Sample Formula Sheet for CIMA® Certification1

Beta:              𝛽! =𝑐𝑜𝑣!,!𝜎!!

=𝜌!,!𝜎!𝜎!

 

 Beta  of  portfolio:        𝛽! = 𝑤!𝛽! + 𝑤!𝛽! + 𝑤!𝛽! +⋯+ 𝑤!𝛽!    

Bond  Price                                P=Coupon  1+R t +

Par  Value1+R n

n

t=1

 

 CAPM:          𝐸 𝑅! = 𝑅! + 𝛽! 𝐸 𝑅! − 𝑅!    Capital  allocation  line:          𝐸 𝑅! =    𝑅! +

𝜎!𝜎!

𝐸 𝑅! − 𝑅!      

 Capital  market  line:          𝐸 𝑅! =    𝑅! +

𝜎!𝜎!

𝐸 𝑅! − 𝑅!  

 Correlation  coefficient:          𝜌!,! =

𝑐𝑜𝑣!,!𝜎!𝜎!

 

   Covariance:                                            𝑐𝑜𝑣!,! = 𝜌!,!𝜎!𝜎!                        

Covariance:                            𝑐𝑜𝑣!,! =𝑅!" − 𝑅! 𝑅!" − 𝑅!

𝑛

!

!!!

   

                         

Downside deviation: DR=n

∑=

−n

1t

20)) , MARt(min(R

 

Effective  annual  rate:              𝐸𝐴𝑅 = 1 +𝑅𝐹

!− 1  

 

Expected  return:                                          𝐸 𝑅 = 𝑃!

!

!!!

𝑅!  

 Expected  return,  risky  asset  with    risk-­‐free  asset:            E 𝑅! = 𝑤!(𝐸(𝑅!)) + 𝑤!𝑅!    

Forward  exchange  rate:      𝐹! = 𝐸!1 + 𝑟!1 + 𝑟!

!

 

 Forward  price:                                                  𝐹𝑃 = 𝑆!(1 + 𝑟! − 𝑑)!    

Future  value:            𝐹𝑉       = 𝐶𝐹!

!

!!!

(1 + 𝑅)!!!  

 Geometric  mean  return:                    𝑅! = 1 + 𝑅!   1 + 𝑅! 1 + 𝑅! … (1 + 𝑅!)

1/n - 1

Holding  period  return:              𝐻𝑃𝑅! =𝑃! − 𝑃!!! + 𝐶𝐹!

𝑃!!!  

 

Information  ratio:  

1

)(1

2

−

−

−=

∑=

n

RRIR

n

tBtPt

BPP

RR  

 

Internal  rate  of  return:    0 =𝐶𝐹!

(1 + 𝐼𝑅𝑅)!

!

!!!

− 𝐶𝐹!  

 Jensen's  alpha:        α! =  𝑅! −   [𝑅! +  𝛽!(𝑅! − 𝑅!]    

Macaulay  duration:  

∑

∑

=

=

+

+=

n

ttt

n

ttt

i

CFi

tCF

D

1

1

)(

)(

1

1  

 Macaulay  duration  of  portfolio:        𝐷! = 𝑤!𝐷! + 𝑤!𝐷! + 𝑤!𝐷! +⋯+ 𝑤!𝐷!    

Modified  duration:                    𝐷∗ =𝐷

1 + 𝑦        ;        

∆𝑃𝑃= −

𝐷1 + 𝑦

 ∆𝑦        

 

Net  Present  Value:    𝑁𝑃𝑉 =𝐶𝐹!

(1 + 𝑅)!

!

!!!

− 𝐶𝐹!  

 

Present  Value:              𝑃𝑉 =  𝐶𝐹!

(1 + 𝑅)!

!

!!!

 

 Modigliani  squared:      𝑀!   =   1 − !!

!!𝑅! +

!!!!

𝑅!      

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:      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!  

 

Treynor  ratio:    𝑇!=𝑅! − 𝑅!𝛽!

 

 

Upside-­‐downside  capture  ratio:    𝐶𝑅 = 100𝑅!𝑅!

 

 Value from normal position return:

𝑅!   = 𝑁𝑜𝑟𝑚𝑎𝑙  𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛  𝑓𝑜𝑟  𝐶𝑙𝑎𝑠𝑠 (𝐶𝑙𝑎𝑠𝑠  𝑏𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘  𝑟𝑒𝑡𝑢𝑟𝑛)!

!!!

Value added from active asset management: 𝑅!"# = 𝐴𝑐𝑡𝑢𝑎𝑙  𝑟𝑒𝑡𝑢𝑟𝑛 −  (𝑁𝑜𝑟𝑚𝑎𝑙  𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛  𝑟𝑒𝑡𝑢𝑟𝑛) Value added from asset mix (timing) decisions:

𝑅! =𝐹𝑢𝑛𝑑  𝑤𝑒𝑖𝑔ℎ𝑡  𝑓𝑜𝑟  𝐶𝑙𝑎𝑠𝑠 − 𝑁𝑜𝑟𝑚𝑎𝑙  𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛  𝑓𝑜𝑟  𝐶𝑙𝑎𝑠𝑠  X𝐶𝑙𝑎𝑠𝑠  𝑏𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘  𝑟𝑒𝑡𝑢𝑟𝑛 − (𝑁𝑜𝑟𝑚𝑎𝑙  𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛  𝑟𝑒𝑡𝑢𝑟𝑛)

!

!!!

Value added from asset selection decision:

𝑅!"# =𝐹𝑢𝑛𝑑  𝑤𝑒𝑖𝑔ℎ𝑡  𝑓𝑜𝑟  𝐶𝑙𝑎𝑠𝑠  X

𝐹𝑢𝑛𝑑  𝑟𝑒𝑡𝑢𝑟𝑛  𝑓𝑜𝑟  𝐶𝑙𝑎𝑠𝑠 − (𝐶𝑙𝑎𝑠𝑠  𝑏𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘  𝑟𝑒𝑡𝑢𝑟𝑛)

!

!!!

 

Value  at  Risk:            𝑉𝑎𝑅 = 𝑉!𝜎!𝑉!𝐷!  (−𝛼)  

 

Variance  of  a  population:            𝜎! =(𝑅! − 𝑅)!

𝑛

!

!!!

 

 

Variance  of  a  sample:            𝑠! =(𝑅! − 𝑅)!

𝑛 − 1

!

!!!