Sample Formula Sheet for CIMA...
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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 − ! ! ! ! ! + ! ! ! ! !
Transcript of Sample Formula Sheet for CIMA...
Sample Formula Sheet for CIMA® Certification1
Beta: 𝛽𝛽! =𝑐𝑐𝑐𝑐𝑐𝑐!,!𝜎𝜎!!
=𝜌𝜌!,!𝜎𝜎!𝜎𝜎!
Beta of portfolio: 𝛽𝛽! = 𝑤𝑤!𝛽𝛽! + 𝑤𝑤!𝛽𝛽! + 𝑤𝑤!𝛽𝛽! +⋯+ 𝑤𝑤!𝛽𝛽!
Bond Price P=Coupon 1+R t +
Par Value1+R n
n
t=1
CAPM: 𝐸𝐸 𝑅𝑅! = 𝑅𝑅! + 𝛽𝛽! 𝐸𝐸 𝑅𝑅! − 𝑅𝑅! Capital allocation line: 𝐸𝐸 𝑅𝑅! = 𝑅𝑅! +
𝜎𝜎!𝜎𝜎!
𝐸𝐸 𝑅𝑅! − 𝑅𝑅!
Capital market line: 𝐸𝐸 𝑅𝑅! = 𝑅𝑅! +
𝜎𝜎!𝜎𝜎!
𝐸𝐸 𝑅𝑅! − 𝑅𝑅!
Correlation coefficient: 𝜌𝜌!,! =
𝑐𝑐𝑐𝑐𝑐𝑐!,!𝜎𝜎!𝜎𝜎!
Covariance: 𝑐𝑐𝑐𝑐𝑐𝑐!,! = 𝜌𝜌!,!𝜎𝜎!𝜎𝜎!
Covariance: 𝑐𝑐𝑐𝑐𝑐𝑐!,! =𝑅𝑅!" − 𝑅𝑅! 𝑅𝑅!" − 𝑅𝑅!
𝑛𝑛
!
!!!
Downside deviation: DR=n
∑=
−n
1t
20)) , MARt(min(R
Effective annual rate: 𝐸𝐸𝐸𝐸𝐸𝐸 = 1 +𝑅𝑅𝐹𝐹
!− 1
Expected return: 𝐸𝐸 𝑅𝑅 = 𝑃𝑃!
!
!!!
𝑅𝑅!
Expected return, risky asset with risk-‐free asset: E 𝑅𝑅! = 𝑤𝑤!(𝐸𝐸(𝑅𝑅!)) + 𝑤𝑤!𝑅𝑅!
Forward exchange rate: 𝐹𝐹! = 𝐸𝐸!1 + 𝑟𝑟!1 + 𝑟𝑟!
!
Forward price: 𝐹𝐹𝐹𝐹 = 𝑆𝑆!(1 + 𝑟𝑟! − 𝑑𝑑)!
Future value: 𝐹𝐹𝐹𝐹 = 𝐶𝐶𝐶𝐶!
!
!!!
(1 + 𝑅𝑅)!!!
Geometric mean return: 𝑅𝑅! = 1 + 𝑅𝑅! 1 + 𝑅𝑅! 1 + 𝑅𝑅! … (1 + 𝑅𝑅!)
1/n - 1
Holding period return: 𝐻𝐻𝐻𝐻𝐻𝐻! =𝑃𝑃! − 𝑃𝑃!!! + 𝐶𝐶𝐶𝐶!
𝑃𝑃!!!
Information ratio:
1
)(1
2
−
−
−=
∑=
n
RRIR
n
tBtPt
BPP
RR
Internal rate of return: 0 =𝐶𝐶𝐶𝐶!
(1 + 𝐼𝐼𝐼𝐼𝐼𝐼)!
!
!!!
− 𝐶𝐶𝐶𝐶!
Jensen's alpha: α! = 𝑅𝑅! − [𝑅𝑅! + 𝛽𝛽!(𝑅𝑅! − 𝑅𝑅!]
Macaulay duration:
∑
∑
=
=
+
+=
n
ttt
n
ttt
i
CFi
tCF
D
1
1
)(
)(
1
1
Macaulay duration of portfolio: 𝐷𝐷! = 𝑤𝑤!𝐷𝐷! + 𝑤𝑤!𝐷𝐷! + 𝑤𝑤!𝐷𝐷! +⋯+ 𝑤𝑤!𝐷𝐷!
Modified duration: 𝐷𝐷∗ =𝐷𝐷
1 + 𝑦𝑦 ;
∆𝑃𝑃𝑃𝑃= −
𝐷𝐷1 + 𝑦𝑦
∆𝑦𝑦
Net Present Value: 𝑁𝑁𝑁𝑁𝑁𝑁 =𝐶𝐶𝐶𝐶!
(1 + 𝑅𝑅)!
!
!!!
− 𝐶𝐶𝐶𝐶!
Present Value: 𝑃𝑃𝑃𝑃 = 𝐶𝐶𝐶𝐶!
(1 + 𝑅𝑅)!
!
!!!
Modigliani squared: 𝑀𝑀! = 1 − !!
!!𝑅𝑅! +
!!!!
𝑅𝑅!
Sample Formula Sheet for CIMA® Certification1
_____________________________________________________________________________________________________________________________________________________________________________________________________________ 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: 𝑅𝑅!=1 + 𝑅𝑅!1 + 𝑅𝑅!
− 1
Sharpe ratio: 𝑆𝑆! = 𝑅𝑅! − 𝑅𝑅!𝜎𝜎!
Sortino ratio: =PSR
n
RRn
t
fP
∑=
−
−
1
20)) , MAR(min(RPt
Standard deviation, ex ante: 𝜎𝜎 = 𝑃𝑃!(𝑅𝑅! − 𝐸𝐸(𝑅𝑅))! !
!!!
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: 𝜎𝜎! = 𝑤𝑤!𝜎𝜎!
Standard deviation of two risky assets: 𝜎𝜎! = 𝑤𝑤!!𝜎𝜎!! + 𝑤𝑤!!𝜎𝜎!! + 2𝑤𝑤!𝑤𝑤!𝜌𝜌!,!𝜎𝜎!𝜎𝜎!
Treynor ratio: 𝑇𝑇!=𝑅𝑅! − 𝑅𝑅!𝛽𝛽!
Upside-‐downside capture ratio: 𝐶𝐶𝐶𝐶 = 100𝑅𝑅!𝑅𝑅!
Value from normal position return:
𝑅𝑅! = 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑓𝑓𝑓𝑓𝑓𝑓 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 (𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏ℎ𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟)!
!!!
Value added from active asset management: 𝑅𝑅!"# = 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 − (𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟) Value added from asset mix (timing) decisions:
𝑅𝑅! =𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤ℎ𝑡𝑡 𝑓𝑓𝑓𝑓𝑓𝑓 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 − 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑓𝑓𝑓𝑓𝑓𝑓 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 X𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏ℎ𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 − (𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟)
!
!!!
Value added from asset selection decision:
𝑅𝑅!"# =𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤ℎ𝑡𝑡 𝑓𝑓𝑓𝑓𝑓𝑓 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 X
𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑓𝑓𝑓𝑓𝑓𝑓 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 − (𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏ℎ𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟)
!
!!!
Value at Risk: 𝑉𝑉𝑉𝑉𝑉𝑉 = 𝑉𝑉!𝜎𝜎!𝑉𝑉!𝐷𝐷! (−𝛼𝛼)
Variance of a population: 𝜎𝜎! =(𝑅𝑅! − 𝑅𝑅)!
𝑛𝑛
!
!!!
Variance of a sample: 𝑠𝑠! =(𝑅𝑅! − 𝑅𝑅)!
𝑛𝑛 − 1
!
!!!
INVESTMENTS & WEALTH INSTITUTE™ is a service mark of Investment Management Consultants Association Inc. doing business as Investments & Wealth Institute. CIMA®, CERTIFIED INVESTMENT MANAGEMENT ANALYST®, CIMC®, CPWA®, and CERTIFIED PRIVATE WEALTH ADVISOR® are registered certification marks of Investment Management Consultants Association Inc. doing business as Investments & Wealth Institute. RMASM and RETIREMENT MANAGEMENT ADVISORSM are marks owned by Investment Management Consultants Association Inc. doing business as Investments & Wealth Institute. 01-171122.03.0617.ctrl
