CFA Level 1, June, 2016 - Formula Sheet

FinQuiz

Formula Sheet

Reading 5: Time Value of Money

•  

1.   Interest Rate (i) •   i = Rf + Inf P + Default Risk P + Liquidity P + Maturity P •   Nominal Rf i rate = Real Rf i Rate + Inf P •  

i rate as a growth rate = g =

% !"# #

$"

5.

•  

PV =

•  

-1

!" &'( #

L G[&

FVOA =

𝑃𝑀𝑇G 1 + 𝑟

% %^_ #

( 1/G

=

&'( # /&

•  

PV (for more than one Compounding

•  

( (- /.×1 .

𝑤ℎ𝑒𝑟𝑒  𝑟7 = 𝑠𝑡𝑎𝑡𝑒𝑑  𝑎𝑛𝑛  𝑖 − 𝑟𝑎𝑡𝑒 FVN = 𝑃𝑉 1 + 𝑟 1 FV (for more than one Compounding per year) = FVN = 1 +

(- .×1 .

•  

FV (for Continuous Compounding) = FVN = 𝑃𝑉𝑒 (-×1

•  

Solving for N =

B1

CD ED

B1 &'(

(where LN =

natural log) Stated & Effective Rates •   Periodic i Rate = FGHGIJ  KLL  M  NHGI

6.

PV of Annuity Factor =

HPR = rt =

•  

PVAD = 𝑃𝑀𝑇

&/

% %^_ #

(

FVAD = 𝑃𝑀𝑇

•  

1 + 𝑅L

3.   HPR =

Q! gNN

$%   /$h '  i% $h

)"h

(

opf $H(/$(MaI

(1 + 𝑟) =

− 𝑐𝑓f

2.   IRR (when project’s CFs are perpetuity) = NPV = - IO +

_1

6.   Bank Discount Yield = BDY = rBD = &'( # /&

Reading 6: Discounted Cash Flow Applications 1.   NPV =

% m

TWR (for the year) = rTWR = [(1+R1)× (1+R2)×… (1+R365)] -1 where R1 =

•  

+ PMT at t =

FVOA ×(1+r)

Q!Z L G[& &'( Z

)"h

)"% /)"h

PVOA + PMT •  

)"% /)"h

TWR (for more than one periods) = rTWR = [(1+rt,1)× (1+rt,2)×… (1+rt,n)] -1 Annualized TWR (when investment is for more than one year) = 1 + 𝑅& 1 + 𝑅k … +

•  

PV & FV of Annuity Due

1O  OP  QO.ROSLJMLT  $I(MOJ7  ML  ULI  VIH(

Effective (or Equivalent) Ann Rate (EAR = EFF%) = 1 + 𝑃𝑒𝑟𝑖𝑜𝑑𝑖𝑐  𝑖  𝑅𝑎𝑡𝑒 . − 1

% _- b×# b _b

= 0 (IRR

5.   TWR: •   TWR (when no external CF) = rTWR =

$"

%^

Q! * M[f &'gNN Z

represents the MWR)

(

Size of Annuity Payment = PMT = &/

$)*

PV of Perpetuity =

•  

= 𝑃𝑀𝑇

&/

4.   MMWR =

$"  OP  KLLSMG`  !HaGO(

per year) = PV= FVN 1 +

4.

$)* L G[& &'( Z

PVOA =

𝑃𝑀𝑇 •  

•  

•   •  

EAR (with Continuous Compounding) = EAR = 𝑒 (- − 1

PV & FV of Ordinary Annuity •  

2.   PV and FV of CF =

CFA Level I 2016

=0

L

 

1−

$H( L  ×  (qr

therefore Price = Par

opf

7.   Holding Period Yield = HPY =

$%   /$h '  i% $h

8.   Effective Annual Yield = EAY = 1 + 𝐻𝑃𝑌 opu/G − 1 (Rule: EAY > BDY) 9.   Money Market Yield (or CD equivalent Yield) rMM: •  

rMM = HPY ×  

•  

rMM = (rBD) ×

opf G

!HaI  "HwSI  OP  GxI  *(IH7S(`  yMww $S(axH7I  $(MaI

FinQuiz

•  

rMM =

Formula Sheet

opf   (qr opf/ G (qr

•  

(Rule: rMM>

rBD) 10.   Bond Equivalent Yield = BDY = Semiannual Yield × 2 Reading 7: Statistical Concepts & Market Returns 1.   Range = Max Value – Min Value 2.   Class Interval = i ≥ •   •   •  

z/B {

where

i = class interval H = highest value L = lowest value, k = No. of classes.

3.   Absolute Frequency = Actual No of Observations (obvs) in a given class interval 4.   Relative Frequency =

K|7OwSGI  !(I}SILa`

6.   Cumulative Relative Frequency = Add up the Relative Frequencies 7.   Arithmetic Mean =

17.   Population Var = σ2 =

For Odd no. of obvs locate

18.   Population S.D = 𝜎 k =

k

•  

FS.  OP  O|~7  ML  JHGH|H7I 1O.OP  O|~7  ML  GxI  JHGH|H7I

8.   Median = Middle No (when observations are arranged in ascending/descending order)

median at

k

# … /ˆ ‰ ƒ„% ƒ

1

m ‰ ƒ„% …ƒ /…

L/&

9.   Mode = obvs that occurs most frequently in the distribution

m … /… ‰ ƒ„% ƒ

20.   Sample S.D = s = L M[& 𝑤M 𝑋M

10.   Weighted Mean = 𝑋• =   (w1X1+ w2X2+….+ wnXn) 11.   Geometric Mean = GM = with Xi≥0 for i = 1,2,…n.

m

𝑋& 𝑋k … 𝑋L

L

!O(  Hww  …ƒ ‹…

m ƒ …ƒ

1

…ƒ /… ‰ L/&

22.   Semi-deviation (Semi S.D) = 𝑠𝑒𝑚𝑖𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 =

!O(  Hww  …ƒ ‹…

% m ƒ„% ‚ ƒ

23.   Target Semi-var = 13.   Population Mean = µ =

L/&

= 21.   Semi-var =

12.   Harmonic Mean = H.M = 𝑋z =  

with 𝑋M > 0

for i = 1,2,.,.,n.

!O(  Hww  …ƒ ‹y

…ƒ /… ‰ L/&

…ƒ /y ‰ L/&

where B = Target Value 24.   Target Semi-Deviation =

14.   Sample Mean = 𝑋 =  

m ƒ …ƒ

L

  where n =

number of observation in the sample 15.   Measures of Location: Quartiles =

•  

Quintiles =

•  

Deciles =

•  

Percentiles = Ly = 𝑛 + 1

&f

!O(  Hww  …ƒ ‹y

…ƒ /y ‰ L/& F …

where s= sample S.D and 𝑋 = sample mean

‡ iM7G(M|SGMOL

u iM7G(M|SGMOL

𝑡𝑎𝑟𝑔𝑒𝑡  𝑠𝑒𝑚𝑖𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 =

25.   Coefficient of Variation = CV =

iM7G(M|SGMOL

•  

, ` &ff

16.   Mean Absolute Deviation = MAD = m ƒ„% …Z /…

1

L'&

19.   Sample Var = s2 =

L

# ‰ ƒ„% …ƒ /ˆ

For Even no of obvs locate L median at

*OGHw  1O  OP  U|~7

5.   Cumulative Absolute Frequency = Add up the Absolute Frequencies

CFA Level I 2016

26.   Sharpe Ratio =

)IHL  $O(GPOwMO  N /)IHL  NP  N F.i  OP  $O(GPOwMO  N

27.   Excess Kurtosis = Kurtosis – 3

FinQuiz

Formula Sheet

28.   Geometric Mean R ≈ 𝐴𝑟𝑖𝑡ℎ𝑚𝑒𝑡𝑖𝑐  𝑀𝑒𝑎𝑛  𝑅 −

"H(MHLaI  OP  N

•  

k

Reading 8: Probability Concepts 1.   Empirical Prob of an event E = P(E) = $(O|  OP  I~ILG  •

•  

CFA Level I 2016

Multiplication Rule for two independent events = P(A & B) = P(AB) = P(A)× P(B) Multiplication Rule for three independent events = P(A and B and C) = P(ABC) = P(A) × P(B) × P(C)

*OGHw  $(O|

2.   Odds for event E =

$(O|  OP  • &/$(O|  OP  •

3.   Odds against event E =

&/$(O|  OP  • $(O|  OP  •  

4.   Conditional Prob of A given that B has occurred = P(A|B) =

$ Ky $ y

→ P(B) ≠ 0.

5.   Multiplication Rule (Joint probability that both events will happen): P(A and B) = P(AB) = P(A|B) × P(B) P(B and A) = P(BA) = P(B|A) × P(A) 6.   Addition Rule (Prob that event A or B will occur): P(A or B) = P(A) + P(B) – P(AB) P(A or B) = P(A) + P(B) (when events are mutually exclusive because P(AB) = 0) 7.   Independent Events: •   Two events are independent if: P(B|A) = P(B) or if P(A|B) = P(A)

8.   Complement Rule (for an event S) = P(S) + P(SC) = 1 (where SC is the event not S) 9.   Total Probability Rule: P(A) = P(AS) + P(ASC) = P(A|S)×P(S) + P(A|SC)×P(SC) P(A) = P(AS1) + P(AS2) +….+ P(ASn) = P(A|S1)×P(S1) + P(A|S2)×P(S2)… P(A|Sn)×P(Sn) (where S1, S2, …,Sn are mutually exclusive and exhaustive scenarios)

L M[&

𝑝 𝑅M − 𝐸𝑅M

𝑤&k 𝑅M + 𝑤kk 𝑅k + 𝑤ok 𝑅o 14.   Correlation (b/w two random variables Ri, Rj) = 𝜌 𝑅M 𝑅” =

𝑅” −

𝐸𝑅” Cov (Ri Rj) = Cov (Rj Ri) Cov (R, R) = σ2 (R) 12.   Portfolio Var = σ2 (Rp) = L L M[& ”[& 𝑤M 𝑤” 𝐶𝑜𝑣 𝑅M 𝑅” σ2 (Rp) = 𝑤&k 𝜎 k 𝑅& + 𝑤kk 𝜎 k 𝑅k + 𝑤ok 𝜎 k 𝑅o + 2𝑤& 𝑤k 𝐶𝑜𝑣 𝑅& , 𝑅k + 2𝑤& 𝑤o 𝐶𝑜𝑣 𝑅& , 𝑅o + 2𝑤k 𝑤o 𝐶𝑜𝑣 𝑅k , 𝑅o

QO~   Nƒ N˜ ™Nƒ ×™N˜

15.   Bayes’ Formula = 𝑃 𝐸𝑣𝑒𝑛𝑡|𝑁𝑒𝑤  𝐼𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 =  

$ 1I•  gLPO(.HGMOL|•~ILG

 ×

$ 1I•  gLPO(.HGMOL

 𝑃 𝑃𝑟𝑖𝑜𝑟  𝑝𝑟𝑜𝑏. 𝑜𝑓  𝐸𝑣𝑒𝑛𝑡 16.   Multiplication Rule of Counting = n factorial = 𝑛! = n (n-1)(n-2)(n-3)…1. 17.   Multinomial Formula (General formula for labeling problem) =  

L! L% !L‰ !…Lž !

18.   Combination Formula (Binomial Formula) = L  𝐶( =

10.   Expected R = E(wiRi) = wiE(Ri) 11.   Cov (Ri Rj) =

13.   Standard Deviation (S.D) =

L (

=

L! L/( !(!

where n = total no. of objects and r = no. of objects selected. 19.   Permutation = L  𝑃( =

L! L/( !

Reading 9: Common Probability Distributions 1.   Probability Function (for a binomial random variable) p(x) = p(X=x) = L Ÿ

𝑝Ÿ 1 − 𝑃

L/Ÿ

==

(for x = 0,1,2….n)

L! L/Ÿ !Ÿ!R

&/R m¡

FinQuiz

Formula Sheet

x = success out of n trials n-x = failures out of n trials p = probability of success 1-p = probability of failure n = no of trials.

•   •   •   •   •  

6.   Roy’s Safety-Frist Criterion = SF Ratio = • NE /N´ ™E

7.   Sharpe Ratio = =

• NE /Nµ ™E

2.   Probability Density Function (pdf) = f(x) &

=

|/H

0           F(x) =

𝑓𝑜𝑟  𝑎 ≤ 𝑥 ≤ 𝑏 = Ÿ/H |/H  

𝑓𝑜𝑟  𝑎 < 𝑥 < 𝑏

3.   Normal Density Funct = 𝑓 𝑥 = & ™ k¥

𝑒𝑥𝑝

/(Ÿ/ˆ)‰ k™ ‰

for − ∞ < 𝑥 < +  ∞

4.   Estimations by using Normal Distribution: •  

Approximately 50% of all obsv fall in k

the interval 𝜇 ± 𝜎 o

•   •   •   •  

Approx 68% of all obvs fall in the interval 𝜇 ± 𝜎 Approx 95% of all obvs fall in the interval 𝜇 ± 2𝜎 Approx 99% of all obvs fall in the interval 𝜇 ± 3𝜎 More precise intervals for 95% of the obvs are 𝜇 ± 1.96𝜎 and for 99% of the observations are 𝜇 ± 2.58𝜎.

5.   Z-Score (how many S.Ds away from the mean the point x lies) 𝑧 = 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑  𝑛𝑜𝑟𝑚𝑎𝑙  𝑟𝑎𝑛𝑑𝑜𝑚  𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒 =  

…/ˆ ™

(when X is normally distributed)

8.   Value at Risk = VAR = Minimum $ loss expected over a specified period at a specified prob level. 9.   Mean (µL) of a lognormal random variable = exp (µ + 0.50σ2) 10.   Variance (σL2) of a lognormal random variable = exp (2µ+ σ2) × [exp (σ2) – 1].

CFA Level I 2016

14.   Continuously compounded return associated with a holding period from 0 to T: R0,T= ln (ST / S0) or 𝑟f,* = 𝑟*/&,* + 𝑟*/k,*/& + ⋯ + 𝑟f,& Where, rT-I, T = One-period continuously compounded returns 15.   When one-period continuously compounded returns (i.e. r0,1) are IID random variables. 𝐸 𝑟f,* = 𝐸 𝑟*/&,* + 𝐸 𝑟*/k,*/& +

11.   Log Normal Price = ST = S0exp (r0,T) Where, exp = e and r0,t = Continuously compounded return from 0 to T 12.   Price relative = End price / Beg price = St+1/ St=1 + Rt, t+1 where, Rt, t+1 = holding period return on the stock from t to t + 1. 13.   Continuously compounded return associated with a holding period from t to t + 1:

⋯ + 𝐸 𝑟f,& = 𝜇𝑇 And 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 =   𝜎 k 𝑟f,* = 𝜎 k 𝑇 S.D. = σ (r0,T) = σ 𝑇 16.   Annualized volatility = sample S.D. of one period continuously compounded returns × 𝑇 Reading 10: Sampling and Estimation 1.   Var of the distribution of the sample mean =

rt, t+1= ln(1 + holding period return) or rt, t+1 = ln(price relative) = ln (St+1 / St) = ln (1 + Rt,t+1)

™‰ L

2.   S.D of the distribution of the sample mean =

™‰ L

FinQuiz

Formula Sheet

3.   Standard Error of the sample mean: •   When the population S.D (σ) is known = 𝜎…   =   •  

™

L

known = 𝑠…   =  

7 L

L% '  L‰ /k

F

7.

L

‰ %/‰ ω % ' ω m% m‰

Power of Test = 1-Prob of Type II Error 𝑧 =  

Î m

(when sample size is large or

small but pop S.D is known)

CI for normally distributed population F L

…% /…‰ / ˆ% /ˆ‰

𝑑𝑓 =   3.

4.

𝑧 =  

…/ˆh m

(when sample size is large but

pop S.D is unknown where s is sample S.D)

7.   Student’s t distribution F L

5.

𝑡L/& =  

…/ˆh m

(when sample size is large or

small and pop S.D is unknown and pop

where 𝑑𝑓 = 𝑛& +   𝑛k −

Test Statistic for a test of diff b/wn two pop means (normally distributed, unequal and unknown pop var unknown) t=

L

…/ˆh

where 𝑆Rk = pooled

2.

when Pop S.D is unknown, the standard error of sample statistic is give by 𝜎…   = ™  

L

with unknown variance = 𝑥 ± 𝑧H/k

L% /& F%‰ '   L‰ /& F‰‰

*

2.

%/‰

estimator of common variance =

when Pop S.D is unknown, the standard error of sample statistic is give by 𝑆…   =  

CI for normally distributed population ™ with known variance = 𝑥 ± 𝑧H/k

µ = 𝑋 ± 𝑡H/k

‰ ω Ð ÏÐ

'

*

where N= population

where S = sample S.D.

…% /…‰ / ˆ% /ˆ‰ m% m‰

𝒔𝒕𝒂𝒏𝒅𝒂𝒓𝒅  𝒆𝒓𝒓𝒐𝒓  𝒐𝒇  𝒔𝒂𝒎𝒑𝒍𝒆  𝒔𝒕𝒂𝒕𝒊𝒔𝒕𝒊𝒄  ∗

6.   Construction of Confidence Interval (CI) = Point estimate ± (Reliability factor × Standard error)

•  

Test Statistic for a test of diff b/w two pop means (normally distributed, pop var unknown but assumed equal) t=

𝑺𝒂𝒎𝒑𝒍𝒆  𝑺𝒕𝒂𝒕𝒊𝒔𝒕𝒊𝒄  𝑯𝒚𝒑𝒐𝒕𝒉𝒆𝒔𝒊𝒛𝒆𝒅  𝑽𝒂𝒍𝒖𝒆  𝒐𝒇  𝒑𝒐𝒑  𝒑𝒂𝒓𝒂𝒎𝒆𝒕𝒆𝒓  

L/&

5.   New Adjusted Estimate of Standard Error = (Old estimated standard error × fpc)

•  

6.

1.   Test Statistic =

m ‰ ƒ„% …ƒ /…

4.   Finite Population Correction Factor = fpc 1/&

x−µ s/ n

Reading 11: Hypothesis Testing

𝑠𝑎𝑚𝑝𝑙𝑒  𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 =

=

sampled is normally or approximately normally distributed)

x−µ σ/ n

where s = sample

S.D estimate of s =   𝑠 k    𝑤ℎ𝑒𝑟𝑒  𝑠 k =

t=

9.   t-ratio =

When the population S.D (σ) is not

1/L

Z=

8.   Z-ratio =

CFA Level I 2016

8.

In this df calculated as

‰ ‰ ω %  ' ω m% m‰ ‰ ‰ ω ω % ‰ m% m‰ ' m% m‰

Test Statistic for a test of mean differences (normally distributed populations, unknown population variances) J/ˆÑh

•  

𝑡 =  

•  

sample mean difference =  𝑑   =  

•  

& L

FJ

L M[& 𝑑M

sample variance = 𝑆Jk =  

m ‰ ƒ„h J% /J

L/&

FinQuiz

•   •  

Formula Sheet

sample S.D = 𝑆Jk sample error of the sample mean difference = 𝑠  𝑑   =  

8.

FÑ

population variance) 𝑋 k = 𝑛 − 1 = 𝑑𝑓  𝑎𝑛𝑑  𝑆 k =

9.

L/& F ‰ ™h‰

where

L/&

Chi Square Confidence Interval for variance Lower limit = L = =U==

‰ …Ò/‰

‰ …%¡Ò/‰

12. Spearman Rank Correlation = 𝑟7 6 LM[& 𝑑&k =1− 𝑛 𝑛k − 1 •   For small samples rejection points for the test based on 𝑟7 are found using table. •   For large sample size (e.g. n>30) t-test can be used to test the hypothesis i.e. 𝑛 − 2 &/k 𝑟7 𝑡 =   1 − 𝑟7k &/k

"

F%‰ F‰‰

 

&ff &'NF

RS =

𝑆&k = 1𝑠𝑡  𝑠𝑎𝑚𝑝𝑙𝑒  𝑣𝑎𝑟  𝑤𝑖𝑡ℎ  𝑛&  𝑜𝑏𝑠   𝑆&k = 2𝑛𝑑  𝑠𝑎𝑚𝑝𝑙𝑒  𝑣𝑎𝑟  𝑤𝑖𝑡ℎ  𝑛k  𝑜𝑏𝑠 𝑑𝑓& =   𝑛& − 1  𝑛𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟  𝑑𝑓   𝑑𝑓k =   𝑛k − 1  𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟  𝑑𝑓

•  

•  

𝑷𝒓𝒊𝒄𝒆  𝒐𝒇  𝒂𝒔𝒔𝒆𝒕   𝑷𝒓𝒊𝒄𝒆  𝒐𝒇  𝒕𝒉𝒆  𝑩𝒆𝒏𝒄𝒉𝒎𝒂𝒓𝒌  𝑨𝒔𝒔𝒆𝒕

3.   Simple Moving Average =

𝑷𝟏 '𝑷𝟐 '𝑷𝟑 ….'𝑷𝒏 𝑵

11. Relation between Chi Square and F…%‰

distribution = 𝐹 =   … ‰ . where: ‰

L

𝑋&k is one chi square random variable with one m degrees of freedom

4.   Momentum Oscillator (or Rate of Change Oscillator ROC): •  

Momentum Oscillator Value M = (VVx)  ×100

where ÝR  axHLTI7   iO•L  axHLTI7

6.   Stochastic Oscillator (composed of two lines %K and %D):

Reading 12: Technical Analysis

2.   Price Target for the •   Head and Shoulders = Neckline – (Head – Neckline) •   Inverse Head and Shoulders = Neckline + (Neckline– Head)

×100

5.   Relative Strength Index = RSI = 100 −

1.   Relative Strength Analysis =

10. F-test (test concerning differences between variances of two normally distributed

•  

•  

and Upper limit

L/& F ‰

populations) F =

(where V = most recent closing price and Vx = closing price x days ago) Alternate Method to calculate M = "

m ‰ ƒ„h …ƒ /…

L/& F ‰

𝑋kk is another chi square random variable with one n degrees of freedom

L

Chi Square Test Statistic (for test concerning the value of a normal

𝑠𝑎𝑚𝑝𝑙𝑒  𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 =    

•  

CFA Level I 2016

7.  

%𝐾 = 100  

Q/B&‡ z&‡/B&‡

where:

C = latest closing price, L14 = lowest price in last 14 days, H14 is highest price in last 14 days %D = Average of the last three %K values calculated daily.

Put/Call Ratio (Type of Sentiment Indicators) =

𝑽𝒐𝒍𝒖𝒎𝒆  𝒐𝒇  𝑷𝒖𝒕  𝑶𝒑𝒕𝒊𝒐𝒏𝒔  𝑻𝒓𝒂𝒅𝒆𝒅 𝑽𝒐𝒍𝒖𝒎𝒆  𝒐𝒇  𝑪𝒂𝒍𝒍  𝑶𝒑𝒕𝒊𝒐𝒏𝒔  𝑻𝒓𝒂𝒅𝒆𝒅

8.   Short Interest Ratio (Type of Sentiment Indicators) =

𝑺𝒉𝒐𝒓𝒕  𝑰𝒏𝒕𝒆𝒓𝒆𝒔𝒕 𝑨𝒗𝒆𝒓𝒂𝒈𝒆  𝑫𝒂𝒊𝒍𝒚  𝑻𝒓𝒂𝒅𝒊𝒏𝒈  𝑽𝒐𝒍𝒖𝒎𝒆

9.   Arms Index TRIN i.e. Trading Index (Type of Flow of funds Indicator) = 𝐴𝑟𝑚  𝐼𝑛𝑑𝑒𝑥  𝑜𝑟  𝑇𝑅𝐼𝑁 =   1O.OP  KJ~HL  g77SI7  ÷1O.OP  iIawML  g77SI7 "OwS.I  OP  KJ~HL  g77SI7÷"OwS.I  OP  iIawML  g77SI7

FinQuiz

Formula Sheet

Reading 13: Demand & Supply Analysis: Introduction

6.   Total Surplus = Total value – Total variable cost

1.   Slope of the demand curve =

7.   Society Welfare = Consumer surplus + Producer surplus

∆  éê  ëìéíî ∆  éê  ïðñêòéòó  ôîõñêöîö

2.   Slope of the supply curve =

8.   Price Elasticity of Demand = %  ∆  éê  ïðñêòéòó  ôîõñêöîö

∆  éê  ëìéíî

3.   Consumer Surplus = Value that a consumer places on units consumed – Price paid to buy those units •   Area (for calculating Consumer Surplus) = ½ (Base × Height) = ½ (Q0 × P 0)

Q2 − Q1 (Q1 + Q2 ) %ΔQ = P2 − P1 %ΔP 1 2 ( P1 + P2 ) 1 2

9.   Income Elasticity of Demand = %  ∆  éê  ïðñêòéòó  ôîõñêöîö %  ∆  éê  úêíûõî  

•   •  

Total revenue = Total quantity sold × Price per unit Area (for calculating Producer Surplus) = ½ (Base × Height) = ½ {(Q0) × (P0 – intercept point on yaxis**)} **where supply curve intersects y-axis

5.   Total Surplus = Consumer surplus + Producer surplus

=

Q2 − Q1 (Q1 + Q2 ) %ΔQ = I 2 − I1 %ΔI 1 2 ( I1 + I 2 )

4.   Producer Surplus = Total revenue received from selling a given amount of a good – Total variable cost of producing that amount

1 2

10.   Cross Elasticity = %  ∆éê  ïðñêòéòó  ôîõñêöîö  ûü  ýûûö  þ %  ∆  éê  ëìéíî  ûü  ýûûö  ÿ

Reading 14: Demand & Supply Analysis: Consumer Demand 1.   Marginal Utility = 2.  

3.   Slope of Budget Constraint Line =

∆  éê  ï% ∆  éê  ï‚

=

ë‚   ë%

4.   Marginal Rate of Substitution =

∆  éê  ï% ∆  éê  ï‚

 =

&ñì'éêñù  "òéùéòó  ûü  ýûûö  þ &ñì'éêñù  "òéùéòó  ûü  ýûûö  ÿ

%  ∆    éê  ëìéíî

∆  éê  ïðñêòéòó  ÷ðøøùéîö

CFA Level I 2016

∆  éê  !ûòñù  "òéùéòó ∆  éê  ïðñêòéòó  #ûê$ðõîö

Equation of Budget Constraint Line = (PX × QX ) + (PY × QY)

Reading 15: Demand & Supply Analysis: The Firm 1.   Profit = Total revenue – Total cost 2.   Accounting Profit = Total Revenue – Explicit Costs (or Accounting costs) 3.   Economic Profit •   = Total Revenue – Explicit Costs – Implicit Costs or •   = Accounting Profit – Implicit Costs or •   = Total Revenue – Total Economic Costs 4.   Economic costs = Explicit costs + Implicit costs 5.   Normal Profit = Accounting Profit – Economic Profit 6.   Accounting profit = Economic Profit + Normal Profit

FinQuiz

Formula Sheet

7.   Economic rent = (New “Higher” Price after ↑ in Demand – Previous Price before ↑ in Demand) × QS before ↑ in Demand 8.   Total Revenue (TR): •   = Price × Quantity or •   = Sum of individual units sold × Respective prices of individual Units sold = Σ (Pi × Qi) 9.   Average Revenue (AR) =

ïðñêòéòó ∆  éê  !ûòñù  )î*îêðî ∆  éê  ïðñêòéòó

11.   Total Variable Cost = Variable Cost per unit × Quantity Produced 12.   Total Cost = Total Fixed + Total Variable 13.   Average total cost (ATC) = !ûòñù  #û$ò

= Avg. Fixed Cost + Avg.

Variable Cost 14.   Marginal cost (MC) =

∆  éê  !ûòñù  #û$ò ∆  éê  ïðñêòéòó  ëìûöðíîö

15.   Marginal Variable Cost = ∆  éê  !ûòñù  +ñìéñ,ùî  #û$ò ∆  éê  ïðñêòéòó  ëìûöðíîö

16.   Marginal revenue (in perfect competition) = Avg. Revenue = Price = Demand

25.   Marginal Product =

∆  éê  !ûòñù  ëìûöðíò ∆  éê  ïðñêéòó  ûü  -ñ,ûì

=

∆  éê  !ûòñù  .ðòøðò ∆  éê  /û  ûü  0ûì1îì$

18.   Profit can be increased by decreasing output when MR< MC

26.   Least-cost optimization Rule: &ñì'éêñù  ëìûöðíò  ûü  -ñ,ûì  

19.   Break-even price: P = ATC è Output level where Price = Average Revenue = Marginal Revenue = Average Total Cost è where, Total Revenue = Total Cost.

!ûòñù  )î*îêðî

10.   Marginal Revenue (MR) =

ïðñêòéòó  ëìûöðíîö

17.   Profit can be increased by increasing output when MR> MC

CFA Level I 2016

20.   Firms earn Economic Profits when Price > Average Total Cost 21.   Profits occur when Total Revenue (TR) ≥ Total Cost (TC) & when Price = Marginal Costè firm will continue operating. 22.   Losses are incurred when there are Operating profits (Total Revenue ≥ Variable Cost) but Total Revenue < Total Fixed Cost + Total Variable Cost AND when Price = Marginal Cost while losses are < fixed costs è firm will continue operating. 23.   Losses are incurred when there are Operating losses (Total Revenue ≤ Variable Cost) AND when losses ≥ fixed costs è firm will shut down. 24.   Average Product =

!ûòñù  ëìûöðíò ïðñêòéòó  ûü  -ñ,ûì

 

=

ëìéíî  ûü  -ñ,ûì   &ñì'éêñù  ëìûöðíò  ûü  ë2ó$éíñù  #ñøéòñù ëìéíî  ûü  ë2óéíñù  #ñøéòñù

27.   Profit is maximized when: MRP = Price or cost of the input for each type of resource that is used in the production process 28.   Marginal Revenue product = Marginal Product of an input unit × Price of the Product = Price of the input = ∆    éê  !ûòñù  )î*îêðî ∆  éê  ïðñêòéòó  ûü  úêøðò  îõøùûóîö

29.   Surplus value or contribution of an input to firm’s profit = MRP – Cost of an input Reading 16: The firm & Market Structures 1.   In perfect competition, Marginal revenue = Avg. Revenue = Price = Demand 2.   Marginal Revenue = Price  × 1 −  

& ëìéíî  7ùñ$òéíéòó  ûü  ôîõñêö

3.   Concentration Ratio = ÷ðõ  ûü  $ñùî$  *ñùðî$  ûü  ò2î  ùñì'î$ò  &f  üéìõ$ !ûòñù  &ñì1îò  ÷ñùî$

FinQuiz

Formula Sheet

4.   Herfindahl-Hirshman Index = Sum of the squares of the market shares of the top N companies in an industry

Reading 17: Aggregate Output, Prices & Economic Growth 1.   Nominal GDP t = Prices in year t × Quantity produced in year t 2.   Real GDP t = Prices in the base year × Quantity produced in year t 3.   Implicit price deflator for GDP or GDP deflator = *ñùðî  ûü  íðììîêò  óì  ûðòøðò  ñò  íðììîêò  óì  øìéíî$ *ñùðî  ûü  íðììîêò  óì  ûðòøðò  ñò  ,ñ$î  óì  øìéíî$

×

100 4.   Real GDP = [(Nominal GDP / GDP deflator) ÷ 100] 5.   GDP deflator =

/ûõéêñù  ýôë )îñù  ýôë  

 ×100

6.   GDP = Consumer spending on final good & services + Gross private domestic invst + Govt. spending on final goods & services + Govt. gross fixed invst + Exp – Imp + Statistical discrepancy 7.   Net Taxes = Taxes – Transfer payments 8.   GDP = National income + Capital consumption allowance + Statistical discrepancy

CFA Level I 2016

9.   National Income = Compensation of employees + Corp & Govt enterprise profits before taxes + Interest income + unincorporated business net income + rent + indirect business taxes less subsidies

17.   Private Sector Saving = Household Saving + Undistributed Corporate Profits + Capital Consumption Allowance 18.   GDP = Household consumption + Private Sector Saving + Net Taxes

10.   Total Amount Earned by Capital = Profit + Capital Consumption Allowance

19.   Domestic saving = Investment + Fiscal balance + Trade balance

11.   PI = National income – Indirect business taxes – Corp income taxes – Undistributed Corp profits + Transfer payments

20.   Trade Balance = Exports – Imports

12.   Personal disposable income (PDI) = Personal income – Personal taxes OR GDP (Y) + Transfer payments (F) – (R/E + Depreciation) – direct and indirect taxes (R) 13.   Business Saving = R/E + Depreciation 14.   Household saving = PDI - Consumption expenditures - Interest paid by consumers to business - Personal transfer payments to foreigners 15.   Business sector saving = Undistributed corporate profits + Capital consumption allowance 16.   Total Expenditure = Household consumption (C) + Investments (I) + Government spending (G) + Net exports (X-M)

21.   Fiscal balance = Government Expenditure – Taxes = (Savings – Investment) – Trade Balance 22.   Average propensity to consume (APC) = 8''ìî'ñòî  #ûê$ðõøòéûê )îñù  úêíûõî

23.   Quantity theory of money equation: Nominal Money Supply × Velocity of Money = Price Level × Real Income or Expenditure 24.   %  ∆ in unit labor cost = %  ∆  in nominal wages - %  ∆  in productivity 25.   Economic growth = Annual %  ∆  in real GDP 26.   Total Factor Productivity growth = Growth in potential GDP – [Relative share of labor in National Income × (Growth in labor) + [Relative share of capital in National Income × (Growth in capital)]

FinQuiz

Formula Sheet

CFA Level I 2016

2.   Money Multiplier = 27.   Growth in potential GDP = Growth in technology + (Relative share of labor in National Income × Growth in Labor) + (Relative share of capital in National Income × Growth in capital] 28.   Capital share =Corporate profits + net interest income + net rental income + (depreciation/ GDP) 29.   Labor share =

ýôë

Reading 18: Understanding Business Cycles 1.   Price index at time t2 = "HwSI  OP  GxI  QO.7S.RGMOL  yH7{IG  HG  G  ‰

×100

"HwSI  OP  GxI  QOL7S.RGMOL  yH7{IG  HG  G  % ëìéíî  úêöî9  ñò  òéõî  òk  

Inflation Rate =

&ff

 )î$îì*î  )îC  ûì  ìî$îì*î  ìñòéû  

3.   Narrow money = M1= currency held outside banks + checking accounts + traveller’s check 4.   Broad money = M2 = M1 + time deposits + saving deposits 5.   M3 = M2 + deposits with non-bank financial institution

7õøùûóîî  #ûõøîê$ñòéûê  

−1

6.   Quantity Theory of Money = M × V = P × Y where, M = Quantity of money V = Velocity of circulation of money P = Average price level Y = Real output

2.   Fisher Index = 𝐼𝑝  ×𝐼𝐿 (where, IL = Laspeyres index and Ip = Paasche Index)

7.   Neutral Rate = Trend Growth + Inflation Target

3.   𝑈𝑛𝑖𝑡  𝑙𝑎𝑏𝑜𝑟  𝑐𝑜𝑠𝑡  (𝑈𝐿𝐶)  𝑖𝑛𝑑𝑖𝑐𝑎𝑡𝑜𝑟   =

8.   Impact of Taxes and Government Spending: The Fiscal Multiplier The net impact of the government sector on AD: •   G – T + B = Budget surplus or Budget deficit where, G = government spending , T =taxes, B =transfer benefits •   Disposable income = Income – Net taxes = (1 – t) Income

!ûòñù  ùñ,ûì  íûõøîê$ñòéûê  øîì  2ûðì  øîì