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CFA formula sheet include time value of money basics, required rate of return, means, variance and standard deviation and binomial model's.
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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®)
Time Value of Money Basics
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: R (^) G = 1 R 1 1 R (^) N 1 (^1) N ( + )× …× (^) ( + ) −
harmonic mean = (^)
=
i X^ i
1 Variance and Standard Deviation Variance: average of squared deviations from mean.
population variance = =
sample variance = s
2
i i=
N (^2)
σ
22 i i=
n 2 =
n 1
Standard deviation: square root of variance. Holding Period Return (HPR) R
t (^) P t t t t
t t t
− (^) − − −
1 1 1
or 1
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 rp r p
− (^) target σ Expected Return/Standard Deviation Expected return : E X P x x E X P x x P x x P x
i n n
x
X P x x E X P x x
n
i i
Probabilistic variance : σ^2 1 11
2 2 2
2 2
E X P x x E X P x (^) n x (^) n E X Standard deviation: take square root of variance. Correlation and Covariance Correlation: covariance divided by product of the two standard deviations.
corr R R
i j R R
i j i j
Expected return, variance of 2-stock portfolio:
var ,
R w R w R w w R R R R
p A A B B A B A B A B
2 2 2 2 2
σ σ σ σ ρ
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.
z = observation^ −^ population mean= x− 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 C entral limit theorem: when selecting simple random samples of size n from population with mean μ and finite variance s^2 , the sampling distribution of sample mean approaches normal probability distribution with mean μ and variance equal to s^2 / n as the sample size becomes large. Standard Error S tandard error of the sample mean is the standard deviation of distribution of the sample means.
known population variance: σ (^) x σ n
unknown population variance: s s x (^) n
Confidence Intervals C onfidence 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: x z n
± (^) α / 2 σ
zα/2 = 1.645 for 90% confidence intervals (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 intervals (significance level 1%, 0.5% in each tail) Null and Alternative Hypotheses Null hypothesis (H 0 ): 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.