Sample Formula Sheet for CIMA ® Certification 1 Beta: ! = !,! ! ! = !,! ! ! Beta of portfolio: ! = ! ! + ! ! + ! ! + ⋯ + ! ! Bond Price P= Coupon 1+R t + Par Value 1+R n n t=1 CAPM: ! = ! + ! ! − ! Capital allocation line: ! = ! + ! ! ! − ! Capital market line: ! = ! + ! ! ! − ! Correlation coefficient: !,! = !,! ! ! Covariance: !,! = !,! ! ! Covariance: !,! = !" − ! !" − ! ! !!! Downside deviation: DR= n ∑ = − n 1 t 2 0)) , MAR t (min(R Effective annual rate: = 1 + ! − 1 Expected return: = ! ! !!! ! Expected return, risky asset with riskfree asset: E ! = ! ((! )) + ! ! Forward exchange rate: ! = ! 1 + ! 1 + ! ! Forward price: = ! (1 + ! − ) ! Future value: = ! ! !!! (1 + ) !!! Geometric mean return: ! = 1 + ! 1 + ! 1 + ! … (1 + ! ) 1/n - 1 Holding period return: ! = ! − !!! + ! !!! Information ratio: 1 ) ( 1 2 − − − = ∑ = n R R IR n t Bt Pt B P P R R Internal rate of return: 0 = ! (1 + ) ! ! !!! − ! Jensen's alpha: α ! = ! − [! + ! (! − ! ] Macaulay duration: ∑ ∑ = = + + = n t t t n t t t i CF i tCF D 1 1 ) ( ) ( 1 1 Macaulay duration of portfolio: ! = ! ! + ! ! + ! ! + ⋯ + ! ! Modified duration: ∗ = 1 + ; ∆= − 1 + ∆Net Present Value: = ! (1 + ) ! ! !!! − ! Present Value: = ! (1 + ) ! ! !!! Modigliani squared: ! = 1 − ! ! ! ! ! + ! ! ! ! !
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_____________________________________________________________________________________________________________________________________________________________________________________________________________ 1This formula sheet, which is provided during CIMA® certification exams, is intended only as a resource and not as a substitute for understanding the formulae and studying the topics in the Candidate Handbook’s detailed content outline. The formula list, which may be updated periodically, is not inclusive of all formulae that may be needed for an exam form. Conversely, all formulae on the list are not necessary for any one exam form. These formulae may be expressed differently in some textbooks. Likewise, the format or nomenclature used by academic publishers and providers of study/review materials may vary. Candidates are encouraged to learn to read formulae and recognize them in different formats, selecting the ones they find most useful to perform the necessary calculations. IMCA® and INVESTMENT MANAGEMENT CONSULTANTS ASSOCIATION® are registered trademarks of Investment Management Consultants Association Inc. CIMA®, CERTIFIED INVESTMENT MANAGEMENT ANALYST®, CIMC®, CPWA®, and CERTIFIED PRIVATE WEALTH ADVISOR® are registered certification marks of Investment Management Consultants
Association Inc. Investment Management Consultants Association Inc. does not discriminate in educational opportunities or practices on the basis of race, color, religion, gender, national origin, age, disability, or any other characteristic protected by law. 01-140212.02.617
Price of Present Put-‐call parity: underlying + Price = Price + value of Equity of put of call exercise price
Real rate of return: 𝑅!=1 + 𝑅!1 + 𝑅!
− 1
Sharpe ratio: 𝑆! = 𝑅! − 𝑅!𝜎!
Sortino ratio: =PSR
n
RRn
t
fP
∑=
−
−
1
20)) , MAR(min(RPt
Standard deviation, ex ante: 𝜎 = 𝑃!(𝑅! − 𝐸(𝑅))! !
!!!
Standard deviation of a population: n
RtRn
t∑=
−
= 1
2)(σ
Standard deviation of a sample: 1
1
2
−
∑=
−
= n
RtRn
ts)(
Standard deviation, risky asset A with risk-‐free asset: 𝜎! = 𝑤!𝜎!
Standard deviation of two risky assets: 𝜎! = 𝑤!!𝜎!! + 𝑤!!𝜎!! + 2𝑤!𝑤!𝜌!,!𝜎!𝜎!