PDF CFA, CFA LII Brochure, June -the best cfa® instruction spring 2019 - CFA Level 1, June, 2016 - Formula Sheet
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CFA Singapore Research Programme Level 1 2 are accredited *All the information above are extracted from the CFA June 2016 exam candidates survey and are accurate at time of summarises key formulas, definitions, and concepts Sep 27, 2018 Next course

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Formula Sheet

Reading 5: Time Value of Money

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 =
- !" &'( #
- % %^_ #
- &'( # /&

- ? FVN =

? 1 FV (for more than one Compounding per year) = FVN = 1 +

- ? (-×1

Solving for N =

- (where LN =

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

HPR = rt =

- % %^_ #

- $% /$h ' i% $h
- opf $H(/$(MaI

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

NPV =

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

- -1 where R1 =
- + PMT at t =

!Z L'G[& &'( Z

- )"% /)"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 +
- ?k … +

PV & FV of Annuity Due

Effective (or Equivalent) Ann Rate (EAR = EFF%) = 1 +

- % _- b×# b _b
- = 0 (IRR

- ! * M[f &'gNN Z
- represents the MWR)

PV of Perpetuity =

- $" OP KLLSMG`
- per year) = PV= FVN 1 +
- $)* L'G[& &'( Z
- ? •
- • •

EAR (with Continuous Compounding) = EAR =

- ? (- − 1

CFA Level I 2016

$H( L' × (qr

- therefore Price = Par

- $% /$h ' i% $h

Effective Annual Yield = EAY = 1 +

? opu/G − 1 (Rule: EAY > BDY) 9

rMM = (rBD) ×

FinQuiz

- opf (qr opf/ G (qr

Bond Equivalent Yield = BDY = Semiannual Yield × 2 Reading 7: Statistical Concepts & Market Returns 1

Range = Max Value – Min Value 2

i = class interval H = highest value L'= lowest value,

- of classes

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

K|7OwSGI

- !(I}SILa`

Arithmetic Mean =

Population Var = σ2 =

- of obvs locate

- median at
- # … /ˆ ‰ ƒ„% ƒ
- m ‰ ƒ„% …ƒ /…

- m … /… ‰ ƒ„% ƒ

- ?• = (w1X1+ w2X2+…
- + wnXn) 11

Geometric Mean = GM = with Xi≥0 for i = 1,2,…n

!O( Hww …ƒ ‹…

- m ƒ …ƒ
- …ƒ /… ‰ L/&

- % m ƒ„% ‚ ƒ

Target Semi-var = 13

Semi-var =

- ?z =
- for i = 1,2,

- …ƒ /… ‰ L/&
- …ƒ /y ‰ L/&
- where B = Target Value 24

- m ƒ …ƒ

where n =

number of observation in the sample 15

Deciles =

- …ƒ /y ‰ L/& F …
- where s= sample S
- ? = sample mean
- ‡ iM7G(M|SGMOL
- u iM7G(M|SGMOL

iM7G(M|SGMOL

- # ‰ ƒ„% …ƒ /ˆ

*OGHw 1O OP U|~7

CFA Level I 2016

Sharpe Ratio =

)IHL $O(GPOwMO N /)IHL NP N F

- i OP $O(GPOwMO N

Geometric Mean R ≈

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)

$(O| OP • &/$(O| OP •

Odds against event E =

&/$(O| OP • $(O| OP •

- $ Ky $ y
- → P(B) ≠ 0

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

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,

…,Sn are mutually exclusive and exhaustive scenarios)

- ?” −

?” Cov (Ri Rj) = Cov (Rj Ri) Cov (R,

- ?” σ2 (Rp) =

- $ 1I• gLPO(

- $ 1I• gLPO(

- ! = n (n-1)(n-2)(n-3)…1

- !…Lž

Cov (Ri Rj) =

Standard Deviation (S

- where n = total no
- of objects and r = no
- of objects selected

Permutation = L'

?Ÿ 1 −

- (for x = 0,1,2…
- &/R m¡

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

• • • • •

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

Sharpe Ratio = =

- • NE /Nµ ™E

- 0 F(x) =
- ? = Ÿ/H |/H

- ? = & ™ k¥
- /(Ÿ/ˆ)‰ k™ ‰
- for − ∞ <
- ? < + ∞

Estimations by using Normal Distribution: •

- the interval
- • • • •

Approx 68% of all obvs fall in the interval

? Approx 95% of all obvs fall in the interval

? Approx 99% of all obvs fall in the interval

? More precise intervals for 95% of the obvs are

? and for 99% of the observations are

- …/ˆ ™

(when X is normally distributed)

50σ2) 10

Variance (σL2) of a lognormal random variable = exp (2µ+ σ2) × [exp (σ2) – 1]

CFA Level I 2016

Continuously compounded return associated with a holding period from 0 to T: R0,T= ln (ST / S0) or

?*/&,* +

- ?*/k,*/& + ⋯ +
- ?f,& Where,

When one-period continuously compounded returns (i

r0,1) are IID random variables

?*/&,* +

?*/k,*/& +

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,

t+1 = holding period return on the stock from t to t + 1

Continuously compounded return associated with a holding period from t to t + 1:

- = σ (r0,T) = σ

of one period continuously compounded returns ×

? Reading 10: Sampling and Estimation 1

t+1= ln(1 + holding period return) or rt,

t+1 = ln(price relative) = ln (St+1 / St) = ln (1 + Rt,t+1)

- ™‰ L

D of the distribution of the sample mean =

- ™‰ L

- ?… = •
- known =
- ?… =

L% ' L‰ /k

‰ %/‰ Ï‰ % ' Ï‰ m% m‰

Power of Test = 1-Prob of Type II Error

- (when sample size is large or
- small but pop S

CI for normally distributed population F L

- …% /…‰ / ˆ% /ˆ‰
- ? = 3
- …/ˆh m

(when sample size is large but

D is unknown where s'is sample S

- …/ˆh m
- (when sample size is large or
- small and pop S

- ?& +

Test Statistic for a test of diff b/wn two pop means (normally distributed,

unequal and unknown pop var unknown) t=

- …/ˆh

- when Pop S

the standard error of sample statistic is give by

- ?… = ™
- with unknown variance =

L% /& F%‰ ' L‰ /& F‰‰

estimator of common variance =

- when Pop S

D is unknown,

the standard error of sample statistic is give by

- ?… =

- ‰ Ï‰ Ð ÏÐ
- where N= population
- where S = sample S

…% /…‰ / ˆ% /ˆ‰ m% m‰

- ? ∗

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=

- m ‰ ƒ„% …ƒ /…

- x−µ s/ n

sampled is normally or approximately normally distributed)

- x−µ σ/ n
- where s'= sample

D estimate of s'=

- ? k

t-ratio =

D (σ) is not

Z-ratio =

CFA Level I 2016

‰ ‰ Ï‰ % ' Ï‰ m% m‰ ‰ ‰ Ï‰ Ï‰ % ‰ m% m‰ ' m% m‰

unknown population variances) J/ˆÑh

- sample mean difference =
- ? =
- sample variance =

- m ‰ ƒ„h J% /J

FinQuiz

- • •

- sample S

- ? =
- population variance)
- ? − 1 =

L/& F ‰ ™h‰

- ‰ …Ò/‰
- ‰ …%¡Ò/‰

?7 6 LM[&

- ?&k =1−

?k − 1 • For small samples rejection points for the test based on

- ?7 are found using table

• For large sample size (e

n>30) t-test can be used to test the hypothesis i

- ? − 2 &/k
- ? = 1 −

?7k &/k

F%‰ F‰‰

- &ff &'NF
- ?&k = 1
- ?ℎ
- ?&k = 2
- ?ℎ
- ?& =
- ?& − 1
- ?k =
- ?k − 1

Simple Moving Average =

- distribution =
- ? = … ‰
- where: ‰

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

where ÝR axHLTI7 iO•L axHLTI7

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

Relative Strength Index = RSI = 100 −

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

- and Upper limit

- populations) F =

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

- m ‰ ƒ„h …ƒ /…

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

- ? =

- ? = 100

L14 = lowest price in last 14 days,

Put/Call Ratio (Type of Sentiment Indicators) =

Short Interest Ratio (Type of Sentiment Indicators) =

Arms Index TRIN i

- ? = 1O

OP iIawML g77SI7 "OwS

I OP iIawML g77SI7

Formula Sheet

Total Surplus = Total value – Total variable cost

∆ éê ëìéíî ∆ éê ïðñêòéòó ôîõñêöîö

Price Elasticity of Demand = % ∆ éê ïðñêòéòó ôîõñêöîö

- ∆ éê ëìéíî

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)

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

Total Surplus = Consumer surplus + Producer surplus

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

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

Slope of Budget Constraint Line =

∆ éê ï% ∆ éê ï‚

∆ 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

Reading 15: Demand & Supply Analysis: The Firm 1

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

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) =

Total Variable Cost = Variable Cost per unit × Quantity Produced 12

Total Cost = Total Fixed + Total Variable 13

Variable Cost 14

- ∆ éê

!ûòñù +ñìéñ,ùî #û$ò ∆ éê ïðñêòéòó ëìûöðíîö

Marginal revenue (in perfect competition) = Avg

Marginal Product =

- ∆ éê

!ûòñù ëìûöðíò ∆ éê ïðñêéòó ûü -ñ,ûì

- ∆ éê

!ûòñù

Profit can be increased by decreasing output when MR< MC

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

Total Revenue = Total Cost

Marginal Revenue (MR) =

CFA Level I 2016

Profits occur when Total Revenue (TR) ≥ Total Cost (TC) & when Price = Marginal Costè firm will continue operating

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

Losses are incurred when there are Operating losses (Total Revenue ≤ Variable Cost) AND when losses ≥ fixed costs è firm will shut down

!ûòñù ëìûöðíò ïðñêòéòó ûü -ñ,ûì

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

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

Surplus value or contribution of an input to firm’s profit = MRP – Cost of an input Reading 16: The firm & Market Structures 1

& ëìéíî 7ùñ$òéíéòó ûü ôîõñêö

Concentration Ratio = ÷ðõ ûü $ñùî$ *ñùðî$ ûü ò2î ùñì'î$ò &f üéìõ$

FinQuiz

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

Reading 17: Aggregate Output,

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

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

GDP = National income + Capital consumption allowance + Statistical discrepancy

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

Private Sector Saving = Household Saving + Undistributed Corporate Profits + Capital Consumption Allowance 18

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

Personal disposable income (PDI) = Personal income – Personal taxes OR GDP (Y) + Transfer payments (F) – (R/E + Depreciation) – direct and indirect taxes (R) 13

Household saving = PDI

- - Consumption expenditures
- - Interest paid by consumers to business
- - Personal transfer payments to foreigners 15

Total Expenditure = Household consumption (C) + Investments (I) + Government spending (G) + Net exports (X-M)

Fiscal balance = Government Expenditure – Taxes = (Savings – Investment) – Trade Balance 22

Average propensity to consume (APC) = 8''ìî'ñòî #ûê$ðõøòéûê )îñù úêíûõî

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

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

CFA Level I 2016

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

"HwSI OP GxI QOL7S

RGMOL yH7{IG HG G % ëìéíî úêöî9 ñò òéõî òk

Inflation Rate =

Narrow money = M1= currency held outside banks + checking accounts + traveller’s check 4

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

Fisher Index =

- ? (where,

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,

B =transfer benefits • Disposable income = Income – Net taxes = (1 – t) Income

!ûòñù ùñ,ûì íûõøîê$ñòéûê øîì 2ûðì øîì