WILEY'S CFA PROGRAM LEVEL I SMARTSHEETS 2020 - FUNDAMENTALS FOR CFA EXAM SUCCESS
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2020
CFA® EXAM REVIEW
Critical
concepts
for the
CFA EXAM
Wiley’s CFA ®
Program Level I
Smartsheets
Fundamentals For CFA Exam Success
WCID184Expected Return
outcome is 1/6. on a Portfolio
The Continuous Uniform Distribution
The Continuous NUniform Distribution
E(R ) = ∑ wi E(R i ) = w1E(R1 ) + w 2 E(R 2 ) + + w N E(R N )
Wiley’s CFA Program Exam Review
® A continuousp uniform distribution is described by a lower limit, a, and an upper limit, b.
The Time Value of money i =1
The Time Value of money
A continuous
These uniform
limits serve distribution
as the parameters is of
described by a lower
the distribution. Thelimit, a, and an
probability ofupper limit, b.
any outcome
These limits serve as the
or range of outcomes outside
where: parameters of theisdistribution.
this interval The probability
0. Being a continuous of any outcome
distribution, individual
The Time
The Time Value
Value of
of Money
Money
QM
or range ofalso
outcomes
QM outcomes have a outside this of
probability interval
0. Theisdistribution
0. Being a continuous distribution,
is often denoted individual
as U(a,b).
Market value of investment i
Effective Annual Rates outcomes also have
Weight of asset i = a probability of 0. The distribution is often denoted as U(a,b).
Effective Annual Rates
The Time Value of money The probability thatMarket value of portfolio
the random variable will take a value that falls between x1 and x2, that
The
bothprobability thatrange,
lie within the the random
a to b, variable will take of
is the proportion a value thatarea
the total fallstaken
between x1 the
up by andrange,
x2, that
EAR = (1 + Periodic interest rate) N − 1
EAR = (1 + Periodic interest rate) N − 1 both
x1 to lie
x2.within
Portfolio Variancethe range, a to b, is the proportion of the total area taken up by the range, pRobabiliT
The Time Value of Money x1 to x2. QUANTITATIVE METHODS
The Future Value of a Single Cash Flow
The Future Value of a Single Cash Flow
Effective Annual Rates N N
P (x1 ≤p )X= ≤∑xreturn
ExpectedVar(R
∑
Return on a Portfolio wx – x1 ,R )
ETHICAL AND QUANTITATIVE METHODS • Expected on
w2 Cov(R
2 ) = ix j – x a portfolio
N
FVN = PV (1 + r) N i j
The median FVN is=the (1 + r)of the middle item of a data set once it has been sorted into an
PVvalue
N P (x1 ≤ XN≤i =x1 2j=)1 = 2b-a 1
EAR = (1 + Periodic interest rate) − 1 b-a
PROFESSIONAL STANDARDS Time Value of Money ascending
The
The
Present
PresentorValue
descending
Value order.Cash
of a Single
of a Single The advantage
Cash Flow
Flow of using the median is that, unlike the mean,E(R p ) = ∑ wi E(R i ) = w1E(R1 ) + w2 E(R 2 ) + + w N E(R N )
it is not sensitive to extreme values. However, the median does not use all the information
The Future Value FVof a Single Cash Flow
FVmagnitude
Variance of a 2 Asset
Remember that P(X
Portfolio
i =1 3 x) is the same as P(X > x) or this distribution because it is a
about thePVPV = and
size of the observations and only focuses on their relativeRemember
positions. that
continuous P(X 3 x)where
distribution is the same
P(X =asx)P(X > x)zero.
equals or this distribution because it is a
= (1 + r) N
N
Ethics in the Investment Profession FV =(1PV
• Present
N
+ r)(1 + r) N
value (PV) and future value (FV) of a single cash where: • Var(R p ) = wof
Variance
continuous distribution
2 2
A σa (R
2-asset
where w2B σ=
A ) +P(X
2
) + 2w zero.
(R Bequals
portfolio
x) A w B Cov(R A ,R B )
The mode of a data set is simply its most frequently occurring value. A data set that Thehas
BinomialQUANTITATIVE
Distribution
MarketMETHODS
value of investment i
The
one mode
flow
The Present
Present
and Future Value of an Ordinary Annuity
and
said Future
is Value ValueCash
toofbea unimodal,of an Ordinary
while one thatAnnuity
has two modes is said to be bimodal. Weight
The Binomial =
It of asset iDistribution
• Challenges to ethical behavior: overconfidence
QUANTITATIVEbias,
METHODS
The Present
is also possible for a
Single
data set to have
Flow
no mode, where all values are different and no value
Var(R p ) = wMarket
2 2 value of
2 portfolio
2
A σ (R A ) + w B σ (R B ) + 2w A w Bρ(R A ,R B )σ (R A )σ (R B )
PVAnnuityFV: # periods N; % interest per period I/Y; amount FV or amount PMT → PV A binomial random variable is the number of successes (X) from a Bernoulli trial that is
situational influences, focusing on the immediate ratheroccurs more
PVAnnuity : # periods
PV =frequently
% interest
N; others.
than Forper period I/Y;
grouped amount
data, FV or interval
the modal amount PMT →interval
is the APVbinomial random variable is the number of successes (X) from a Bernoulli trial that is
FV : # periods N; % interest per period I/Y; amount FV or amount PMT → carried
FV out “n” times. A Bernoulli experiment is an experiment that has only 2 possible
than long-term outcomes/consequences. The
withmedian
the FV is (1
the
Annuity N
value
+:frequency.
#r) of N;
periods the%middle
modeitem
interest ofonly
perthe a data
period I/Y;set onceofFV
amount itcentral
has been
or amountsorted
PMT into
→ FVan
Variance
Portfolio of “n”
a 3 Asset
Variance times.Portfolio
highest
Annuity The is
Quantiles
ascending
measure
or descending
tendency that can beout
carried
data. order. The advantage of using the median is that, unlike the
Binomial Distribution
A Bernoulli experiment is an experiment that has only 2 possible
outcomes
mean,
which are labeled “success” and “failure.” Further, these two outcomes are
• General ethical decision-making framework: identify, used
The
The
with nominal
Present
Present
it is not
The Present
and
• sensitive
PV and
and Future
andFuture
toFV
Future
extreme Value
ofValue
Value of
ordinary an
of an
values.
of
Annuity
annuity
anHowever,
Ordinary
Annuity
Due
and
Annuity
the
Due median
outcomes
annuity
does not
which areand
mutually exclusive
due
labeled “success”
collectively
use all the information
and “failure.” Further, these two outcomes are
exhaustive.
N2 σ N 2 (R ) + w 2 σ 2 (R ) + w 2 σ 2 (R )
consider, decide and act, reflect. mutuallyVar(R p) = w
exclusive andA collectively B exhaustive.
• Var(R p ) = ∑ ∑of
A QM B C C
A quantile
about is aand
the size value at, or below
magnitude of the which a stated and proportion of theonobservations inpositions.
a data Probability wixwsuccesses
jCov(R i ,R j ) in n trials (where the
The weighted mean is calculated byobservations
assigning differentonlyweights
focuses their relative
toamount
observations in theprobability
The of x
+ successes in n trials is given by:
PV : # periods N; % interest per period I/Y; amount FV or PMT → PV 2w =1A w B Cov(R A ,R B ) + 2w B w C Cov(R B ,R C ) + 2w C w A Cov(R C ,R A )
• CFA Institute Professional Conduct Program sanctions: set lie. Examples
PVAnnuity
data set toPVaccount
of quantiles
Annuity Due
Annuity Due for
= PVOrdinary
= PV
the
include:
disproportionate
Ordinary Annuity
× (1 + r)
Annuity × (1 + r)
effect of certain observations on the arithmetic
The probability
probability of
i
x
=1 j
of
successes success,
in n p,
trials is
is equal
given for
by: all trials) is given by:
The mode FV
FVAnnuity : #Dueperiods
= FV N; % interest ×per
(1 +period
r) I/Y; amount or amount
FV value. PMTset→that
FV has
public censure, suspension of membership and use of mean. TheFVof a data
Annuity
arithmetic set
Annuity Due =mean
is Ordinary
FV simply its equal
most
Annuity
assigns
Ordinary Annuity × (1 +frequently
r)
weights to occurring
every observation A in
data
the data set, Formula
Bayes’
one •mode quartiles,
is said which
to be divide
unimodal, the distribution
while one inhas
that quarters
two or fouris equal
modes said parts.
to be Variance
bimodal. It of a 2 Asset Portfolio
P(X = x) = nCx (p) (1 – p)x n–x
the CFA designation, and revocation of the CFA charter which makes it very sensitive to extreme values.
The •Present
quintiles,
and which
Future divide theandistribution into fifths.
is also
Present •possible
Value
PV ofof offor a dataValue
aaa perpetuity
Perpetuity set toof have Annuity
no mode, Due
where all values are different and no valueP(X = x) = nCx (p)x (1 – p)n – x
(but no monetary fine). Present
• moreValue
deciles, Perpetuity
which divide the data into tenths.data, the modal interval is the interval Var(R ) = w2 σ 2 (R ) + w P 2(Information Event) × P (Event)
occurs
The geometric frequently
meanPMT than to
is used others.
averageFor grouped
rates of change over time or to calculate the • • The Expected
expected
P(Event value
p Information)
A valueA and σ 2 (R B ) +random
Bvariance
of= a binomial 2wofA waBbinomial
Cov(R A ,R
variable Brandom
(X)) is given by:
with• therate
percentiles,
highest
PVAnnuity which
= PVover
frequency.
= PMT
divide
The the distribution
mode ×is(1ther)onlytointo
+order measurehundredths.
ofthe
central tendency that can
• beThe expected value of a binomialP random (Information)
variable (X) is given by:
Standards of Professional Conduct growth PV
PV of a variable
Due
Perpetuity =data.
Perpetuity
I/Y
a
Ordinary period.
Annuity In calculate geometric mean for variable
used with nominal
FV
returns data,Annuity
we must =
Due I/Y FV
addOrdinary
1 to each × (1 + r)
return observation (expressed as a decimal) and then Var(R
Annuity E(x) = n × p2 2 2 2
Measures of Dispersion Counting Rulesp ) = w A σ (R A ) + w B σ (R B ) + 2w A w Bρ(R A ,R B )σ (R A )σ (R B )
Continuous
subtract 1 from
Continuous
Compounding
the result. and
Compounding
and Future Values
Future Values different weights to observations in the
E(x) = n × p QM
I. Professionalism QM Present Statistical Concepts
The weighted
Dispersion
Value of mean is calculated
a Perpetuity
is the variability
data set toFVaccount
by assigning
or spread of a random effect ofvariable around its central •
The number
on thetendency.
Variance
The variance
of aof3different
of
ways that the krandom
Asset Portfolio
a binomial tasks can variable
be doneisequals
given nby:
1 × n2 × n3 × … nk .
PVefor
N = PVe
r ⋅N the disproportionate
r ⋅N
s certain observations arithmetic
• The variance of a binomial random variable is given by:
A. Knowledge of the Law N== n (1 +PMT
FVGarithmetic
R 1 ) × (1
Rmean + R 2 ) ×…× (1 + R n ) to
− 1every observation in the data set,
s
mean. The assigns equal weights
= the most basic measures of variability of data. It is simply the
The •
rangePVis
Data one scales:
Perpetuityof
which makes it very sensitive I/Y Nominal (lowest),
to extreme values. Ordinal, Interval, Ratio Combinations
σ 2
Var(R
= n × p × 2 (l-p)
2 2 2 2 2
p ) = w A σ (R A ) + w B σ (R B ) + w C σ (R C )
B. Independence and Objectivity difference(highest)
between the highest and lowest values in a data set. Normal
2
Distribution
σ = n × p × (l-p)
Important Relationships
Continuous Compounding Between theValues
and Future Arithmetic Mean and Geometric Mean + 2w w Cov(R ,R ) + 2w w
n A n!B C Cov(R B ,R C ) + 2w C w A Cov(R C ,R A )
C. Misrepresentation The geometric mean ismean: used to average A B B
• Arithmetic simplerates of change over time or to calculate the
average n Cr = =
n − r )!( r!)
common pRobabiliTy Dis
growth
• rate FVNof
The =aPVe
=variable
geometric
Range overvalue
r ⋅N mean
Maximum isa always
period. In order
− Minimum
less toorcalculate
than,value geometric mean
equal to the arithmetic mean.Bayes’ 50% ofr all (observations
for •Formula lie in the interval µ ± (2/3)σ
D. Misconduct returns• Geometric
s
mean return: used to average rates of change
• data, we must add
The geometric mean1 toequals
each return observation
the arithmetic mean(expressed
only whenasall
a decimal) and thenare
the observations• 68%
1(or growth) over time Remember: Theofcombination
all observationsformula islie in the
used wheninterval 1σ the items are
the orderµin±which
II. Integrity of Capital Markets subtractidentical.
from the result. z‐Score
P (Information Event) × P (Event)
The difference between the geometric and arithmetic mean increases as the • ofP(Event
The•mean absolute deviation (MAD) is the average of the absolute values of assigned 90%
deviations the labels is NOT
of Information)
all important.
observations= lie in the interval µ ± 1.65σ
A. Material Nonpublic Information observations in a data set from values their mean. 38 P (Information) © 2018 Wiley
dispersion
R G = n (1in+ observed
R1 ) × (1 + R 2 ) ×…×increases.
(1 + R n ) − 1 38 • z95%
= (observed
Permutations value − populationlie
of all observations mean)/standard
in the interval µ ±= 1.96σ
deviation (x − µ)/σ
© 2018 Wiley
B. Market Manipulation common pRobabiliTy Dis
The harmonic mean n is used in the investment management arena to determine the • 99% ofn!all
average
Roy’s Safety‐First
Counting Rules
observations lie in the interval µ ± 2.58σ
Criterion
III. Duties to Clients Pr =
Important
cost of•shares
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Relationships
purchased XBetween
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n1 × n2 × n3 × … ofnka. 7 March 201
shares
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weight =1 an observation is inversely proportional
= iof
purchased over time Minimize P(RP< RT)
to its magnitude. z‐Score
A. Loyalty, Prudence, and Care normally distributed random variable
c03.indd 38 7 March 2018
• The geometricnmean is always less than, or equal to the arithmetic mean.
Combinations
© Wiley 2018
B. Fair Dealing • The geometric mean equals the arithmetic mean only when all the observations where: areall Rights Reserved. any unauthorized copying or distribution will constitute an infringement of copyright.
N z = (observed
return value − population mean)/standard deviation = (x − µ)/σ
identical.
Harmonic
The variance is the mean:
averageX Hof=theN squared deviations around the mean. The standard RP = portfolio
C. Suitability 1geometric and arithmetic mean increases as the n n!
• The difference between
deviation is the positive square root∑ xof the variance. While the variance has no units,
the RT = target return
n Cr = =
• Roy’s safety-first
the
Roy’s Safety‐First ( n − r )!( r!criterion:
r Criterion ) used to compare shortfall risk
D. Performance Presentation dispersion in observed values
i =1 i increases.
standard deviation has the same units as the random variable. Shortfall of portfolios (higher SF ratio indicates lower shortfall risk)
Ratio
Minimize P(R < R )
E. Preservation of Confidentiality • Variance:
The harmonic
Mathematically,
Population mean
unless
Variance isaverage
used
and
ofinvestment
the
in observations
all the the
Standard
squared
Deviation
deviations
in management
the data set arearena around
to determine
identical theinthe
(equal
Remember:
average The
value),
P combination
T formula is used when the order in which the items are
assigned the labels is NOT important. E (RP ) − RT
IV. Duties to Employers 22 cost
the of2018
harmonic
© Wiley mean
shares purchased
mean
all Rights over
will always
Reserved. any time. It may
be less
unauthorized thanbeor
copying viewed
the geometric
distributionas
willaconstitute
special
mean, an type
which ofitself
weighted
infringement ofwill mean
be lessShortfall ratio (SF Ratio) =
copyright.
where:
© Wiley 2018 all Rights Reserved. any unauthorized copying or distribution will constitute an infringement of copyright.
wherethe
than thearithmetic
weight ofmean.an observation is inversely proportional to its magnitude. R σP
P = portfolio return
Permutations QUANTITATIVE METHODS
A. Loyalty n
RT = target return
N
∑ (X i − µ)2 n! Continuously Compounded Returns
B. Additional Compensation Arrangements σ = mean: X H = N 2 i =1
Harmonic Pr =
Shortfall nRatio ( n −r r )!
Sample Variance and n Standard Deviation1
∑ x copying or distribution will constitute Sampling
EAR = e −1 Theory
rcc = continuously compounded annual rate
cc
C. Responsibilities of Supervisors 2 © Wiley 2018 all Rights Reserved. any unauthorized an infringement of copyright.
i =1 i sampling anD esTimaTion E (RP ) − RT
V. Investment Analysis, Recommendations, and Actions • HPR
© Wiley 2018Central
Shortfall r ×limit
all Rights Reserved.
ratio t
(SF Ratio) =
anytheorem:
unauthorized copying
σGiven
or distribution will constitute an
a population infringement
with any of copyright.
t =e −l
n cc
n
∑∑(X 2 P
Mathematically,
© 2018 Wiley (Xi −
unless all2the observations in the data set are identical (equal in value), probability distribution,
X) 21 with mean, μ, and variance,
A. Diligence and Reasonable Basis i − µ)
the harmonic 2 mean
i =1
sσ == i =1 will always be less than the geometric mean, which itself will be less
Continuouslyσ , the
2
sampling
Compounded Sampling
distribution
Returns and Estimation
of the sample mean x,
−n1 sampling anD esTimaTion
B. Communication with Clients and Prospective than the arithmeticn mean. computed from sample size n will approximately be
SamplingEAR
Error
Clients c02.indd 21 = e r − 17 March 2018r7:04
normal cc = PMcontinuously compounded annual rate
with mean, μ (the population mean), and
cc
sTaTisTical concepTs
C. Record Retention pRobabiliTy concepTs • Standardn deviation: positive square root of the variance variance,
Sampling
sTaTisTicalrerrorσ2of/n,
concepTs when
mean =the
Sampling
the sample
and
Sample −size
Estimation
mean is greater
Population mean =than
x − µ or
VI. Conflicts of Interest
∑ (X i − X)
• Coefficient of
2
variation: used to compare relative equal
HPR t =e
×t
to 30. −l cc
i =1
s =of Variation Sampling Error
Standard Error of Sample Mean when Population Variance is known
Coefficient
Expecteddispersions
Value n − 1 of data sets (lower is better) • The standard deviation of the distribution of sample
A. Disclosure of Conflicts Coefficient of Variation
© 2018 Wiley means is
Sampling known
error of the21 as QM
mean the standard
= Sample mean −errorPopulationof sample
mean = xmean. −µ
s σx = σ
B. Priority of Transactions 22 Coefficient= P(Xdeviationof)Xvariation
1 + P(X
= n
n )X nbe less than or equal to the standard • When the population variance is known, the standard
© 2018 Wiley
The meanE(X) absolute 1 (MAD)
2 )X s2 + will
X … P(X always
deviation.Coefficient
This is because, of variation =
by squaring all deviations from the mean, the standard Standard Error of Sample Mean when Population Variance is known
C. Referral Fees X where: error of sample mean is calculated as
c02.indd 21 deviation attachesn a greater weight to larger deviations from the mean.
where: 7 March 2018 7:04 PM
VII. Responsibilities as a CFA Institute Member or CFA = ∑ P(X σ x = the standard error of the sample mean
c02.indd 22 = sampleE(X)
swhere: standard i )X i
deviation = σ2018 7:04 PM
σ7xMarch
• Sharpe ratio: used to measure excess return per unit of σ = the population nstandard deviation
Candidate sThe
X semivariance
==sample
the sample
standard
i
mean. = 1 isdeviation
the average of squared deviations below the mean, while the
n = the sample size
Xsemideviation risk (higher
= the sample is
mean. the positive is better) square root of the semivariance. The target semivariance where: • When the population variance is not known, the standard
A. Conduct as Participants in CFA Institute Programs where:
Sharpe
refers toRatiothe sum of the squared deviations from a specific target return and its square root.
Xi = one of n possible outcomes. σ x = the
Standard error
Error of
standard of sample
Sample
error of theMean mean
sample when is Population
mean calculated as is not known
Variance
B. Reference to CFA Institute, the CFA Designation, Sharpe Ratio σ = the population standard deviation
Chebyshev’s Inequality r − r
and the CFA Program Variance and Standard
Sharpe ratio = Deviation
p f n = the sample size
sx =
s
rp s−p rf
pRobabiliTy concepTs Sharpe ratio = gives n
Chebyshev’s inequality an
2 approximate value for the proportion of observations in aError of Sample Mean when Population Variance is not known
Global Investment Performance σ 2 (X) = E{[X − E(X)]
sp
data set that fall within k standard deviations from the mean. }
Standard
where: • Positive skew: mode < median < mean where: • Confidence interval for unknown population parameter sampling anD
Standards (GIPS®) rp = mean portfolio
where: Value nreturn s x = standard s of sample mean
error
Expected • Kurtosis:
rrpf == risk‐free (X) = ∑
return leptokurtic (positive excess kurtosis), x =
sbased
n on z-statistic
within k standard deviations from mean = 1 –s 1/k = sample standard deviation.
meanσ 2
portfolio return 2
i ) [X i − E(X)]
P(X 2
Proportion of observations
• Compliance by investment management firms with GIPSsrfp == risk‐free platykurtic
standard deviation
return i =1 of(negativeportfolio returns excess kurtosis), mesokurtic (same
E(X) = P(X 1 )X1 + P(X 2 )X 2 + … P(X n )X n σ
is voluntary. s p = kurtosis
standard deviation as ofnormal
portfolio distribution;
returns i.e. zero excess kurtosis) Confidence
where: x ±Intervalsz α /2
Sample skewness, alsoRuleknown n sample mean
The Total Probability
advantage of Chebyshev’s forasExpected
sample relative
inequality is thatskewness,
Value it holds foris calculated
samples and as: populations
s x = standard
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• Comply with all requirements of GIPS on a firm-wide Sample for discrete skewness,
E(X)
n
and= continuous
∑ Probability Concepts
also knowndata
P(X )X
as sample
regardless relative
of the skewness,
shape of is the
calculated as:
distribution. s = samplePoint estimate
standard ± (reliability factor × standard error)
deviation.
basis in order to claim compliance. 1. E(X) = E(X | S)P(S) + E(X | S )P(S ) 3 i i
∑
n c c where: • Confidence interval for unknown population parameter
n (X| S i −) X)
pRobabiliTy concepTs i =1
2. E(X) = E(X | S ) × P(S ) + E(X × P(S ) + . . . + E(X | S ) × P(S ) Confidence
x = The sample
© Wiley 2018based Intervals
mean (pointanyestimate ofcopying
population mean)will constitute an infringement of copyright.
Coefficient ofVariation 1 n 1 2 2 n n where: on t-statistic
all Rights Reserved. unauthorized or distribution
• Third-party verification of GIPS compliance is optional. where: • SExpected K =
( n − 1)(
value and ∑ variance
i =1 (X − X)3
n n − 2 ) i =1 s3
i of a random variable (X) zPoint α/2 = estimate = value of the sample statistic that is used to estimate the population
where: using
S Kn=possible
(of probabilities 2 ) which
parameterThe standard
Point estimatenormal± random
(reliability variable
factor × for which
standard the probability of an observation
error)
• Present a minimum of five years of GIPS-compliant The
X
Expected
E(X)
coefficient
i = one of
= theValue
unconditional
variation,
n − 1)(outcomes. n −expected s3is the
value of X
ratio of the standard deviation of the data set to
σ lyingfactor
Reliability in either tail
= aerror is σ /based
number 2 (reliability
on the factor). distribution of the point estimate and
assumed
its mean, is used to compare the relative dispersions of data sets. A lower coefficient =ofThe standard of the sample mean.
historical performance when first claiming compliance, E(X As n becomes large, the expression
| S1) = the expected value of X given Scenario 1
Variance and Standard Deviation
reduces to the mean cubed deviation.
then level of confidence for the interval (1 − α).
where:
variation
As n1)becomesisprobability
better.
large, QUANTITATIVE METHODS
or since inception of the firm or composite if less than P(S = the
E(X) = P(Xthe ofexpression
)X Scenario 1reduces occurring
1 + P(X 2 )X 2 + … P(X n )X n
to the mean cubed deviation. Standard error = value
Point estimate the standard error ofstatistic
of the sample the samplethat statistic
is used to (point estimate)
estimate the population
five years, then add one year of compliant performance The set of events {S n 1
, S2, . . . 3, Sn} is mutually exclusive and exhaustive. parameter • Whensto use z-statistic or t-statistic
σ 2 (X) = ∑
1 si =n1
nE{[X
1
(X i −− X) E(X)] 2
} © Wiley 2018 ± Rights
xall t α Remember:
Reserved.
Reliability factor =n a number any unauthorized copying or distribution will constitute an
The based on the assumed distribution of the point estimate and infringement of copyright.
each subsequent year so that the firm eventually Covariance CV
S K ≈= ∑ (X i3− X)
3
2 CV measures risk Small Sample Large Sample
E(X) n1=X∑ P(X s i )X i the level of Whenconfidence
Sampling for
from
per unit of a: interval (1 − α).
the
return. n < 30 n > 30
presents a (minimum) performance record for 10 years. SK ≈ ii==11n 3 Standard error = the standard error of the sample statistic (point estimate)
• Nine major sections: Fundamentals of Compliance; Inputwhere: Cov(XY)∑
σ 2 (X)n = = P(X s i ) [X i − E(X)]2
E{[X − E(X)][Y − E(Y)]} where: Normal distribution with known variance z‐statistic z‐statistic
i =1 x = sample mean (the point estimate of the population mean)
where:
= sampleCov(R
swhere: standard B ) = E{[R A − E(R A )][R B − E(R B )]}
A ,Rdeviation tα
data; Calculation Methodology; Composite Construction;X = one of n possible outcomes.
Normal distribution with unknown variance
= the t‐reliability factor
t‐statistic t‐statistic*
Disclosures; Presentation and Reporting; Real Estate; Correlation =i sample
sThe •
Total
Sample Kurtosis
standard deviation
Covariance
Probability
Coefficient
Ruleand forcorrelation
Expected Value of returns
uses standard deviations to the fourth power. Sample excess kurtosissis = standard
2
Non-normal distribution with known variance not available z‐statistic
error of the sample mean
Private Equity; and Wrap Fee/Separately Managed Variance
calculated
Sample
1. E(X)Kurtosis
and Standard Deviation
=as:E(X | S)P(S) uses standard+ E(X | S deviations
c)P(Sc) to the fourth power. Sample excess kurtosis nis Non-normal distribution with unknown variance not available t‐statistic*
Account (SMA) Portfolios. s = sample standard deviation
2. E(X) =as:E(X | S1) × P(S1) + E(X | S2)Cov(R
calculated × P(SA2),R + .B.). + E(X | Sn) × P(Sn)
B) = − ρE(X)]
Corr(R 2 )=
σ 2 (X) =A ,R E{[X (R A ,R }B n (σ )(σ4 ) * Use of z‐statistic is also acceptable
where: n(n + 1)
∑ n (X i −
A X) B
3(n − 1) 2
E(X) = the E =
n
K unconditional
(n − 1)(n
expected value
n(n−+2)(n
∑
i =1 (X − X)
1) − 3) i =1 2 s4
ofi X −
4
− 1)−2 3)
− 2)(n
Sample Biases
Wiley © 2020
E(X
© 2018 | SWiley
1) =
K
2
σthe(X) = ∑ P(X
E =expected i ) [Xof
value i −XE(X)]given Scenario
4
(n3(n
1− (n − 2)(n − 3) Data‐Mining Bias 23
(n − 1)(n
P(S1) = the probability of Scenario 1 occurring
i = 1 − 2)(n − 3) s
The set of events {S1, S2, . . . , Sn} is mutually exclusive and exhaustive. Data mining is the practice of extensively searching through a data set for statisticallySample statistic − Hypothesized value
Test statistic =
Standard error of sample statistic
Power of a Test economicS
Wiley’s CFA Program Exam Review
Power of a test = 1 − P(Type II error) ®
•
The point of intersection of the AD curve and the SRAS curve defines the
Decision Rules for Hypothesis Tests
economy’s short run equilibrium position. Short‐run fluctuations in equilibrium
Decision H0 is True H0 is False real GDP may occur due to shifts in either or both the AD and SRAS curves. Short
Do not reject H0 Correct decision Incorrect decision run equilibrium may be established at, below or above potential output. Deviations
Topics in DemanD anD supply analysis
Type II error of short run equilibrium from potential output result in business cycles.
Reject H0 Incorrect decision Correct decision ○ In an expansion, real GDP is increasing, the unemployment rate is falling
Type I error Power of the test and capacity utilization is rising. Further, inflation tends to rise during an
Total, Average, Marginal, Fixed, and Variable Costs
Significance level = = 1 − P(Type II error) expansion.
P(Type I error)
Table: Summary of Cost Terms ○ In a contraction, real GDP is decreasing, the unemployment rate is rising
Confidence Interval Costs Calculation and capacity utilization is falling. Further, inflation tends to fall during a
contraction.
sample critical standard population sample critical standard
Hypothesis Testing
statistic − value error ≤ parameter ≤ statistic + value
error Shutdown Analysis
Total fixed cost (TFC) Sum of all fixed expenses; here defined to include all Factors causing
Shift in Aggregate Demand
• a shift in aggregate demand (AD)
opportunity costs
x − (z α /2 ) (s n) ≤ µ0 ≤ x + (z α /2 ) (s n)
oThesis TesTing • One-tailedSummary
versus two-tailed tests • Total variable cost (TVC)
Profits are maximizedSum of all variable expenses, or per unit variable cost
when the difference between total
times quantity; (per unit VC × Q)
An Increase in the
Following Factors Shifts the AD Curve Reason
Null Alternate Fail to reject revenue (TR) and total cost (TC) is at its highest. The level
Type of test hypothesis hypothesis Reject null if null if P‐value represents Total costs (TC) Total fixed cost plus total variable cost; (TFC + TVC)
One tailed H0 : μ ≤ μ0 Ha : μ > μ0 Test statistic > Test statistic ≤ Probability that lies of output at which this occurs is the point where: Stock prices Rightward: Increase in AD Higher consumption
Hypothesiscritical
Testing Average fixed cost (AFC) Total fixed cost divided by quantity; (TFC / Q)
• Marginal revenue (MR)
(upper tail) critical valuevalue above the computed test
test statistic. equals marginal cost (MC); and Housing prices Rightward: Increase in AD Higher consumption
Average variable cost (AVC)
Test StatisticH0 : μ ≥ μ0
One tailed
(lower tail)
Ha : μ < μ0 Test statistic <
critical value
Test statistic ≥
critical value
Probability that lies
below the computed test
• MC is not falling Total variable cost divided by quantity; (TVC / Q) Consumer confidence Rightward: Increase in AD Higher consumption
test
Sample statistic − Hypothesized value
statistic.
• Average total cost (ATC)
Breakeven occurs when Total cost divided by quantity; (TC / Q) orEC(AFC + AVC)
TR = TC, and price (or average Business confidence Rightward: Increase in AD Higher investment
: μ = μ0 =Ha : μ ≠ μ0
Two‐tailed TestH0statistic Test statistic <
Standard error
lower
Lower critical
of sample
critical value ≤ statistic
test
Probability that lies
above the positive
revenue)
Marginal equals average
cost (MC) Changetotal
in total cost (ATC)
cost divided at thein breakeven
by change quantity; Capacity utilization Rightward: Increase in AD Higher investment
(ΔTC / ΔQ)
value
Test statistic >
statistic ≤
upper critical
value of the computed
test statistic plus the
quantity of production. The firm is earning normal profit. Government spending Rightward: Increase in AD Government spending a component
Power of a Test upper critical
value
value probability that lies
below the negative
• Breakeven,
Short-run and long-run
Shutdown, operating decisions
and Exit Points
of AD
value of the computed Taxes Leftward: Decrease in AD Lower consumption and investment
Power of a test = 1 − P(Type II error) test statistic. Revenue/ Cost Relationship Short-run Decision Long-run Decision
Bank reserves Rightward: Increase in AD Lower interest rate, higher
TR = TC Continue operating Continue operating investment and possibly higher
• Decision
Type I Rules
versus
forType II errors
Hypothesis Tests
TR > TVC, but < TC Continue operating Exit market
consumption
16 © Wiley 2018 all Rights Reserved. any unauthorized copying or distribution will constitute an infringement of copyright. Exchange rate (foreign Leftward: Decrease in AD Lower exports and higher imports
Decision H0 is True H0 is False TR < TVC Shut down production Exit market
currency per unit
Do not reject H0 Correct decision Incorrect decision domestic currency)
Type II error
Global growth Rightward: Increase in AD Higher exports
Reject H0 Incorrect decision
Type I error
Correct decision
Power of the test
Market Structures economicS
Significance level = = 1 − P(Type II error) • Shift
Factors causing a shift in aggregate supply (AS)
P(Type I error) • Perfect competition
hypoThesis TesTing
in Aggregate Supply
• Minimal barriers to entry, sellers have no pricing power. An Increase in Shifts SRAS Shifts LRAS Reason
• Confidence
Hypothesis Intervaltest concerning the mean of a single hypoThesis TesTing Supply of labor Rightward Rightward Increases resource base
t‐Statisticpopulation • Demand curve faced by an individual firm is perfectly Supply of natural resources Rightward Rightward Increases resource base
sample critical standard population sample critical standard elastic (horizontal).
statistic − value error ≤ parameter ≤ statistic + value error
Chi Squared x − µ0
Test‐Statistic Supply of human capital Rightward Rightward Increases resource base
t-stat = • Average revenue (AR) = Price (P) = MR. 94 © 2018 Wiley
x s −n (z α /2 ) (s n) ≤ µ0 ≤ x + (z α /2 ) (s n) hypoThesis TesTing Supply of physical capital Rightward Rightward Increases resource base
2 ( n − 1) s2 • In the long run, all firms in perfect competition will Productivity and technology Rightward Rightward Improves efficiency of inputs
χ
where: • Summary = make normal profits.
Hypothesis σ 20 test concerning the variance of a normally c04.indd 94
Nominal wages Leftward No impact Increases labor cost 7 March 2018 7:05 PM
xChi = sample mean
Squared
μ0 = hypothesized
Test‐Statistic
distributed
Null population population
Alternate mean Fail to reject • Monopoly Input prices (e.g., energy) Leftward No impact Increases cost of production
Type of test where:hypothesis P‐value represents • High barriers to entry, single seller has considerable
s = standard deviationhypothesis
2of the sample Reject null if null if Expectation of future prices Rightward No impact Anticipation of higher costs and/or
n = sample2size( n − 1) s
H0 :χμsize
≤= μ0 2 Ha : μ > μ0
perception of improved pricing
One tailed n2= sample Test statistic > Test statistic ≤ Probability that lies pricing power.
s = sample variance σ0 power
upper tail)σ 2 critical value critical value above the computed test
est 0 = hypothesized value for population variance
z‐Statistic statistic. • Product is differentiated through non-price strategies. • taxes
Business Reduce exposureLeftward
25
to equities inNoanticipation
impact of a decline
Increases in output and profit
cost of production economicS
anD anD supplywhere:
analysis © Wiley 2018 all Rights Reserved. any unauthorized copying or distribution will constitute an infringement of copyright. margins coming Rightward
under pressure.
• Hypothesis test related to the equality of the variance of • Demand curve faced by the monopoly is the industry Subsidy No impact
• Increase investments in commodities and/or commodity‐oriented companies
Lowers cost of production
EC
One tailed n = sample ≥ μ0
H0 : μsize Ha : μ < μ0 Test statistic < Test statistic ≥ Probability that lies
lower tail)s2 z-stat
= sample
two
Test‐Statisticx − µfor 0populations
the F‐Test
critical value
x − µ0
below the computed test demand curve (downward sloping).
• Reduce
Exchange rate
because
exposure to equities
theirunder
Rightwardin anticipation
prices
No impact of a decline in output
Lowers and profit
cost of production
and profits are likely to rise (due to higher prices).
= variance Topics in Demand andz-stat
Supply =
critical value
Analysis margins coming pressure.
σ n value for population variance
σ 20 = hypothesized s n
est
s12
statistic. • An unregulated monopoly can earn economic profits •
• Conclusions
Impact
Increase investments
oftheirchanges
in commodities
inprofits
AD are and
and/or commodity‐oriented
ASto rise (due to higher prices).
companies
Cycles on
Business because AD andand
prices AS likely
The demand
Two‐tailed where:
F = function
H0 : μ = sμ20
captures the effect of all where:
Ha : μ ≠ μ0 Test statistic <
these factors on demand for a good.
Lower critical Probability that lies in the long run.
x = sample mean 2
lower critical x = sample mean
value ≤ test above the positive • Monopolistic competition Conclusions
Fluctuations in on AD
aggregate and
demandAS and aggregate supply in the short run explain whyAggregate
Unemployment short Level
Test‐Statistic for the F‐Test
μ = hypothesized
Demand population mean μ = hypothesized population mean run real GDP deviates from potential GDP. These deviations of actual GDP from full‐
function: QD x = f(P x , I, Py , …) … statistic
value (Equation ≤ 1) value of the computed employment GDP form phases of Real GDP Rate Aggregate Level of Prices
where:
σ = standard deviation of the population s = standard deviation of the sample • Low barriers to entry, sellers have some degree of
the business cycle.
Unemployment
ECONOMICS
2
2 Test statistic
s1 sample drawn from Populationn1= sample size > upper critical test statistic plus the Real GDP Rate of Prices
s1n = Variance
sample
F =size of upper critical value probability that lies pricing power. Investment Applications of an Increase in AD Resulting in an Inflationary Gap
An increase in AD Increases Falls Increases
2 Topics
2
sEquation 1 is sread2 as “the quantity demanded
2 = Variance of sample drawn fromvalue Populationof2Good X (QDX) dependsbelow on thethe price of in DemanD anD supply analysis
negative An
A increase
decrease datainsuggest
inAD ADthat Increases Falls FallsanIncreases Increases Falls
Tests
Goodfor X (PMeans
), when
consumers’ Population
incomes Variances
(I) and the are
price Assumed
of Good Equal
Y (P ), etc.” • Product is differentiated through advertising and other
If economic
increase
A decrease in AD,in going
AD forward:
the economy is undergoing expansion caused by an
value of the computed in AS Falls Increases Increases Falls Falls
Demand Elasticities An increase Falls
X Y
Hypothesis
where: tests concerning the variance test statistic. non-price strategies. An•increase
A decrease in AS
Corporate inprofits
AS will Increases
be expected to
Falls rise. Falls
Increases
Falls
Increases
sIncome
2 Elasticity
= Variance
1Hypothesis
(x
t = Test of − xof
1 sample
Demand
2 ) − (drawn
µ1 − µ 2from ) Population 1
• Demand curve faced by each firm is downward sloping. aggRegaTe ouTpuT,
A decrease
pRice,
• Commodity
anD economic
in ASprices will beFalls
gRoWTh
Increases
expected to increase. Increases
The own‐price Concerning
elasticity of1/2demand is calculated Appropriate
as: Test Statistic • Interest rates will be expected to rise.
2
sIncome • elasticity
Own-price
2 = Variance of sample
2
sof elasticity
s2pdrawn ofthe
from Populationdemand 2 is calculated as: • Effect
Effect of combined changes
• Inflationary pressures will build in the economy.
in AD ADand AS
Variance of a single, p demand
n +normally
measures
distributed responsiveness
Chi‐square of statdemand for a particular good • In the long run all firms will make normal profits. Effect ofofCombined
Combined Changes
Changes in ASin andASADand
to a change in income,
population %1∆QD nholding
2 all other things constant. Aggregate Output, Price, And Economic Growth
Hypothesis tests
EDPx = concerning x the variance
… (Equation 6) • Oligopoly
Topics in DemanD anD supply analysis Effect on Real on Real
Effect Effect on Aggregate
Effect on Aggregate
%∆ofPxtwo independent, Same as coefficient Change inin ASAS Change in ADin AD GDP GDP Price Level Price Level
6 Equality of variance
Hypothesis
where: © WileyTest 2018Concerning
F‐stat
all Rights Reserved. any unauthorizedAppropriate
normally distributed populations
Test Statistic
copying or distribution Nominal
will constitute an infringement •GDPHigh
of copyright. costs
on I inrefers
market
demand function
to theofvalue
entry, sellers
of goods and enjoy
servicessubstantial
included in GDP pricing
measured at Change Change
Variance of a2 single, normally ∆QD distributed Chi‐square stat current prices.
power.
(Equation 11) Increase Increase Increase Uncertain
Income •1)sIf the
(n −Elasticity +% (n∆of absolute
QD
− 1)s 2
Demand
x2
x
value
QDx of price ∆QDx elasticity
I of demand Increase
© 2018 Wiley
Decrease Increase
Decrease DecreaseIncrease Uncertain Uncertain
95
spopulation
2
= 1 ED I1 = 2 =
∆I is
= … (Equation 8)
divided • Product GDPis differentiated onYear quality, features,
Ifp we expressn1equals
+the %2∆1, I demand
n 2 −percentage change X as the
I in said ∆toI change
be QDunitx X
in elastic. by the value of X, Nominal = Quantity produced in t × Prices in Year t Decrease
Increase Decrease
Decrease UncertainDecrease Decrease Uncertain
Equation
Income 6 can
Equalityelasticity
of variance
•distributed
Ifin the
beofexpanded
demand to the following
measures
of two independent,
absolute value
form:
the responsiveness
F‐stat of demand for a particular good marketing and other non-price strategies. Increase
Decrease Decrease
Increase Uncertain Uncertain Increase Decrease
otherof price elasticity of demand
c04.indd 95 7 March 2018 7:05 PM
sto a change
2normally income,
1 = variance of the first sample
holding all
populations things constant. Decrease Increase Uncertain Increase
lies between
% change 1, demand is said to be relatively Real GDP• refers
0 anddemanded
in quantity Pricing to the strategies:
value of goods pricing interdependence
and services included in GDP measured (kinkedat Economic Growth
mand 2
s2 = variance E I =of the second sample
inelastic. % change∆in base‐year demand
Same as coefficient
prices. curve), Cournot assumption, game theory Business Cycles
QDincome on I in market
Economic
Economic growth Growth may be calculated as:
n1 = number of observations
•EDIfPxthe %∆QDx ∆in QD firstx
sample ∆QDx Px
x QD xof price
(Nash equilibrium), Stackelberg model (dominant
demand function
=%∆absolute
QDx = ∆value QDx = ∆QDx elasticity of(Equation
demand 7) is
n (Equation 11)
n2 = number EDgreater
of = % ∆
observationsP = in P
second =
sample ∆ P
I …
QD … (Equation 8)
Real GDP = Quantity produced in Year t × Base-year prices
firm). • Phases:
• The annual
Economic trough,
growth mayexpansion,
percentage change in real
be calculated peak,
as:GDP, which contraction (or the
tells us how rapidly
%∆Ithan 1,∆demand is∆Isaid
x to be
QDx x relatively elastic.
nd I x x
I Px
Cross‐Price Elasticity of Demand I • Firms always maximize profits at the output level where recession) economy is expanding as a whole; or
degrees•ofIncomefreedom =elasticity n1 + n2 −2 of demand is calculated as: • The annual change in real per capita GDP. Real GDP per capita is calculated as
• The annual percentage change in real GDP, which tells us how rapidly the
GDP Deflator MR = MC • Theories total real GDP divided by total population. It is a useful indicator of the standard
Cross
Arc elasticity
elasticity is of demand as:
calculated measures the responsiveness of demand for a particular good to ofeconomy
living in a is expanding as a whole; or
country.
a change EinI price
=
% change
of another in quantity demanded
good, holding all other things constant. • Identification of market structure
Value of current year output at current year prices
• •Neoclassical
The annual change (Say’sinLaw). real per capita GDP. Real GDP per capita is calculated as
% change in income = × 100 The total
Production real GDP
Function divided
and Potentialby totalGDP population. It is a useful indicator of the standard
(Q 0 - Q1 )
× 100
GDP
• N-firm
Same deflator
concentration
as coefficient
on PY in market Value of current ratio.
year output at base year prices • Austrian of living
(misguided
in a country.
government intervention).
% change in quantity demanded % ∆ Q d (Q 0 + Q1 )/2
•
demand function The production function asserts that an increase in an economy’s potential GDP can be
EP =
• Positive for a ∆normal
QD
% change in price good. =
∆ PPy
=
(P - P ) • HHI
(Equation (add
11) up the squares of the market shares of each Keynesian (advocates government intervention during
QDx ∆QD%
x caused
aggRegaTe ouTpuT, pRice, by:
anD economic gRoWTh
x
0 1
%∆QD × 100 The aProduction
recession). Function and Potential GDP
Cross‐Price Elasticity
Py =
•EDNegative
ofx Demand
= = (P…+(Equation
P )/2 9) of the largest NominalN companies
GDP in the market).
%∆Pyfor an∆Pinferior y good.
∆Py QDx 0 1 GDP deflator = × 100 • An increase in the quantity of inputs used in the production process (e.g., capital
measuresPythe
Real GDP • Monetarist
The production
and labor). function (steady growth
asserts that an rateincrease of money supply).
in an economy’s potential GDP can be
• Cross-price
Cross elasticity of demand elasticity of responsiveness
demand is calculated of demand for as: a particular good to
Aggregate Supply and Demand
a change in price of another good, holding all other things constant. Household saving = Personal disposable income • •New
caused Anby:increase
Classical in the productivity of these inputs with the application of better
(business cycles have
technology. Improving technology enables an economy to produce more output
real causes, no
% change in quantity demanded The Components of GDP − Consumption expenditures
Same as coefficient government intervention).
EC =
% change in price of substitute or complement aggRegaTe ouTpuT, pRice, anD economic • gRoWTh
Components
on PY in market of− GDP
Interest paid by consumers to businesses • using the same quantity
An increase of inputs. of inputs used in the production process (e.g., capital
in the quantity
© Wiley 2018 all Rights Reserved. any ∆ unauthorized
QDx copying or distribution will constitute an infringement of copyright.
demand function
Based on the(Equation
expenditure11) 17 approach,
− Personal GDP transfer
may be payments
calculated to foreigners
as: … (Equation 5) • Neo-Keynesian
and labor). (prices and wages are downward
%∆QDx QDx ∆QDx Py • Expenditure approach •sticky, government
An increase intervention
in the productivity of theseisinputsuseful withinthe eliminating
application of better
•
ED Py =
Positive for =substitutes.
∆ P
= … (Equation 9)
%∆Py any unauthorized
© Wiley 2018 all Rights Reserved. y ∆
copying y QDwill
orPdistribution x constitute an infringement of copyright. GDP = C + I + 19
Income Approach G + (X − M) technology. Improving technology enables an economy to produce more output
unemployment and restoring macroeconomic
Py
• Negative for complements. Business sector saving = Undistributed corporate profits using
© 2018equilibrium).
Wiley
the same quantity of inputs. 97
GDP+ Capitalandconsumption
prices mayallowance … as:(Equation 6)
• Normal good: substitution and income effects reinforce Under •theIncome
C = Consumer income approach,
spending on final
approach at
goods market services be calculated
% change in quantity demanded I = Gross private domestic investment, which includes business investment in capital goods • Unemployment: natural rate vs frictional vs structural
E C = another.
© Wiley 2018oneall Rights Reserved.in
% change anyprice
unauthorized copying or
of substitute ordistribution
complement will constitute an infringement of copyright. (e.g. plant
GDP and = National 19income
equipment) and+changes in inventory (inventory
Capital+ Total
consumption allowance investment) c04.indd 97 vs cyclical. 7 March 2018 7:
GDP = Household consumption private sector saving + Net taxes
• Inferior good: income effect partially mitigates the G = Government+spending Statisticalondiscrepancy
final goods and services … (Equation 1) • Prices indices: using a fixed basket of goods and
substitution effect. X = Exports © 2018 Wiley
M = equality
Imports of expenditure and income services to measure the cost of living results in an
The
• Giffen good: inferior good where the income effect National • Equality
income equals of Expenditure
the sum of incomes andreceived
Income by all factors of production used to upward bias in the computed inflation rate due to
outweighs the substitution effect, making the demand generate final output. It includes: substitution bias, quality bias and new product bias.
Expenditure S = IApproach
+ (G − T) + ( X − M) … (Equation 7) c04.indd 97
curve upward sloping. • Economic indicators
• Employee compensation
• Veblen good: status good with upward sloping demand Under • •the Toexpenditure
finance
Corporate approach, GDP
a fiscal deficit
and government at market
enterprise (Gprofits
–T prices
0),may
>before the be calculated
private
taxes, as:
sector
which includes: • This
Leading (used to predict economy’s future state).
© Wiley 2018 all Rights Reserved. any unauthorized copying or distribution will constitute an infringement of copyright. The IS Curve ○ (Relationship
Dividends paidbetween Income and the Real Interest Rate) equation is just
curve. must save more to households
than onit invests (S > I) and/or imports
GDP○ =Corporate
Consumer spending
profits retainedgoods
by and services
businesses • aexpression
Coincident for GDP (used to identify current state of the
breakdown of the
must
Disposable +exceedincome
Business exports
= GDP
gross fixed (M
−to the>government
Business X).saving − Net taxes
investment economy).
we stated in the
Profit Maximization, Breakeven and ○ Corporate
• Interest income
taxes
+ Change in inventories
paid previous LOS, i.e.
GDP = C + I + G +
(X − M).
+ Government spending on goods and
• Rent and unincorporated business net income (proprietor’s income): Amountsservices
S − I = (G − T) + ( X − M
+ Government (Equation
) …fixed
gross investment 7)
earned by unincorporated
+ Exports − Imports
proprietors and farm operators, who run their own Wiley © 2020
businesses.
The LM Curve + Statistical discrepancy
• Indirect business taxes less subsidies: This amount reflects taxes and subsidies that
Quantityare included
theory in the final
of money: MV =price PY of a good or service, and therefore represents thecuRRency exchange RaTes
Monetary And Fiscal Policy
Wiley’s CFA Program Exam Review
® Forward Premium/(Discount)
Required reserve ratio = Required reserves / Total deposits
Fiscal policy Using the previous relationship between forward and spot rates, the forward premium/
(discount) approximately equates to the price currency (foreign) interest rate versus base
Money multiplier = 1/ (Reserve requirement) currency (domestic) interest rate.
Monetary And Fiscal Policy
Quantity Theory of Money FP B
Required reserve ratio = Required reserves / Total deposits (1 + rP )
= UndeRstanding the Balance sheets
SP B (1 + rB )
M = PY / V
FP B Understanding the Balance Sheets
Money multiplier = 1/ (Reserve requirement) (1 + rP )
−1 = −1
Where: • Lagging (used to identify the economy’s past • + rB ) are expressed using the convention Gains and Losses on Marketable Securities
Exchange
SP B (1 rates
M = Money
Quantity condition).
supplyof Money
Theory A/B; i.e.=number
(1 + rP ) (1of
−
+ runits
B) r of
= P B
− rcurrency A (price currency) Held‐to‐Maturity
Securities Available‐for‐Sale Securities Trading Securities
V = velocity of transactions
P = price level
required(1to+ rpurchase
B ) (1 + rB ) one(1 + unit
rB ) of currency B (base Balance Sheet Reported at cost or Reported at fair value. Reported at fair value.
Monetary and Fiscal Policy
M = PY / V
Y = real output currency). USD/GBP = 1.5125 means that it will take
amortized cost.
Unrealized gains or losses due
cuRRency exchange RaTes
1.5125 USD to purchase 1 GBP. This can be different from
A higher base currency (domestic) interest rate results in a forward discount of
to changes in market values are
reported in other comprehensive
Where: • Quantity
Quantity Equation oftheory
Exchange of money market
approximately conventions
the interest differentialso care needs
percentage, totobebase
leading taken when
currency (domestic)
income within owners’ equity.
M = Money supply
dealing
appreciation of that with
Currency
familiar
percentage.
Exchange
currency Rates
pairs.
Items recognized Interest income. Dividend income. Dividend income.
on the income
V = velocity of
MV = PYtransactions statement Realized gains and Interest income. Interest income.
P = price level • Real rate
Real exchange exchange
This relationship must hold orratearbitrage will take place to realign spot and forward prices
losses.
Realized gains and losses. Realized gains and losses.
•
Y = real output
Contractionary monetary
The Fischer effect states that the policy
nominal interest rate(reduce money
(RN) reflects the realsupply with the ratedifferential. However, the expected spot exchange rate may differ from the
interest rate Unrealized gains and losses
(R ) and
Quantity
R and
the increase
expected rate interest
of
Equation of Exchange inflation rates)
(IIe
). is meant to rein in an forward exchange
Real rate.
exchange rate DC/FC = SDC/FC × (PFC /PDC )
due to changes in market
values.
overheating economy. Expansionary monetary policy The forward rate may be calculated as:
N ==RPY
(increase
RMV
e
R + Πmoney supply and reduce interest rates) is where:• Forward exchange rate (arbitrage-free)
• Common-size
Liquiditybalance
Ratios sheet: expresses each balance
meant to stimulate a receding economy SDC/FC = Nominal spot exchange rate sheet as aLiquidity % ofratios
total assets
indicate toability
a company’s allow to meetanalysts to compare
current obligations.
The Fiscal
The Fischer Multiplier
• Limitations of monetarye policy: N
effect states that the nominal interest rate (R ) reflects the real interest PFC = Foreign price level quoted in terms of the foreign currency
rate firms
formulaof different sizes Current assets
This version of the
is perhaps
PDC = Domestic 1 (1 + rDC )in terms of the domestic(1 + rDC ) Current ratio =
FDC/FC =price level × quoted or FDC/FC = SDC/FC × currency
easiest to remember
(RR) and the expected rate of inflation (II ). Current liabilities
Ignoring •taxes,
because it contains
Central bank cannot
the multiplier can also becontrol
calculatedamount
as: of savings. SFC/DC (1 + rFC ) (1 + rFC )
Cash Flow
the DC term in Quick ratio
=
Cash + Marketable securities + Receivables
Relative Currency Movement numerator for all (acid test) Current liabilities
• NCentral
R = R R + Πbank
e
cannot control willingness of banks to three components:
FDC/FC, SDC/FC and Cash + Marketable securities
Cash ratio =
extend 1 loans.1
= = 10
Where•P Exchange rate regimes:
is the price currency dollarization,
(or quote currency) monetary
and B is the union,
base currency: • CFO (direct method)
(1 + rDC) Current liabilities
○
The Fiscal (1 − MPC)bank
• Multiplier
Central (1 −may
0.9) lack credibility. fixedareparity,
Forward rates target
sometimes zone,ascrawling
interpreted pegs,
expected future fixed
spot rates.parity • Step 1: Start
Solvency with
Ratios sales on the income statement.
• Contractionary fiscal policy (reduceas:as: spending and/
with
FtE=(%S∆
crawling E ( SPbands,
B) managed float, independently • Step 2: Go through
Solvency each
ratios indicate income
a company’s statement
financial leverage account
and financial risk.
Ignoring
Assuming taxes,
taxes,the
themultiplier
multipliercan canalso bebecalculated
also calculated 1 P B) =
t +S −1
or increase taxes) is used to control inflation in an floating rates.SP B
and adjust it for changesTotal inL-T alldebtrelevant working capital
L-T debt-to-equity =
expansion.1
1
Expansionary
1
fiscal policy (increase spending (St +1 ) (r − r ) accounts on the balance Total sheet. equity
and/or − t)]= taxes)
reduce = 10 − 1 = ∆%S(DC/FC)t +1 = DC ofFCprice currency.
(1 − 0.9) is used to raise employment and Premium when
− MPC(1 Total debt
○[1
(1 − MPC) S E(S) > S; expect depreciation (1 + rFC ) • Step 3: Check whether Debt-to-equity =
changes
Total equity in these working
output in a recession
FINANCIAL REPORTING
Discount when E(S) < S; expect appreciation of price currency.
capital accounts indicate Total debt = a debt
Total source or use of cash.
• Fiscal
Assuming multiplier
taxes, the multiplier can also be calculated as:
Currency
ExchangeCross
RatesRates • Step 4: IgnoreFinancial all non-operating
Total assets
items and non-cash
AND ANALYSIS
and the Trade Balance leverage =
Total assets
1 charges. Total equity
Marshall-Lerner condition: ω x ε x + ω M (ε M − 1) > 0
[1 − MPC(1 − t)] P1 P2 P1 B P1
÷ = × = • CFO (indirect method)
where:
Financial
B B B P2Reporting P2 Basics 40• Step 1: Start© Wiley 2018with net any
all Rights Reserved. income.
unauthorized copying or distribution will constitute an infringement of copyright.
• Limitations of fiscal policy: recognition, action and ωx = Share of exports in total trade
impact lags Arbitrage• Types
ωM = Share of audit
Relationship
of imports in totalopinions:
trade unqualified, qualified, adverse, • Step 2: Go up the income statement account and
εx = Pricedisclaimer.
elasticity of demand for exports remove the effect of all non-cash expenses and gains
• Relationships between monetary and fiscal policy Forward
εM = Price pricing is based
elasticity on a sum
of demand forof money invested domestically in the base currency
imports from net income.
• Easy fiscal policy/tight monetary policy – results in spot • Accruals:
at the domestic interestunearned or deferred
rate, rB, as equivalent to the revenue
same sum of (liability),
money converted at the
rate unbilled
for P units of price (foreign) currency, invested
or accrued revenue (asset), prepaid expenses at the foreign rate rP for the same • Step 3: Remove the effect of all non-operating activities UndeRstanding cash FloW
higher
© Wiley 2018 all output
Rights Reserved. and higher
any unauthorized copyinginterest
or distributionrates (government
will constitute an infringement of copyright.
time, and converted back to domestic currency at a forward price set at the beginning of from net income.
expenditure would form a larger component of © Wiley
the term. (asset),
2018 accrued
all Rights Reserved. expenses
any unauthorized (liability).
copying or distribution will constitute an infringement of copyright. 35
UndeRstanding cash FloW
UndeRstanding cash FloW stateMents • Step 4: Make Financial adjustments Analysis forTechniques
changes in all working
national income). • Qualitative characteristics of financial information: capital accounts. UndeRstanding cash FloW
• Tight fiscal policy/easy monetary policy – private relevance, faithful representation,
1 comparability, Activity Ratios Financial Analysis Techniques
sector’s share of overall GDP would rise (as a result (1 + rB ) = SP B (1timeliness,
verifiability, + rP ) understandability (first two are Free •
Cash Free
Flowcash
to the flow
Firm to the firm (FCFF) UndeRstanding cash FloW
FP B Activity Ratios Financial Analysis Techniques
© Wiley 2018 all
ofRights
lowReserved.
interestany unauthorized
rates), copying
whileor distribution
the public will constitute
sector’s shareof copyright. fundamental
an infringement qualitative characteristics).
(1 + rP ) FCFF = NI + NCC + [Int Cost
* (1 of
− goods
tax sold
rate)] − FCInv − WCInv UndeRstanding cash FloW
FP B = SP B Inventory turnover =
would fall. • General features
(1 + rB ) of financial statements: fair Activity Ratios Financial Average Analysis
inventoryTechniques
Cost of goods sold
• Easy fiscal policy/easy monetary policy – this would presentation, going concern, accrual basis, materiality Activity Ratios Inventory
FCFF = CFO [Int *=(1Average
turnover
+ Financial − tax Analysis
rate)] − FCInv
inventoryTechniques
UndeRstanding cash FloW
lead to a sharp increase in aggregate demand, loweringThe last term and1/F aggregation, no offsetting, frequency of reporting,
P/B in the first equation can also be written FB/P or Fd/f. Inventory turnover =
Cost of goods sold UndeRstanding cash FloW
interest rates and growing private and public sectors. comparative information, consistency. Activity
Free Cash• Ratios
Free
Flowcash
to Equity
Financial
flow to Average
equity
Cost of
Analysis
(FCFE)Techniques
inventory
goods=sold
365
Days of inventory on hand (DOH) UndeRstanding cash FloW
• Tight fiscal policy/tight monetary policy – this would Inventory turnover = Inventory turnover
Income Statements Activity Ratios
FCFEof= CFO −Financial
FCInv on +hand
Average
Net of Analysis
inventoryTechniques
borrowing
goods=sold
365
lead to a sharp decrease in aggregate demand, higher Days inventory
Inventory turnover =
Cost (DOH)
Inventory turnover
UndeRstanding cash FloW
Activity Ratios Financial Average Analysis
inventoryTechniques
interest rates and a decrease in demand from both DaysRatios
of inventory on hand Cost of goods=sold
(DOH)
365
private and public sectors. • Revenue recognition methods: percentage of Performance
Activity Financial
Inventory
Ratios
turnover
Financial =
Analysis Analysis Techniques
Inventory
Techniques turnover
Average inventory
Revenue 365
completion, completed contract, installment method, Receivables
Days turnover
of inventory on hand=Cost of goods=sold
(DOH)
Inventory turnover = Average receivables Inventory turnover
International Trade 34 cost recovery method. Activity
Receivables
Days
Ratios
© Wiley 2018 all Rights Reserved. any unauthorized copying or distribution will constitute an infringement of copyright. • Activity ratios
of CF turnover
inventory on =
Cost of
hand CFO
Average
goods=sold
(DOH)
inventory
Revenue 365
Inventory to revenue
turnover ==
• Discontinued operations: reported net of tax as a Average receivables
Net Revenue
Average inventory
Revenue
Inventory turnover
365
• Comparative advantage: a country’s ability to produce separate line item after income from continuing Receivables
Days
Inventory
turnover
of inventory
turnover on
==
=
Cost
hand of goods
(DOH)
Average CFO =sold
receivables
Cash return on assets Inventory 365turnover
a good at a lower opportunity cost than its trading operations. Days of salesturnoveroutstanding Average
(DSO
Average inventory
Revenue
= assets 365
)total
Receivables
Days of inventory on hand = (DOH) =Receivables turnover
partners Average receivables
Inventory 365turnover
• Unusual or infrequent items: listed as separate line Revenue
)=
CFO 365
on = ÷
Days
Cash of of saleson
return outstanding
equity (DSO
• Ricardian model: labor is the only variable factor of items, included in income from continuing operations,
Receivables
Days turnover
inventory = Average
hand (DOH) =Receivables
shareholders'
Average receivables Inventory
turnover
equity
365turnover
production and differences in technology are the key reported before-tax. Days of
Receivables
Days ofCash
sales outstanding
turnover
inventory on = =
hand
( Revenue
DSO )
CFO = 365
(DOH) =Receivables turnover
to income
source of comparative advantage. Payables turnover
Average
= Operating
receivables
PurchasesincomeInventory 365turnover
• Accounting changes Days of sales
Receivables outstanding
turnover = (DSO
Average
Revenue
) = payables
trade
• Heckscher-Ohlin model: capital and labor are variable CF per share =
( CFO
Purchases
Average −Receivables
receivables 365
turnover )
Preferred dividiends
factors of production and differences in factor Financial RepoRting and analysis • Change in accounting principle (applied Payables
Days of sales
Receivables
turnover =
outstanding
turnover Average(DSO
= Number
Revenue
)of= common
trade payables shares outstanding
Receivables turnover
endowments are the primary source of comparative retrospectively). Payables turnover =
Average receivables
Purchases
Revenue 365
Days of sales
Receivables outstanding
turnover = (DSO
Average ) = payables
trade
advantage. If•a company
Change in an
declares accounting
a stock split or a stockestimate
dividend during (applied
the year, the calculation of CoverageNumber Ratios of days of payables Average
=
Receivables
365
receivables
Purchases turnover
Payables turnover = 365
• Effect of tariffs, import quotas, export subsidies and prospectively).
the weighted average number of issued shares outstanding is based on the assumption that Days of sales outstandingAverage(DSO ) = payables
Payables
trade turnover
the additional (newly issued) shares have been outstanding since the date that the original UndeRstanding incoMe stateMents Purchases Receivables
365 turnover
Number of days of payables = 365
voluntary export restraints • Correction
shares were outstanding offrom.
prior-period errors (restate all prior- Payables
Days of sales turnover =
outstanding ( DSO ) =
Payables
CFO trade payables
Average turnover
Debt coverage
Debt coverage = = Receivables
365 turnover
• Price, domestic production and producer surplus period
A complex financial
capital statements).
structure includes
Understanding Income
securities thatStatements
can be converted into common Number
Payables
Days of sales
of days of =payables
turnover
outstanding
Total Purchases
=
debt
Total(DSO
debt ) = payables
Payables
365
turnover
increase. stock (e.g., convertible bonds, convertible preferred stock, warrants and options). These Average
CFO + trade
Interest
CFO =+Purchases Revenue
paid +
365+ Taxes paid
Receivables Taxes turnover
• securities
Basic are EPSpotentially dilutive so companies with complex capital structures are Working
Number Debtcapital
Payablesof
coverage
days of
turnover
turnover
=
Interest paid
=
=payables Average
paid
Basic EPS working capital
• Domestic consumption and consumer surplus inTeRnaTional TRaDe anD capiTal FloWs
required to report basic and diluted EPS. A dilutive security is one whose conversion into Average trade
Interest
Payables paid
payables turnover
Revenue
365
shares of common stock would result in a reduction in EPS. EPS calculated after taking Working
Number capital
of turnover = Purchases
days of =payablesAverage CFO
= CFO working capital
decrease. Net income
into account all dilutive securities in the−capital
Preferred dividends
structure is known as diluted EPS.
Payables turnover
Reinvestment = Average trade Payables turnover
International Trade And Capital Flows Basic EPS = Cash paid for payablesRevenue
L-T assets
• Balance of payments components Weighted average number of shares outstanding Working capital
Number
Payablesof days of
turnover
turnover =Purchases
=
=payables Average
365
working
CFO capital
In determining which potentially dilutive securities should be included in the calculation
Average Payables
Revenue
trade CFO
payables turnover
=
• Payment
Balance of CurrentComponents
account (merchandise trade, services, income of diluted EPS, each of the securities must be evaluated individually and independently to Fixed
Working
Number
Debt
asset payment
turnover
capital
of days of
=Cash=paid for L-T365
turnover
payables
Average
Revenue
= fixed working debt repayment
assets
determine
Diluted• EPS whether they are dilutive. Any anti-dilutive securities must be ignored from the Average capital
receipts and unilateral transfers).
A country’s balance of payments is composed of three main accounts: Diluted
diluted EPS (taking into account all dilutive securities)
EPS calculation. Fixed asset turnover =
Payables
Revenue
CFO 365
turnover
Revenue
Working
Dividend
Number capital
of payment
days of =
turnover
payables = = fixed assets
• The• Capital account (capital transfers and sales/purchases
current account balance largely reflects trade in goods and services.
Convertible Convertible Fixed asset turnover =
Average
Cash paid for
Average dividends
working
Payables turnover
Revenue capital
• Theof capital account balance non-financial
mainly consists of assets).
capital transfers and net sales of Revenue
365
non-produced, Preferred Convertible Convertible
income−− Preferred ++ preferred
preferred+ + debt debt× (1 − t)× (1 − t ) Number
Workingof capital
days of turnover
payables = = fixed CFO
Average assets capital
non‐produced, non‐financial assets. NetNet
income
dividends
dividends
UndeRstanding cash FloW stateMents
Investing/financing = Average
Revenue
Payables
Revenue working
turnover
Cash outflows for investing/financing
• The• Financial account
financial account (financial
measures net capitalassets abroad
flows based and
on sales andforeign-
purchases of Diluted EPS
=
dividends
dividends interest
interest
Total asset
Fixed asset turnover
turnover
Working capital turnover
==
=
Average total
Revenue
IFRS requires theDiluted EPS = Shares from Average fixedassets
assets capital
owned
domestic and financial assets
foreign financial in the reporting country). use
assets. of a similar Weighted
conversion of
Shares from Shares
Total asset turnover ==
Average
Revenue
Revenue working
Revenue
method, but does
average + Shares from Sharesoffrom
+ conversion + issuable from Shares Fixed
Working asset turnover
capital turnover =
Average total
Weighted convertible fixedassets
Current •Account
not refer to it convertible
Current account surplus or deficit. as the Treasury shares
average +
conversion of
preferred shares
+ debt
conversion ofstock+options Liquidity Ratios
issuable from• Liquidity ratios =
AverageAverage
Revenue
RevenueRevenue
assets capital
working
stock method.
convertible convertible Total asset
1 Fixed asset turnover
turnover =
The proceeds of
shares stock options Working capital turnover =
Average total assets
option exercise are
preferred shares debt Average fixed
Revenue assets
Average working capital
assumed to be used Both U.S. GAAP and IFRS require the presentation of EPS (basic EPS and their diluted Current
== assets Revenue
CA = X – M = Y – (C + I + G) to repurchase shares
at the average Balance Sheets
EPS) on the face of the income statement.
Total asset
© Wiley 2018Current
Fixed
all Rights
turnover
ratio
asset = any unauthorized
turnover
Reserved.
CurrentAverage
copying
liabilities
Average total or distribution will constitute an infringement of copyright.
fixedassets
assets
market price and Revenue
Revenue
these shares are Total
© Wiley 2018Fixed asset
asset turnover
turnover ==
Currency Exchange Rates known as inferred
shares. The excess
Treasury Stock
Comprehensive Income Method
• Accounting for gains and losses on marketable securities 42 © Wiley 2018
all Rights
all Rights
Reserved.
Reserved.
any unauthorized
any Average
Average
unauthorized
copying
total
fixed
copying
Revenue
Revenue
orassets
or
distribution
assets
will constitute an infringement of copyright.
distribution will constitute an infringement of copyright.
of new issued shares
over inferred shares In the calculation of diluted EPS, stock options and warrants are accounted for by using © Wiley 2018Fixed Total asset
asset
all Rights turnover
turnover
Reserved. ==
any unauthorized copying orassets
distribution will constitute an infringement of copyright.
is added to the Net income + Other comprehensive income = Comprehensive
the treasury stock method (required under U.S. GAAP). The treasury stock method income Cash + Average
Average
Short-term total
fixed assets
marketable investments + Receivables
weighted average Quick ratio = Revenue
number of shares assumes that all the funds received by the company from the exercise of options and
© Wiley 2018Total asset
all Rights turnover
Reserved. =
any unauthorized Current
copying orassets liabilities
distribution will constitute anWiley
infringement of copyright.
outstanding.
warrants are used by the company to repurchase shares at the average market price. The Average total © 2020
FRA Ending resulting
Shareholders’ Equity Revenue
net increase in the number of shares equals the increase in shares from exercise Total asset turnover =
of options and warrants minus the decrease in the number of outstanding shares from © Wiley 2018 all Rights Reserved. any unauthorized
Average copying
totalorassets
distribution will constitute an infringement of copyright.
Ending shareholders’ equity = Beginning shareholders’ equity + Net income +
repurchases. Revenue
Total asset turnover =You can also read
