LEVEL I
SCHWESER’S
QuickSheet
CritiCal ConCepts for the 2021 Cfa® exam
ETHICAL AND PROFESSIONAL
STANDARDS
I Professionalism
I(A) Knowledge of the Law.
I(B) Independence and Objectivity.
I(C) Misrepresentation.
I(D) Misconduct.
II Integrity of Capital Markets
II(A) Material Nonpublic Information.
II(B) Market Manipulation.
III Duties to Clients
III(A) Loyalty, Prudence, and Care.
III(B) Fair Dealing.
III(C) Suitability.
III(D) Performance Presentation.
III(E) Preservation of Confidentiality.
IV Duties to Employers
IV(A) Loyalty.
IV(B) Additional Compensation Arrangements.
IV(C) Responsibilities of Supervisors.
V Investment Analysis, Recommendations,
and Actions
V(A) Diligence and Reasonable Basis.
V(B) Communication with Clients and
Prospective Clients.
V(C) Record Retention.
VI Conflicts of Interest
VI(A) Disclosure of Conflicts.
VI(B) Priority of Transactions.
VI(C) Referral Fees.
VII Responsibilities as a CFA Institute
Member or CFA Candidate
VII(A) Conduct as Participants in CFA Institute
Programs.
VII(B) Reference to CFA Institute, the CFA
Designation, and the CFA Program.
Global Investment Performance Standards
(GIPS®)
• Compliance statement: “[Insert name of firm] has
prepared and presented this report in compliance
with the Global Investment Performance
Standards (GIPS).” Compliance must be applied
on a firm-wide basis.
• Nine sections: fundamentals of compliance,
input data, calculation methodology, composite
construction, disclosures, presentation and
reporting, real estate, private equity, and wrap
fee/separately managed account portfolios.
QUANTITATIVE METHODS
Time Value of Money Basics
• Future value (FV): amount to which investment
grows after one or more compounding periods.
• Future value: FV = PV(1 + I/Y)N.
• Present value (PV): current value of some future
cash flow PV = FV/(1 + I/Y)N.
• Annuities: series of equal cash flows that occur at
evenly spaced intervals over time.
• Ordinary annuity: cash flow at end-of-time period.
• Annuity due: cash flow at beginning-of-time period.
• Perpetuities: annuities with infinite lives.
PVperpetuity = PMT/(discount rate).
Required Rate of Return
Components:
1. Real risk-free rate (RFR).
2. Expected inflation rate premium (IP).
3. Risk premium.
E(R) = (1 RFR )(1 IP)(1 RP
)1
real
++
+−
Approximation formula for nominal required rate:
ER RFRI
PR
P()
+ +≅
Means
Arithmetic mean: sum of all observation values in
sample/population, divided by # of observations.
Geometric mean: used when calculating investment
returns over multiple periods or to measure
compound growth rates.
Geometric mean return:
R= 1R 1R 1
G1 N
1N
+
()
××+
()
−…
harmonic mean =
=
∑
N
Xi
i
N1
1
Variance and Standard Deviation
Variance: average of squared deviations from mean.
population variance = =
()
N
sample variance = s
2
i
i=1
N2
σ
µx
∑−
22
i
i=1
n2
=
()
n1
xx
∑−
−
Standard deviation: square root of variance.
Holding Period Return (HPR)
RPP D
P
PD
P
ttt t
t
tt
t
=
++
−
−−
−−
1
11
1 or
Coefficient of Variation
Coefficient of variation (CV): expresses how much
dispersion exists relative to mean of a distribution;
allows for direct comparison of dispersion across
different data sets. CV is calculated by dividing
standard deviation of a distribution by the mean or
expected value of the distribution:
CV s
X
=
Roy’s Safety-First Ratio
rr
p
p
−target
σ
Expected Return/Standard Deviation
Expected return: EX Px x
EX Px xPxx Px
in
n
()
=
()
()
=
()
+
()
++
(
∑
11 22
))
()
=
()
−
()
=
()
∑
x
XPxx EX
Px x
n
ii
Probabilistic variance:
σ22
111
2
22
2
2
−
()
+
()
−
()
++
()
−
()
EX Px xEX
Px xEX
nn
Standard deviation: take square root of variance.
Correlation and Covariance
Correlation: covariance divided by product of the
two standard deviations.
corr RR COVR R
RR
ij
ij
ij
,,
()
=
()
()
()
σσ
Expected return, variance of 2-stock portfolio:
ER wE
RE
R
pA
AB
()
=()
()
+ wB
var
,
RwRwR
ww RRRR
pAABB
AB AB
AB
()
=
()
+
()
+
()()
()
22 22
2
σσ
σσρ
Normal Distributions
Normal distribution is completely described by its
mean and variance.
68% of observations fall within ± 1s.
90% fall within ± 1.65s.
95% fall within ± 1.96s.
99% fall within ± 2.58s.
Computing Z-Scores
Z-score: “standardizes” observation from normal
distribution; represents # of standard deviations a
given observation is from population mean.
zx
=
−
=
−
observationpopulation mean
standard deviation
µ
σ
Binomial Models
Binomial distribution: assumes a variable can take
one of two values (success/failure) or, in the case of
a stock, movements (up/down). A binomial model
can describe changes in the value of an asset or
portfolio; it can be used to compute its expected
value over several periods.
Sampling Distribution
Sampling distribution: probability distribution of
all possible sample statistics computed from a set of
equal-size samples randomly drawn from the same
population. The sampling distribution of the mean is
the distribution of estimates of the mean.
Central Limit Theorem
Central limit theorem: when selecting simple
random samples of size n from population with
mean µ and finite variance s2, the sampling
distribution of sample mean approaches normal
probability distribution with mean µ and variance
equal to s2/n as the sample size becomes large.
Standard Error
Standard error of the sample mean is the standard
deviation of distribution of the sample means.
known population variance: σ
σ
xn
=
unknown population variance: ss
n
x=
Confidence Intervals
Confidence interval: gives range of values the mean
value will be between, with a given probability (say
90% or 95%). With known variance, formula for a
confidence interval is:
xz n
±α
σ
/2
zα/2 = 1.645 for 90% confidence inter vals
(significance level 10%, 5% in each tail)
zα/2 = 1.960 for 95% confidence intervals
(significance level 5%, 2.5% in each tail)
zα/2 = 2.575 for 99% confidence inter vals
(significance level 1%, 0.5% in each tail)
Null and Alternative Hypotheses
Null hypothesis (H0): hypothesis that contains the
equal sign (=, ≤, ≥); the hypothesis that is actually
tested; the basis for selection of the test statistics.
Alternative hypothesis (Ha): concluded if there is
sufficient evidence to reject the null hypothesis.
Difference Between One- and Two-Tailed Tests
One-tailed test: tests whether value is greater than or
less than a given number.
