2018 CFA一级公式大全
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Approximation formula for nominal required rate: E(R) = RFR + IP + RP 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:
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.
Coefficient o f Variation Coefficient o f 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:
E(R a ) +
wenku.baidu.com
w b E(Rb)
^
I 1(A) 1(B) 1(C) 1(D) II 11(A) 11(B) III III (A) III(B) III(C) III(D) III(E) IV IV(A) IV(B) IV(C) V V(A) V(B) V(C) VI VI (A) VI(B) VI (C) VII VII(A) VII(B)
C r i t i c a l C o n c e pt
d
s for t he
2018 CFA® E x a m
Expected return, variance o f 2-stock portfolio:
E ( R P) =
w a
ETHICAL AND PROFESSIONAL STANDARDS
cv = 4
X
Sharpe Ratio Sharpe ratio: measures excess return per unit of risk. Sharpe ratio =
rP ~ rf
QUANTITATIVE METHODS
Time Value o f M oney 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 ^W-of-time period. • Annuity due: cash flow at beginning-of-time period. • Perpetuities: annuities with infinite lives. PVperpetuity . = PMT/(discount rate). v ' Required Rate o f Return Components: 1. Real risk-free rate (RFR). 2. Expected inflation rate premium (IP). 3. Risk premium.
Professionalism Knowledge of the Law. Independence and Objectivity. Misrepresentation. Misconduct. Integrity of Capital Markets Material Nonpublic Information. Market Manipulation. Duties to Clients Loyalty, Prudence, and Care. Fair Dealing. Suitability. Performance Presentation. Preservation of Confidentiality. Duties to Employers Loyalty. Additional Compensation Arrangements. Responsibilities of Supervisors. Investment Analysis, Recommendations, and Actions Diligence and Reasonable Basis. Communication with Clients and Prospective Clients. Record Retention. Conflicts of Interest Disclosure of Conflicts. Priority of Trans actio ns. Referral Fees. Responsibilities as a CFA Institute Member or CFA Candidate Conduct as Participants in CFA Institute Programs. Reference to CFA Institute, the CFA Designation, and the CFA Program.
V 1
Normal Distributions Normal distribution is completely described by its mean and variance. 68% of observations fall within ± la . 90% fall within ± 1.65a. 95% fall within ± 1.96a. 99% fall within ± 2.58a. Computing Z-Scores Z-score: “standardizes” observation from normal distribution; represents # of standard deviations a given observation is from population mean. z= observation —population mean standard deviation x —/x < 7
Variance and Standard Deviation Variance: average of squared deviations from mean.
2
population variance = cr = — -----N
n
!>.— u
N
P)'
sample variance - s2- i=i
Var( R p) = WAa 2 (R a ) + W2 B<72 ( R b )
+ 2w a w b< t (R a ) ^ ( R b ) p ( r
a -r b )
Rc= (1 + R,)x...x(l + RN) P - 1
harmonic mean = N N Jl^
E i=i .5 c ,
x)2 n —1
Standard deviation: square root of variance. H olding Period Return (HPR) P , - P ^ + D, P.-i + P«-i
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 o f the mean is the distribution of estimates of the mean. Central Limit Theorem Central lim it theorem: when selecting simple random samples of size n from population with mean p, and finite variance a 2, the sampling distribution of sample mean approaches normal probability distribution with mean |i and variance equal to o2ln as the sample size becomes large. Standard Error Standard error o f the sample mean is the standard deviation of distribution of the sample means. known population variance: cr- = a ■r*
Approximation formula for nominal required rate: E(R) = RFR + IP + RP 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:
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.
Coefficient o f Variation Coefficient o f 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:
E(R a ) +
wenku.baidu.com
w b E(Rb)
^
I 1(A) 1(B) 1(C) 1(D) II 11(A) 11(B) III III (A) III(B) III(C) III(D) III(E) IV IV(A) IV(B) IV(C) V V(A) V(B) V(C) VI VI (A) VI(B) VI (C) VII VII(A) VII(B)
C r i t i c a l C o n c e pt
d
s for t he
2018 CFA® E x a m
Expected return, variance o f 2-stock portfolio:
E ( R P) =
w a
ETHICAL AND PROFESSIONAL STANDARDS
cv = 4
X
Sharpe Ratio Sharpe ratio: measures excess return per unit of risk. Sharpe ratio =
rP ~ rf
QUANTITATIVE METHODS
Time Value o f M oney 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 ^W-of-time period. • Annuity due: cash flow at beginning-of-time period. • Perpetuities: annuities with infinite lives. PVperpetuity . = PMT/(discount rate). v ' Required Rate o f Return Components: 1. Real risk-free rate (RFR). 2. Expected inflation rate premium (IP). 3. Risk premium.
Professionalism Knowledge of the Law. Independence and Objectivity. Misrepresentation. Misconduct. Integrity of Capital Markets Material Nonpublic Information. Market Manipulation. Duties to Clients Loyalty, Prudence, and Care. Fair Dealing. Suitability. Performance Presentation. Preservation of Confidentiality. Duties to Employers Loyalty. Additional Compensation Arrangements. Responsibilities of Supervisors. Investment Analysis, Recommendations, and Actions Diligence and Reasonable Basis. Communication with Clients and Prospective Clients. Record Retention. Conflicts of Interest Disclosure of Conflicts. Priority of Trans actio ns. Referral Fees. Responsibilities as a CFA Institute Member or CFA Candidate Conduct as Participants in CFA Institute Programs. Reference to CFA Institute, the CFA Designation, and the CFA Program.
V 1
Normal Distributions Normal distribution is completely described by its mean and variance. 68% of observations fall within ± la . 90% fall within ± 1.65a. 95% fall within ± 1.96a. 99% fall within ± 2.58a. Computing Z-Scores Z-score: “standardizes” observation from normal distribution; represents # of standard deviations a given observation is from population mean. z= observation —population mean standard deviation x —/x < 7
Variance and Standard Deviation Variance: average of squared deviations from mean.
2
population variance = cr = — -----N
n
!>.— u
N
P)'
sample variance - s2- i=i
Var( R p) = WAa 2 (R a ) + W2 B<72 ( R b )
+ 2w a w b< t (R a ) ^ ( R b ) p ( r
a -r b )
Rc= (1 + R,)x...x(l + RN) P - 1
harmonic mean = N N Jl^
E i=i .5 c ,
x)2 n —1
Standard deviation: square root of variance. H olding Period Return (HPR) P , - P ^ + D, P.-i + P«-i
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 o f the mean is the distribution of estimates of the mean. Central Limit Theorem Central lim it theorem: when selecting simple random samples of size n from population with mean p, and finite variance a 2, the sampling distribution of sample mean approaches normal probability distribution with mean |i and variance equal to o2ln as the sample size becomes large. Standard Error Standard error o f the sample mean is the standard deviation of distribution of the sample means. known population variance: cr- = a ■r*