratios
) &cc ? &%-, +/ >- =
fd
*…* 7*
H*, ? &%-, +/ >- =
fd + v*/c* ?/«+* ,c
,* *c, ?/«+* ,c + v*/c* ?/«+* ,c
) &cc ? &%-,
*…* 7*
?* /,- > ? &%-, +/ >- =
*,/\ +/ >- =
ed
b*—,-,&-./?-,/8 /,-& =
?* /,- > - .&+*
*…* 7*
H*, - .&+*
*…* 7*
36
CFA Level 1 (2024) Formula Sheet – Noesis Exed
0=
?* /,- > - .&+*
0…* />* ,&,/8 /cc*,c
0=
H*, - .&+*
0…* />* ,&,/8 /cc*,c
f=
H*, - .&+*
0…* />* ,&,/8 *¯7-,«
*,7
*,7
& - …*c,*: ./?-,/8 =
& .&++& *¯7-,« =
fd × 1 − f%%*.,-…* ,/\ /,*
0…* />* ,&,/8 :*—, / : *¯7-,«
H*, - .&+* − *%* *: :-…-:* :c
0…* />* .&++& *¯7-,«
DuPont Analysis
f=
0 × 4- / .-/8 v*…* />*
s
fd
/\
,* *c,
&,/8 /cc*, 4- / .-/8
×
×
×
×
+/ >8*…* />*
—7 :*
—7 :*
,7 &…*
H*, - .&+*
fd
fd
,* *c, —7 :* =
fd
N
/\ —7 :* =
oe
where:
si
f=
&…* × 4- / .-/8 8*…* />*
Ex
f = H*, ? &%-, +/ >- × &,/8 /cc*, ,7
ed
?* /,- >
Business Risk
k,/ :/ : :*…-/,-& &% &?* /,- > - .&+*
3&*%%-.-* , &% …/ -/,-&
=
&% &?* /,- > - .&+*
0…* />* &?* /,- > - .&+*
k,/ :/ : :*…-/,-& &% *, - .&+*
3&*%%-.-* , &% …/ -/,-&
=
&% *, - .&+*
0…* />* *, - .&+*
k,/ :/ : :*…-/,-& &% *…* 7*
3&*%%-.-* , &% …/ -/,-&
=
&% *…* 7*
0…* />* *…* 7*
37
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Financial Sector Ratios
*c* …*c ℎ*8: /, .* , /8 —/ ~
5& *,/ « *c* …* *¯7- *+* ,
=
3/cℎ *c* …* /,-&
k?*.-%-*: :*?&c-, 8-/—-8-,-*c
H*, - ,* *c, +/ >- =
H*, - ,* *c, - .&+*
&,/8 - ,* *c, */ - > /cc*,c
H*, - ,* *c, +/ >- =
H*, - ,* *c, - .&+*
&,/8 - ,* *c, */ - > /cc*,c
v-¯7-: /cc*, *¯7- *+* , =
0?? &…*: */:-8« +/ ~*,/—8* c*.7 -,-*c
k?*.-%-*: :*?&c-, 8-/—-8-,-*c
ed
Learning Module 4: Introduction to Financial Statement Modeling
N
oe
si
s
Ex
Nothing new.
38
CFA Level 1 (2024) Formula Sheet – Noesis Exed
EQUITY INVESTMENTS
Learning Module 1: Market Organization and Structure
5/\-+7+ 8*…* />* /,-& =
1
Minimum margin requirement
Total return on leveraged stock investment:
k/8*c
5/ >k/8*c
+ b-…-:* :c − v&/ −
−
? &.**:c
- ,* *c, .&++-cc-&
&,/8 *,7 =
-,-/8
7 .ℎ/c*
+
*¯7-,« .&++-cc-&
-,-/8 *¯7-,« =
5- -+7+ +/ >× &,/8 ?7 .ℎ/c* ? -.*
*¯7- *+* ,
-.* =
1 − -,-/8 5/ >1 − 5/- ,* / .* 5/ >-
Ex
5/ >- 3/88
ed
Video (Return on Leveraged Stock Position): https://youtu.be/tZd4XtvjjlI
Learning Module 2: Security Market Indexes
@^ÃÄ =
b
oe
= the number of units of constituent security i held in the index portfolio
H = the number of constituent securities in the index
= the unit price of constituent security i
b = value of the divisor
N
where:
si
s
Price Return Index,
∑A
Price return of an index,
Total Return Index,
Ä =
Ä =
@^ÃÄ − @^ÃÄ
@^ÃÄ
@^ÃÄ − @^ÃÄ +
@^ÃÄ
.Ä
where:
@^ÃÄ = value of the price return index at the end of the period
@^ÃÄ = value of the price return index at the beginning of the period
.Ä = total income (dividends and/or interest) from all securities in the index held
over the period
39
−1
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Weighting Methods
Price weighting,
w^ =
∑A
†
†
Video (Recalculating the divisor of a price weighted index): https://youtu.be/eYiZNK-ETrg
Equal weighting,
Market-capitalization weighting,
w` =
1
H
wÎ =
q† †
wÎ =
Ex
where:
% = fraction of shares outstanding in the market float
q = number of shares outstanding of security i
= share price of security i
H = number of securities in the index
w– =
oe
si
s
Fundamental weighting,
where Fi denotes a fundamental size measure of company i
No formula
N
Learning Module 3: Market Efficiency
Learning Module 4: Overview of Equity Securities
Return on Equity (using average total book value of equity)
H
f =
d@f + d@f E /2
Return on Equity (using beginning book value of equity)
H
f =
d@f E
where BVE = book value (Assets – Liabilities)
40
4
∑A
†
4†
%q
%† q† †
∑A
†
ed
Float-adjusted market capitalization weighting,
q
∑A
†
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Learning Module 5: Company Analysis: Past and Present
5/ ~*, cℎ/ * =
*…* 7*
5/ ~*, c-9*
k/8*c ?&,* ,-/8 = 100% − 5/ ~*, cℎ/ *%
H*, c/8*c = 0…* />* c*88- > ? -.* × q7/ ,-,« c&8:
*…* 7* */ *: % &+ , / c/.,-& c
× 100%
&,/8 , / c/.,-& …&87+*
− @3 − 43
where:
q = Units sold in a period
= Price per unit
@3 = Variable operating cost per unit
43 = Fixed operating costs
− @3 = Contribution margin per unit
ed
?* /,- > - .&+* = q ×
Ex
/~* /,* =
%ΔOperating income
%ΔSales
s
b*> ** &% &?* /,- > 8*…* />* b v =
si
%ΔNet income
%ΔOperating income
6*->ℎ, ) &cc .&c,
6*->ℎ,
3&c, &%
×
× 1 − ,/\ /,* +
×
&% :*—,
&% :*—,
&% *¯7-,« *¯7-,«
N
6033 =
oe
b*> ** &% %- / .-/8 8*…* />* b4v =
Learning Module 6: Industry and Company Analysis
Herfindahl-Hirschman Index (HHI)
22 =
Ö
c
where:
c = Market share of participant - (stated as a whole number)
41
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Learning Module 7: Company Analysis: Forecasting
%@/ -/—8* .&c, ≈
%Δ 3&c, &% *…* 7* + ?* /,- > *\?* c*
%Δ *…* 7*
%4-\*: .&c, ≈ 1 − %@/ -/—8* .&c,
H7+—* &% 7 -,c c&8: H7+—* &% 7 -,c c&8:
f\?*.,*:
=
−
?&c,-./ -—/8-9/,-&
? *-./ -—/8-9/,-&
./ -—/8-9/,-&
H7+—* &% 7 -,c c&8: 3/ -—/8-9/,-&
f\?*.,*:
=
×
%/.,&
? *-./ -—/8-9/,-&
./ -—/8-9/,-&
@ =
#
b
1+
+
#
1+
#
Ex
Dividend Discount Model (DDM)
ed
Learning Module 8: Equity Valuation: Concepts and Basic Tools
oe
si
s
where:
@ = Intrinsic value of a share at , = 0
b = expected dividend in year t
= required rate of return on stock
# = expected price per share at t = n (terminal value)
Ö
434f
1+
Free-cash-flow-to-equity (FCFE) Valuation Model
N
@ =
where:
434f = 34 − 43 … + H*, d& &w- >
43 … = Fixed capital investment
H*, d& &w- > = Borrowings minus repayments
Value of preferred stock (non-callable, non-convertible, perpetual)
b
@ =
#
b
1+
/ …/87*
1+ #
Value of preferred stock (non-callable, non-convertible, maturity at time n)
@ =
+
42
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Gordon Growth Model
b
b 1+>
=
−>
−>
=
where:
b = Most recent annual dividend
b = Expected dividend in the next period
> = Constant growth rate
= Required return on equity
>=—×
Sustainable growth rate
f
where:
b = earnings retention rate (= 1 – Dividend payout ratio)
f = Return on equity
+
@#
1+
si
where:
>] = Long-term stable growth rate
>G = Short-term growth rate
b#e
b 1 + >G 1 + >]
@# =
=
− >]
− >]
b 1 + >G
1+
s
@ =
Ex
#
Two-Stage Dividend Discount Model
ed
Video: https://youtu.be/MnfRRRhuGpA
b-…-:* : ?/«&7, /,-&
−>
oe
N
Justified forward P/E
3/cℎ / :
5/ ~*, …/87*
5/ ~*, …/87*
5/ ~*, …/87*
+
+
− cℎ& , ,* +
&% *¯7-,«
&% ? *%* *: c,&.~
&% :*—,
- …*c,+* ,c
Enterprise Value
f@ =
f
=
5/ ~*, …/87* 5/ ~*, …/87*
0:¡7c,*:
=
−
&% /cc*,c
&% 8-/—-8-,-*c
—&&~ …/87*
Asset-based Valuation
43
CFA Level 1 (2024) Formula Sheet – Noesis Exed
FIXED INCOME
Learning Module 1: Fixed-Income Instrument Features
37 * , «-*8: =
d& : ? -.* =
0
7/8 .&7?&
d& : ? -.*
3&7?&
3&7?&
3&7?& + 4/.* …/87*
+
+ ⋯+
1+
1+
1+ #
where:
3&7?& ?* ?* -&: = Coupon rate per period × Face value
= Yield to maturity per period
= Number of payments
ed
Floating-rate Note (FRN) coupon rate = MRR + Spread
Ex
Learning Module 2: Fixed-Income Cash Flows and Types
× - .-?/8
1 − 1 + EA
Fully Amortizing Loan with Level Payment
s
oe
si
where:
0 = Periodic payment
= Market interest rate per period
H = Number of payment periods
0=
N
If the periodic payment is monthly:
Monthly interest payment = Interest rate per month × Beginning principal of loan
Monthly principal payment = Total monthly payment – Monthly interest payment
Ending principal of loan = Beginning principal of loan – Monthly principal payment
Capital-Index Bond (e.g., TIPS)
Inflation-adjusted principal = Principal amount × (1 + Inflation adjustment)
Coupon per period = Coupon rate per period × Inflation-adjusted principal
44
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Deferred Coupon Bond
Video: https://youtu.be/erRbAUOGIyM
Convertible Bonds
3& …* ,-—8* —& : ?/ …/87*
3& …* c-&
=
/,-&
3& …* c-& ? -.*
37 * , cℎ/ *
3& …* c-&
3& …* c-&
=
×
? -.*
…/87*
/,-&
Zero-Coupon Bond
ed
Original issue discount = Bond par value – Issuance price
Learning Module 3: Fixed-Income Issuance and Trading
Ex
No formula
*?7 .ℎ/c* ? -.* =
-.* &% —& : × ×1 + *?& /,* ×
N
oe
si
Repurchase Agreements
s
Learning Module 4: Fixed-Income Markets for Corporate Issuers
-,-/8 +/ >- =
2/- .7, =
@/ -/,-& +/ >- =
*?& ,* + - :/«c
Ø
H7+—* &% :/«c - / «*/
k*.7 -,« ? -.*
7 .ℎ/c* ? -.*
k*.7 -,« ? -.* − 7 .ℎ/c* ? -.*
k*.7 -,« ? -.*
-,-/8 +/ >- × 7 .ℎ/c* ? -.* − k*.7 -,« ? -.*
Learning Module 5: Fixed-Income Markets for Government Issuers
No formula.
45
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Learning Module 6: Fixed-Income Bond Valuation: Prices and Yields
@=
5
1+
+
where:
5 = Coupon that occurs in , periods
= Market discount rate per period
H = Number of periods to maturity
4@ = Face value of bond
5
1+
+ ⋯+
Full Price, Flat Price, and Accrued Interest
5 A + 4@A
1+ A
(Video: https://youtu.be/l7G075JAu5w)
ed
PVFull = PVFlat + Accrued Interest
= @_Ù^ × 1 + /
where:
Accrued Interest = × 5
s
Ex
, = number of days from the last coupon payment to the settlement date
= number of days in the coupon period
,/ = fraction of the coupon period that has gone by since the last payment
@_Ù^ = price on the previous coupon date (before the settlement date)
Matrix Pricing
* & IVzN − * & C
D × ƒ-*8:] − ƒ-*8:C
* & ]− * &C
oe
si
,* ?&8/,*: «-*8: = ƒ-*8:C + B
N
where:
ƒ-*8:C = Yield of shorter-term bond
ƒ-*8:] = Yield of longer-term bond
* & C = Tenor of shorter-term bond
* & ] = Tenor of longer-term bond
* & IVzN = Tenor of the subject bond
* & C < * & IVzN < * & ]
Required yield spread = Bond YTM – Government Bond YTM (Similar maturity)
46
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Learning Module 7: Yield and Yield Spread Measures for Fixed Rate Bonds
Periodicity Conversion
B1 +
0
F
F
D = B1 +
0
+
where:
0 F = Annual percentage rate for + periods per year
0 # = Annual percentage rate for periods per year
7/8 .&7?&
d& : ? -.*
+* , *¯7-…/8* , «-*8:,
k-+?8* «-*8: =
Callable Bonds
4@ − @
‰
H
48/, ? -.*
3&7?&
@=
ƒ-*8:Œ² ⁄Œ² =
+ˆ
5
1+ƒ 3
+
5
1+ƒ 3
365
× ƒ-*8:r ⁄rÚ
360
ed
)&…*
0
#
D
+ ⋯+
5 + 3/88 ? -.*
1+ƒ 3 A
Ex
37 * , «-*8: =
#
si
s
where:
@ = Price of the callable bond
5 = Coupon payment per period
ƒ 3 = Yield to call per period
H = Number of periods to when the bond can be called at the call price
oe
Option-adjusted price = Flat price of bond + Value of embedded call option
N
Value of call option = Price of option-free bond – Price of callable bond
G-spread = Bond YTM – Interpolated sovereign bond YTM
I-spread = Bond YTM – Swap rate
Z-Spread
@=
5
1+9 +Û
where:
Û = Z-spread
9A = Spot rate for H periods
+
5
1+9 +Û
+ ⋯+
OAS = Z-spread – Option value (in basis points per year)
47
5 + 4@
1 + 9A + Û A
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Learning Module 8: Yield and Yield Spread Measures for Floating-Rate Instruments
Value of Floating Rate Note (FRN)
+ q5
5
+ q5
5
+ q5
‰ × 4@ ˆ
‰ × 4@
ˆ
‰ × 4@ + 4@
+
+
+
@=
+
+⋯+
5
+ b5 #
5
+ b5
5
+ b5
ˆ1 +
‰
+
ˆ1 +
‰
ˆ1
‰
+
+
+
ˆ
5
ed
where:
q5 = Quoted Margin
b5 = Discount Margin
5
= Market reference rate
+ = Periodicity (i.e., number of payment periods per year)
FV = Face Value of FRN
H = Number of evenly spaced periods to maturity
Video: https://youtu.be/zqYOtVLkYR8
Ex
Yield Measures for Money Market Instruments
Discount Rate Basis
@ = 4@ × B1 −
b/«c
×b D
ƒ*/
ƒ*/
4@ − @
×B
D
b/«c
4@
@=
4@
b/«c
ˆ1 + ƒ*/ × 0
si
s
b =
N
oe
where:
@ = present value of money market instrument
4@ = future value paid at maturity
b/«c = number of days between settlement and maturity
ƒ*/ = number of days in the year
b = discount rate (stated as annual percentage rate)
Add-on Rate Basis
0
=
‰
ƒ*/
4@ − @
×B
D
b/«c
@
d& : *¯7-…/8* , «-*8: =
48
365
4@ − @
×B
D
b/«c
@
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Learning Module 9: The Term Structure of Interest Rates: Spot, Par, and Forward Curves
Calculation of Bond Price Using Spot Rates
@=
5
1+Û
+
5
1+Û
5 + 4@
1 + ÛA A
+⋯+
where:
@ = Price of bond
5 = Bond coupon payment
ÛA = Spot rate (or zero-coupon yield or zero rate) for period H
4@ = Face value of bond
Forward Rates, IFR
5
1+Û
+
5
1+Û
5 + 100
1 + ÛA A
+ ⋯+
Ex
100 =
/,* % × 4@
ed
Given a Par Rate, 4@ = @ and 5 = /
1 + 9Œ Œ × 1 + 4 Œ,_EŒ _EŒ = 1 + 9_ _
s
where:
4 Œ,_EŒ = Forward rate for d − 0 periods that starts in period 0
oe
si
9_
9Œ
N
0
A
4 Œ,_EŒ
d
−0
Learning Module 10: Interest Rate Risk and Return
Duration Gap
b7 /,-& >/? = 5/./78/« :7 /,-& −
…*c,+* , ℎ& -9&
5
5
E ⁄
E ⁄
,
1+
1+
5/./78/« :7 /,-& = B1 − D Ü
Ý + B2 − D Ü
Ý+⋯
–JKK
–JKK
@
@
Macaulay Duration
,
5 + 4@
1 + AE ⁄
+ BH − D Ü
Ý
@–JKK
,
49
CFA Level 1 (2024) Formula Sheet – Noesis Exed
5/./78/« :7 /,-& = Þ
1+
−
1 + + ;H × . − <
,
ß−
A
.×; 1+
− 1< +
where:
= Yield per period
. = Coupon rate per period
H = Number of evenly spaced periods to maturity as of the beginning of the current period
, = Number of days from the last coupon payment to the settlement date
= Number of days in the coupon period
Video: https://youtu.be/USgjcdCk7Fs
Learning Module 11: Yield-Based Bond Duration Measures and Properties
5&:-%-*: b7 /,-& =
Approximate Modified Duration
5&:b7 ≈
@E − @e
2 × ∆ƒ-*8: × @
Ex
0
5/./78/« b7 /,-&
1+
ed
Modified Duration
5&:b7 × ∆ƒ-*8:
Money Duration
5&:b7 × @ oJKK
oe
Money duration = 0
si
s
%∆ @ –JKK ≈ −0
N
∆ @ –JKK ≈ −5& *«b7 × ∆ƒ-*8:
Duration of Zero-Coupon Bond
5/.b7 = -+* ,& +/,7 -,«
5&:b7 =
Duration of Perpetual Bond
-+* ,& +/,7 -,«
1+
5/.b7 =
1+
5&:b7 =
50
1
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Duration of Floating-Rate Notes
5/.b7 =
−,
=
4 /.,-& &% ?* -&: *+/- - > 7 ,-8
,ℎ* *\, *c*, :/,*
Learning Module 12: Yield-Based Bond Convexity and Portfolio Properties
3& …*\-,« =
Approximate Annualized Convexity
0?? &\3& … ≈
Money Convexity
@
@–JKK
1+ƒ 5
, ,+1 ×
@E + @e − 2 @
∆ƒ-*8: × @
5&:b7 × ∆ƒ-*8: +
5& *«3& = 0
1
×0
2
3& …*\-,« × ∆ƒ-*8:
Ex
%∆ @ –JKK ≈ −0
A
ed
Convexity
3& …*\-,« × @ –JKK
oe
si
s
1
∆ @ –JKK ≈ − 5& *«b7 × ∆ƒ-*8: + - × 5& *«3& × ∆ƒ-*8: ®
2
Portfolio Duration and Convexity
N
& ,%&8-& 5&:-%-*: b7 /,-& =
& ,%&8-& 3& …*\-,« =
A
where:
w = Weight of bond -, measured in market value
51
A
w × 5&:b7
w × 3& …*\-,«
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Learning Module 13: Curve-Based and Empirical Fixed-Income Risk Measures
Effective Convexity
f%%b7 =
f%%3& =
@E − @e
2 × Δ37 …* × @
@E + @e − 2 × @
Δ37 …* × @
%∆ @ –JKK ≈ −f%%b7 × ∆37 …* +
Key Rate Duration
€*« /,*b7 O = −
1
× f%%3& × ∆37 …*
2
1
Δ @
×
@ ΔO
ed
Effective Duration
s
si
O
€*« /,*b7 O = f%%b7
oe
where:
O = ~th key rate
#
Ex
%Δ @ = −€*« /,*b7 O × Δ O
Learning Module 14: Credit Risk
N
Expected Loss
where:
b = Probability of default
v)b = Loss given default
ff = Expected exposure
= Recovery rate
1−
= Loss severity
3 *:-, c? */: ≈
fv = v)b ×
v)b = ff × 1 −
b × v)b
52
b
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Decomposing Bond Yields
ƒ-*8: c? */: = d& : ƒ 5 − )&…*
+* , —& : ƒ 5
v-¯7-:-,« c? */: = d& : ƒ 5 d-: − d& : ƒ 5
3 *:-, c? */: = ƒ-*8: c? */: − v-¯7-:-,« c? */:
Price Impact Given a Change in Yield Spread
%∆ @ –JKK ≈ −0
0
5&:b7 ≈
@E − @e
2 × ∆ƒ-*8: × @
3& …*\-,« ≈
@E + @e − 2 @
∆ƒ-*8: × @
1
×0
2
3& …*\-,« × ∆k? */:
ed
0
%%*
Ex
where:
5&:b7 × ∆k? */: +
k-+-8/ +/,7 -,«
Learning Module 15: Credit Analysis for Government Issuers
s
No formula.
si
Learning Module 16: Credit Analysis for Corporate Issuers
+/ >- =
oe
fd
,& - ,* *c, *\?* c* =
N
fd
?* /,- > - .&+*
*…* 7*
b*—, ,& fd b0 =
34 ,& *, :*—, =
?* /,- > - .&+*
,* *c, *\?* c*
b*—,
fd b0
*,/- *: ./cℎ %8&w
b*—, − 3/cℎ / : +/ ~*,/—8* c*.7 -,-*c
44 ,& :*—, =
44
b*—,
where:
44 = Net income from continuing operations + Depreciation & amortization
+ Deferred income taxes + Other non-cash items
53
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Learning Module 17: Fixed-Income Securitization
No formula.
Learning Module 18: Asset-Backed Security (ABS) Instrument and Market Features
No formula.
Learning Module 19: Mortgage-Backed Security (MBS) Instrument and Market Features
Loan-to-value (LTV) ratio
v @=
=
5& ,ℎ8« :*—, ?/«+* ,
5& ,ℎ8« ? *-,/\ > &cc - .&+*
ed
b
603 =
A
. B
s
Mortgage Pass-Through Securities
Ex
Debt-to-income (DTI) ratio
v&/ /+&7 ,
2&7c* ? -.*
3d
55 B
D
3d
oe
si
605 =
A
3d
D
3d
N
where:
603 = Weighted average coupon
605 = Weighted average maturity
. = Coupon rate on mortgage 55 = Number of months to maturity for mortgage H = Number of mortgages in MBS
3d = Current balance on mortgage 3d = Total current balance of mortgages in MBS
Commercial Mortgage-Backed Securities (CMBS)
Debt Service Coverage Ratio (DSCR)
bk3 =
H*, &?* /,- > - .&+*
b*—, c* …-.*
Net Operating Income (NOI)
H = * ,/8 - .&+* − 3/cℎ &?* /,- > *\?* c*c − *?8/.*+* , *c* …*c
54
CFA Level 1 (2024) Formula Sheet – Noesis Exed
DERIVATIVES
Learning Module 1: Derivative Instrument and Derivatives Market Features
No formula.
Learning Module 2: Forward Commitments and Contingent Claim Features and
Instruments
Forward Contract
Buyer (Long) payoff = k − 4
For one futures contract:
s
Futures Contract
Ex
where:
k = Spot price on contract’s maturity
4
= Forward price with maturity of
<
ed
Seller (Short) payoff = −;k − 4
si
Long Futures daily mark-to-market = %
N
oe
Short Futures daily mark-to-market = −;%
where:
%
= Closing price of futures contract on day ,
%E
= Closing price of futures contract on day , − 1
= Maturity of futures contract
−%E
−%E
<
If margin balance < maintenance margin:
@/ -/,-& 5/ >- =
-,-/8 +/ >- − 5/ >- —/8/ .*
55
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Options Contract
LONG Call option
/«&%% & @/87* /, *\?- /,-& , . = max 0, k −
&%-, /, *\?- /,-& , Π = max 0, k −
−.
where:
. = Call premium
= Exercise/Strike price
k = Spot price at expiration
SHORT Call option
−. <
Ex
&%-, /, *\?- /,-& , Π = −;max 0, k −
LONG Put option
−k
−?
oe
si
&%-, /, *\?- /,-& , Π = max 0,
s
/«&%% & @/87* /, *\?- /,-& , ? = max 0,
SHORT Put option
ed
/«&%% & @/87* /, *\?- /,-& , . = − max 0, k −
N
/«&%% & @/87* /, *\?- /,-& , ? = − max 0,
&%-, /, *\?- /,-& , Π = −;max 0,
−k
−k
−k
−? <
Credit Default Swap (CDS)
3bk 5 5 3ℎ/ >* = Δ3bk k? */: × 3bk H&,-& /8 × f%%b7 ²aC
In a credit event, payment from CDS seller to CDS buyer ≈ v)b % × H&,-& /8
Learning Module 3: Derivative Benefits, Risks, and Issuer and Investor Uses
No formula.
56
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Learning Module 4: Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives
If there are no underlying costs or benefits:
Forward price, 4
=k 1+
If there are underlying costs or benefits in present value terms:
Forward price, 4
= ;k − @
.&+* + @ 3&c, < 1 +
where:
k = Current spot price
= Risk-free rate
= Tenor of forward contract
= k *V
ed
Under continuous compounding, 4
Ex
Under continuous compounding, with income (-) and cost (.) expressed in %:
4
= k * Ve¦E
Foreign Exchange Forward Contract
= k ,o⁄U
s
4 ,o⁄U
* Vâ EVã
N
oe
si
where:
4 ,o⁄U = Forward exchange rate
k ,o⁄U = Spot exchange rate
o = Continuously compounded risk-free rate (for price/quote currency)
U = Continuously compounded risk-free rate (for base currency)
= Maturity of forward contract
Learning Module 5: Pricing and Valuation of Forward Contracts and for an Underlying
with Varying Maturities
Value of LONG Forward Prior to Expiration
@
@
=k −
4
1+
@
E
=0
=k −4
=k −4
57
× 1+
E
E
CFA Level 1 (2024) Formula Sheet – Noesis Exed
If the asset incurs cost or generates income from time , through maturity,
@
= ;k − @
.&+* + @ 3&c, < − 4
× 1+ E
@
= k ,o⁄U − 4 ,o⁄U
For foreign exchange forward contract,
Value of SHORT Forward Prior to Expiration
@
@
=0
4
1+
= − ×k −
@
× * ELVâ EVãQ
= −;k − 4
E
E
E Ø
<
ed
Interest Rate Forward Contracts (Forward Rate Agreements (FRA))
Ex
1 + 9Œ Œ × 1 + 4 Œ,_EŒ _EŒ = 1 + 9_ _
4 Œ,_EŒ Q × H&,-& /8 ? - .-?/8 × * -&:
si
_EŒ −
oe
Payoff for a Long FRA = L5
s
where:
9Π= Spot rate for 0 periods
9_ = Spot rate for d periods
4 Œ,_EŒ = Implied forward rate for d − 0 periods, starting in 0 periods
N
Payoff for a Short FRA = −L5
_EŒ −
4 Œ,_EŒ Q × H&,-& /8 ? - .-?/8 × * -&:
Learning Module 6: Pricing and Valuation of Futures Contracts
If there are no underlying costs or benefits:
Futures price, %
=k 1+
If there are underlying costs or benefits in present value terms:
%
= ;k − @
.&+* + @ 3&c, < 1 +
Under continuous compounding, %
= k *V
Under continuous compounding, with income (-) and cost (.) expressed in %:
%
= k * Ve¦E
58
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Foreign Exchange Forward Contract
% ,o⁄U
= k ,o⁄U
* Vâ EVã
Interest Rate Futures Contract
%Œ,_EŒ = 100 − L100 × 5 Œ,_EŒ Q
where:
%Œ,_EŒ = Futures price for a market reference rate for d − 0 periods
that begins in 0 periods
Futures contract basis point value, d @ = H&,-& /8 ? - .-?/8 × 0.01% × * -&:
Learning Module 7: Pricing and Valuation of Interest Rates and Other Swaps
si
s
where:
cA = Fixed swap rate
5
= Market reference rate
A
4
1+9
oe
Calculating Par Swap Rate
N
where:
4 = Implied forward rates
cA = Fixed swap rate
H = Tenor of swap contract
× kw/? H&,-& /8 × * -&:
Ex
For a fixed-rate receiver in an interest rate swap:
* -&:-. c*,,8*+* , …/87* = cA − 5
ed
For a fixed-rate payer in an interest rate swap:
* -&:-. c*,,8*+* , …/87* = 5
− cA × kw/? H&,-& /8 × * -&:
=
A
cA
1+9
Valuation of Interest Rate Swap
Value of a pay-fixed interest rate swap on a settlement date after inception
37 * , c*,,8*+* ,
=
+ Σ 48&/,- > ?/«+* ,c − Σ 4-\*: ?/«+* ,c
…/87*
Value of a receive-fixed interest rate swap on a settlement date after inception
37 * , c*,,8*+* ,
=
+ Σ 4-\*: ?/«+* ,c − Σ 48&/,- > ?/«+* ,c
…/87*
59
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Learning Module 8: Pricing and Valuation of Options
Option value = Exercise value + Time value
At time , (prior to option expiration):
3/88 &?,-& *\* .-c* …/87* = 5/\•0, k −
3/88 &?,-& ,-+* …/87* = . − 5/\•0, k −
7, &?,-& *\* .-c* …/87* = 5/\•0,
7, &?,-& ,-+* …/87* = ? − 5/\•0,
1+
1+
1+
E
1+
E
E
E
E
E
E
E
Ž
−k Ž
Ž
−k Ž
1+
ed
Lower bound of call option value = 5/\•0, k −
Upper bound of call option value = k
1+
Ex
Lower bound of put option value = 5/\•0,
si
s
Upper bound of put option value =
N
oe
where:
k = Spot price at time ,
= Exercise price (or strike price)
= Maturity of option
= Risk-free rate
Learning Module 9: Option Replication Using Put-Call Parity
Put-Call Parity
Put-Call Forward Parity
4
Value of the Firm
Value of debt = @ b*—, − ?
Value of equity = .
k +? =. +
1+
E
1+
+? =. +
E
1+
@ = . + @ b*—, − ?
60
E
E
E
E
E
Ž
−k Ž
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Learning Module 10: Valuing a Derivative Using a One-Period Binomial Model
Risk-neutral probability of a price increase in underlying
1+ − U
å= J
− U
where:
kJ
J
= s? %/.,& =
>1
k
kU
U
= b&w %/.,& =
<1
k
k = Current asset price
k J = One-period asset price when price moves up
k U = One-period asset price when price moves down
Hedge ratio
Ex
.J − .U
kJ − kU
s
where:
. J = max 0, k J −
. U = maxL0, k U − Q
ℎ∗ =
ed
Video: https://youtu.be/ymUlKgz-rAw
N
@ J = ℎk J − . J
oe
@ = ℎk − .
si
Riskless portfolio with a Call: ç of the underlying, è, and short call position, é
@ U = ℎk U − . U
Riskless portfolio with a Put: ç of the underlying, è, and long put position, ê
@ = ℎk + ?
@ J = ℎk J + ?J
@ U = ℎk U + ?U
61
CFA Level 1 (2024) Formula Sheet – Noesis Exed
å. J + 1 − å . U
1+
Value of a one-period call option
. =
Value of a one-period put option
å?J + 1 − å ?U
? =
1+
where:
?J = max 0,
?U = maxL0,
− kJ
− kUQ
N
oe
si
s
Ex
ed
Video: https://youtu.be/bXEC-78y_AU
62
CFA Level 1 (2024) Formula Sheet – Noesis Exed
ALTERNATIVE INVESTMENTS
Learning Module 1: Alternative Investment Features, Methods, and Structures
GP Compensation Structure
Ignoring management fee; with catch-up clause
^ = max;0, ¦J + ?
− T <
− T − ¦J <
Ex
where:
^ = GP’s rate of return
? = Performance fee as a percentage of total return
= Single-period rate of return
T = Hard hurdle rate
¦J = Catch-up clause
ed
Ignoring management fee; no catch-up clause
^ = max;0, ?
Multiple on Invested Capital
*/8-9*: …/87* &% - …*c,+* , + s */8-9*: …/87* &% - …*c,+* ,
&,/8 /+&7 , &% - …*c,*: ./?-,/8
si
3=
oe
5
s
Learning Module 2: Alternative Investment Performance and Returns
N
Leveraged Portfolio Return
] =
+
where:
= Periodic rate of return on invested funds
n = Periodic cost of borrowing
@n = Amount of borrowed funds
@¦ = Amount of cash (investor’s own capital)
@n
@¦
63
− n
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Investor’s Return Net of Fees
^ =
=
−
−
× F + max;0,
^
−
× ?<
where:
= Beginning-of-period asset value
= End-of-period asset value
? = GP performance fee
^ = GP’s return in current terms
F = GP’s management fees as a percentage of assets under management
Calculating Hedge Fund Fees and Returns
5/ />*+* , %5/ />*+* , d*>- - > 5/ ~*,
=
×
4**
4**
@/87*
Ex
ed
Management Fee Based on Beginning Market Value
5/ />*+* , %5/ />*+* , f :- > 5/ ~*,
=
×
4**
4**
@/87*
s
Management Fee Based on Ending Market Value
.* ,-…* % .* ,-…*
=
× )/4**
4**
oe
si
Incentive Fee Calculated Independent of Management Fee
.* ,-…* % .* ,-…*
=
× )/- − 5/ />*+* , 4**
4**
4**
N
Incentive Fee Calculated Net of Management Fee
.* ,-…* % .* ,-…*
=
× )/- − 27 :8*
4**
4**
Incentive Fee with Hard Hurdle (Independent of Management Fee)
.* ,-…* % .* ,-…*
=
× )/- − 5/ />*+* , 4** − 27 :8*
4**
4**
Incentive Fee with Hard Hurdle (Net of Management Fee)
27 :8* = 27 :8* /,* × d*>-
- > +/ ~*, …/87*
Note: 1) No incentive is paid if hedge fund incurs loss for the year.
2) Gain may be subject to high watermark.
Video: https://youtu.be/0DKmCgsAAdc
64
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Learning Module 3: Investments in Private Capital: Equity and Debt
No formula.
Learning Module 4: Real Estate and Infrastructure
Loan-to-Value (LTV) Ratio
v @=
5& ,>/>* 8-/—-8-,«
& ,%&8-& …/87*
Required reduction in mortgage liability = Mortgage liability – Required mortgage liability
Learning Module 5: Natural Resources
ed
No formula.
Ex
Learning Module 6: Hedge Funds
No formula.
si
s
Learning Module 7: Introduction to Digital Assets
N
oe
No formula.
65
CFA Level 1 (2024) Formula Sheet – Noesis Exed
PORTFOLIO MANAGEMENT
VOLUME 2
Learning Module 1: Portfolio Risk and Return: Part I
Expected Return on Asset
1+f
= 1 + V– × ;1 + f å < × ;1 + f
where:
V– = Real risk-free rate
f å = Expected inflation
f
= Expected risk premium for the asset
1
− 0„
2
s=f
ed
Utility on Investment
si
Capital Allocation Line (CAL)
s
Ex
where:
s = Utility of investment
f
= Expected return of investment
0 = Risk aversion coefficient
„ = Variance of investment (Note: Substitute „ in decimals)
N
oe
For a portfolio of risky assets (Weight: w ) and risk-free asset:
fL ž Q =
f
o +×
„
−
o
where:
o = Rate of return on risk-free asset
f
= Expected return of risky asset
fL ž Q = Expected return of portfolio
„ = Standard deviation of risky asset’s returns
„ž = Standard deviation of portfolio’s returns = w × „
f
− o
= 5/ ~*, ? -.* &% -c~
„
Two-asset portfolio
Portfolio expected return, fL ž Q = w
+w
Portfolio variance, „ž = w „ + w „ + 2w w 3&…
66
,
Ø „ž
<
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Portfolio standard deviation, „ž =
Note: 1) 3&…
,
=‹ „„
w „ + w „ + 2w w 3&…
2) n securities requires n variances and
# #E
,
covariances
Video: https://youtu.be/lUwulZ9ONC0
Foreign Asset
Return of a foreign asset in domestic currency
a = 1 + K¦ × 1 +
–{
−1
Standard deviation of return of a foreign asset in domestic currency
ed
„a = ¥„K¦ + „–{ + 2 × ‹ × „K¦ × „–{
„
H−1
„
H−1
+
3&… =
+
‹„
H
H
H
H
si
Portfolio of Many Risky Assets
s
Ex
where:
K¦ = Return of foreign asset (in local currency)
–{ = Change in exchange rate (FX rate quoted as domestic currency/foreign currency)
„K¦ = Standard deviation of foreign asset’s returns
„–{ = Standard deviation of the exchange rate (DC/FC)
‹ = Correlation coefficient between returns on foreign asset and exchange rate
oe
„ž =
N
where:
H = Number of assets in portfolio
„ = Average variance
3&… = Average covariance
67
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Learning Module 2: Portfolio Risk and Return: Part II
fL ž Q = wo o + 1 − wo f
F
„ž = 1 − wo „F
Return-Generating Models
f
=
o+×
f
−
o =œ
•f
The Single-Index Model
f
−
o =B
−
F
„F
F
where:
f
− o = Expected excess return on asset ~ = Number of factors
œ † = Factor weights (also called factor loadings)
f F = Expected return on market
−
Ø „ž
oŽ +
†
O
œ † fL4† Q
Ex
„
D •f
„F
o
ed
Capital Market Line (CML)
−
oŽ
N
The Market Model
Beta of security ë
œ =
3&…
,
„F
F
f
=
oe
Capital Asset Pricing Model
si
s
where:
„
= 4/.,& 8&/:- > & %/.,& w*->ℎ,
„F
F
=
o + œ •f
=› +œ
F
−
F+*
oŽ
‹ ,F „
„F
Portfolio beta, œž = ∑# w œ
Total variance = Systematic variance + Nonsystematic variance
„ = œ „F + „N
Total risk, „ = ¥œ „F + „N
68
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Arbitrage Pricing Theory (APT) Model
f
^
=
– + ì œ^,
where:
f ^ = Expected return on portfolio
– = Risk-free rate
ì† = Risk premium for factor ¡
œ^, = Sensitivity of the portfolio to factor ¡
€ = Number of risk factors
Fama-French Model
f
= › + œ ,Îí 5€
= › + œ ,Îí 5€
+ œ ,CÎ_ k5d + œ , Î] 25v
+ œ ,CÎ_ k5d + œ , Î] 25v + œ ,°Îa s5b
ed
Carhart Model
f
+ ⋯ + ìí œ^,í
oe
si
s
Ex
where:
f
= Return on an asset in excess of the one-month T-bill return
5€ = Excess return on the market portfolio
k5d = Difference in returns between small-capitalization stocks and large-capitalization
stocks (Size)
25v = Difference in returns between high-book-to-market stocks and low-book-to-market
stocks (Value versus growth)
s5b = Difference in returns of the prior year’s winners versus losers (Momentum)
Portfolio Performance Appraisal Measures
ž−
„ž
o
N
Sharpe ratio =
Treynor ratio =
5 =L ž−
oQ
ž−
„F
+
„ž
5 /8?ℎ/ = 5 −
Jensen’s Alpha,
œž
F
o
o = kℎ/ ?*
›ž =
/,-& × „F +
ž − • o + œž L F −
69
o QŽ
o
CFA Level 1 (2024) Formula Sheet – Noesis Exed
Security Characteristic Line (SCL)
Information ratio =
›
„N
−
o =›
+œL F−
oQ
VOLUME 6
Learning Module 1: Portfolio Management: An Overview
No formula.
Learning Module 2: Basics of Portfolio Planning and Construction
ed
No formula.
Ex
Learning Module 3: The Behavioral Biases of Individuals
No formula.
s
Learning Module 4: Introduction to Risk Management
N
oe
si
No formula.
70