FinTree
JuiceNotes 2023
Quantitative Methods|Economics
Chartered Financial Analyst - Level I
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INDEX
Quantitative Methods
1
The Time Value of Money
5
2
Organizing, Visualizing and Describing Data
8
3
Probability Concepts
16
4
Common Probability Distributions
21
5
Sampling and Estimation
27
6
Hypothesis Testing
31
7
Introduction to Linear Regression
36
e
Economics
Name of Reading
Topics in Demand and Supply Analysis
9
The Firm and Market structures
45
10
Aggregate Output, Prices and Economic Growth
49
11
Understanding Business cycles
55
12
Monetary and Fiscal Policy
59
13
Introduction to Geopolitics
65
14
International Trade and Capital Flows
68
15
Currency Exchange rates
73
Fi
nT
re
8
42
Quantitative Methods
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The Time Value of Money
5
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6
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Organizing, Visualizing & Describing Data
Identify and compare data types
LOS a
Types of data
Categorical data
Aka Qualitative data
Numerical data
Continuous data
Discreet data
Eg. Price returns
of a stock
Coupon rates
in Bonds
Classification of
publicly listed
stocks
into 11 sectors
Morningstar and
Standard & Poor's
star ratings for
investment funds
Time Series
Data are a sequence of observations for a
single observational unit of a specific
variable collected over time and at discrete
and typically equally spaced intervals of
time.
Data are a list of the observations
of a specific variable from multiple
observational units at a given point
in time.
Ordinal data
ee
Cross-Sectional
Nominal data
Fi
nT
r
For example, January inflation rates
for each country
For example, the daily closing prices of a
particular stock.
Panel Data
Panel data are a mix of time-series and
cross-sectional data that are frequently used
in financial analysis and modeling. Panel
data consist of observations through time on
one or more variables for multiple
observational units
Structured Data
Unstructured Data
Structured data are highly organized
in a pre-defined manner, usually with
repeating patterns.
Unstructured data, in contrast, are data
Eg. data issued by stock exchanges,
such as intra-day
Eg. Some common types of
unstructured data are text—such as
financial news, posts in social media etc
that do not follow any conventionally
organized forms
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LOS b
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Describe how data are organized for quantitative analysis
A one-dimensional array is the
simplest format for representing a
collection of data of the same data
type, so it is suitable for
representing a single variable.
A two-dimensional rectangular array
(also called a data table) is one of the
most popular forms for organizing
data for processing by computers or
for presenting data visually for
consumption by humans.
LOS c
Interpret frequency and related distributions
LOS d
Interpret a contingency table
Portfolio Frequencies by Sector and Market Capitallization
Market Capitalization Variable (3 Levels)
Sector Variable (5 Labela)
Small
Mid
Large
Total
Communication Services
55
35
20
110
Consumer Staples
50
30
30
110
Energy
175
95
20
290
Health care
275
105
55
435
Utilities
20
25
10
55
Total
575
290
135
1,000
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Relative Frequencies as Percentage of Total
Market Capitalization Variable (3 Levels)
Sector Variable (5 Labela)
Small
Mid
Large
Total
Communication Services
5.5%
3.5%
2.0%
11.0%
Consumer Staples
5.0%
3.0%
3.0%
11.0%
Energy
17.5%
9.5%
2.0%
29.0%
Health care
27.5%
10.5%
5.5%
43.5%
Utilities
2.0%
2.5%
1.0%
5.5%
Total
57.5%
29.0%
13.5%
100%
LOS e
Describe ways that data may be visualized and evaluate uses of specific
visualizations
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LOS f
Describe How to Select among Visualization Types
● Histogram
Numerical
Data
Polygon
● Cumulative
● Scatter Plot
Distribution
(Two Variables)
● Scatter Plot Matrix
Relationship
(Multiple Variables)
● Heat Map
What to
explore or
Present ?
Chart
Distribution
● (Multiple Variables)
Categorical
Data
Comparison
Among
Categories
● Bar Chart
● Tree Map
● Heat Map
LOS g
● Frequency
● Bar Chart
● Tree Map
● Heat Map
Over time
Unstructured
Data
● World Cloud
● Line Chart
(Two Variables)
● Bubble Line Chart
(Two Variables)
Calculate and interpret measures of central tendency
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LOS h
Deciding which central tendency measure to use
Collect Sample
Include all
values,
including
outllers?
Yes
Compounding ?
Yes
Extreme
Outllers?
Yes
Arithmetic Mean
Geometric Mean
Harmonic Mean
Trimmed Mean
Winsorized Mean
12
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LOS i
Calculate quantiles and interpret related visualizations
LOS j
Calculate and interpret measures of dispersion
LOS k
Calculate and interpret target downside deviation
Starget =
n
For all X-i<B
(Xi - B)2
n-1
Where B is the target and n is the total number of sample observations
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LOS l
Interpret skewness
LOS m
Interpret kurtosis
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LOS n
Interpret correlation between two variables
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Probability Concepts
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Common Probability Distribution
21
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Sampling and Estimation
27
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Hypothesis Testing
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k
Eg.
r=0.4
n=62
confidence level= 95%
Step 1:
Define hypothesis
Step 2:
Calculate test statistic
Step 3:
Calculate critical values
Perform a test of significance
H 0 : r = 0, H a : r ≠ 0
rx
n-2
1-r
2
0.4 x
62 - 2
3.3806
1 - 0.4 2
t-distribution, DoF = 60
-2
+2
Since calculate test statistic lies outside the range, conclusion is ‘Reject the null hypothesis’ ‘r’ is
statistically significant, which means that population ‘r’ would be different than zero
Assumption of the test- The two populations (x and y) follow a normal distribution
(normally called bivariate normal distribution)
If this assumption is violated
use spearman rank correlation coefficient
l
Non Paramatic test is used in the following situations
● Data used does NOT meet distribution requirements
Example : We want to test a hypothesis with respect to mean but sample size is small and
population is non - normal ( z or t-test won’t work!)
● Data is given in RANKS
Example : Hypothesis test on ranks of fund manager
● Hypothesis is not with respect to parameter
Example : Test whether a sample is random or not or whether a population follows a normal
distribution or not
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Some important nonparametic tests
Parametric
Tests concerning a single mean
t-test
z-test
Tests concerning differences
between means
t-test
Approximate t-test
Tests concerning mean difference
(paired comparison tests)
t-test
Nonparametric
Wilcoxon signed - ranked test
Mann-Whitney U test
Wilcoxon signed-ranked test
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Introduction to Linear Regression
Dependent variable
Independent variable
Aka response variable
Aka the regressor
Variable you are seeking to
explain
Variable you are using to explain
changes in the dependent variable
Also referred to as explained
variable/endogenous
variable/predicted variable
Also referred to as explanatory
variable/exogenous
variable/predicting variable
Rp =
Dependent
variable
RFR
+
(Rm − RFR)
Independent
variable
Intercept
LOS b
β
y
Dependent
variable
LOS a
Slope
Independent
variable
x
Describe the least squares criterion, how it is used to estimate regression
coefficients, and their interpretation
Sum of squared errors (SSE):
Regression line:
Slope coefficient (beta):
Sum of the squared vertical distances between the estimated
and actual Y-values
Line that minimizes the SSE
Describes change in ‘y’ for one unit change in ‘x’
Cov (x,y)
Variance (x)
LOS c
Assumptions underlying linear regression
ΠRelationship between dependent and independent variable is linear
 Independent variable is uncorrelated with the error term
Ž Expected value of the error term is zero
 Variance of the error term is constant (NOT ZERO).
The economic relationship b/w variables is intact for the entire time period
(eg. change in political regime)
 Error term is uncorrelated with other observations (eg. seasonality)
‘ Error term is normally distributed
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LOS d&e
Analysis of variance (ANOVA)
Y: Mean
Yi: Actual value
Sum of squared errors
(SSE)
Measures unexplained
variation
aka sum of squared
residuals
^
Yi: Predicted value
Regression sum of
squares (RSS)
Total sum of squares
(SST)
Measures explained
variation
Measures total
variation
^
∑ (Yi − Yi)2
∑ (Yi − Yi)2
^
∑ (Yi − Yi)2
ª Higher the RSS, better the quality of regression
ª R2 = RSS / SST
ª R2 = Expained Variation / Total Variation
ANOVA Table
Source of variation
DoF
Sum of squares
Mean sum of squares
Regression
(explained)
k
RSS
MSR = RSS/k
Error
(unexplained)
n−k−1
SSE
MSE = SSE/n − k − 1
Total
n−1
SST
F-statistic = MSR/MSE with ‘k’ and ‘n − k − 1' DoF
When to use F-test and t-test
F-test
Y = b 0 + b 1 x1 + b 2 x2 + ε
t-test
To test the engine of the car
Use t-test
t-test
To test if the car is operating as a
whole
Use f-test
To test individual tyres of the car
Use t-test
37
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Standard error of estimate, coefficient of determination
and confidence interval for regression coefficient
Eg.
‘x’
10
15
20
30
Actual ‘y’
17
19
35
45
Predicted ‘y’
15.81
23.36
30.91
46.01
Errors
1.19
−4.36
4.09
−1.01
Squared errors
1.416
19
16.73
1.02
Standard error of estimate (SEE) =
Coefficient of determination (R2):
√
SSE
n−2
=
Sum of squared errors
(SSE)
38.166
√
38.166
2
= 4.36
% variation of dependent variable explained by % variation of
the independent variable
For simple linear equation, R2 = r2
LOS f
Eg.
Formulate a null and an alternative hypothesis about a population value
of a regression coefficient, and determine whether the null hypothesis is
rejected at a given level of significance
^
b1 = 0.48
SE = 0.35
n = 42
Confidence interval = 90%
^
Step 1:
Define hypothesis
Step 2:
Calculate test statistic
Step 3:
Calculate critical values
Perform a test of significance
^
H0: b1 = 0, Ha: b1 ≠ 0
Sample stat. − HV
0.48 − 0
Std. error
0.35
1.371
t-distribution, DoF = 40
−1.684
1.684
Since calculated test statistic lies inside the range, conclusion is ‘Failed to reject the null hypothesis’
Slope is not significantly different from zero
One Tailed Test
Eg.
^
b1 = 0.48
SE = 0.35
n = 42
Step 1:
Define hypothesis
Step 2:
Calculate test statistic
Step 3:
Calculate critical values
Confidence interval = 90%
^
Perform a test of significance
^
H0: b1 < 0, Ha: b1 > 0
Sample stat. − HV
0.48 − 0
Std. error
0.35
1.371
t-distribution, DoF = 40
0
1.684
Since calculated test statistic lies inside the range, conclusion is ‘Failed to reject the null hypothesis’
Slope is not significantly different from zero
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LOS g
Calculate and interpret the predicted value for the dependent variable, and a
prediction interval for it
Confidence interval for the predicted
Predicted value of
value of dependent variable
dependent variable
^
Y
^
^
Intercept
Predicted
value (y)
Eg.
^
b0 + b1 × Xp
=
Y
Forecasted
value (x)
Predicted
value (y)
Slope
Forecasted return (x) = 12%
Critical value
(t-value)
Intercept = −4%
Slope = 0.75
Predicted value
^
=
Standard
error
Standard error = 2.68
Calculate predicted value (y) and 95% confidence interval
n = 32
Y
± (tc × SE)
^
Confidence interval
^
Y
^
b0 + b1 × Xp
± (tc × SE)
5 ± (2.042 × 2.68)
Y = −4 + 0.75 × 12 = 5%
−0.472 to 10.472
LOS h
Describe different functional forms of simple linear regressions
Log-lin
Model Model
Lin-Log
Model
Log-Log
Model
Dependent variable is
logarithmic but the
independent variable is
linear
Dependent variable is
linear but the independent
variable is logarithmic
Similar to probit and logit
but uses financial ratios as
independent variables
Selecting the Correct Functional Form
The key to fitting the appropriate functional form of a simple linear
regression is examining the goodness of fit measures:
Ÿ The coefficient of determination (R2),
Ÿ The F-statistic,
Ÿ The standard error of the estimate (se)
Ÿ As well as examining whether there are patterns in the residual
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Topics in Demand And Supply Analysis
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The Firm And Market Structures
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LOS a
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Aggregate Output, Prices And
Economic Growth
GDP using expenditure and income approach
ª Gross domestic product (GDP) is the total market value of final goods and
services produced within a country during a certain time period
ª It is most widely used measure of the size of a nation’s economy
ª It includes only purchases of newly produced goods and services
ª Sale or resale of goods produced in previous periods is excluded
ª Goods and services provided by government are included in GDP (valued at cost)
ª Value of owner-occupied housing is also included in GDP (value is estimated)
Expenditure approach -
Total amount spent on goods and services produced
during the period
Calculated as;
Consumption (C) + Investment (I) + Government
expenditure (G) + [Exports − Imports] (X − M)
Income approach -
Total income earned by households and companies
during the period
Calculated as;
Consumption (C) + Savings (S) + Taxes (T)
LOS b
LOS c
Expenditure approach
Sum of value
added
Value of final
output
GDP is calculated by adding
the value created at each
stage of production
GDP is calculated using only
the final value of good and
services
Nominal GDP
Real GDP
Output - Current year
Output - Current year
Prices - Current year
Prices - Base year
GDP deflator -
Nominal GDP
× 100
Real GDP
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LOS d
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National income - Compensation to employees
+ Corporate and govt. profits before tax
+ Non corporate business income
+ Rent
+ Interest
+ (Indirect taxes − Subsidies)
Personal income - National income
+ Transfer payments by govt.
− Corporate and indirect taxes
− Undistributed corporate profits
Personal disposable income - Personal income
− Personal taxes
GDP under income approach can also be calculated as :
National
income
+
Capital consumption
+
allowance
Depreciation of
physical capital
Statistical
discrepancy
Adjustment for difference
between GDP under
income and expenditure
approach
GNP = GDP + [Net income earned by domestic residents Business from overseas investments]
- [Net income earned by foreign residents / businesses from domestic investments]
GDP of a country = 1000 million
Income earned by domestic residents = 80 million
Income earned by Foreign residents = 60 million
Therefore , GNP = 100 + 80 - 60 = 120
LOS e
Fundamental relationship among C, S, T, I, G and (X − M)
Total income must equal total expenditures
GDP under income approach = GDP under expenditure approach
C + S + T = C + I + G + (X − M)
S = I + (G − T) + (X − M)
Fiscal
deficit
Trade
surplus
(G − T) = (S − I) + (M − X)
Fiscal deficit must be financed by
some combination of trade deficit or
excess of savings over investment
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LOS f
IS and LM curves
IS - Investment and Savings
LM - Liquidity and Money supply
Real interest
rate (r)
Real interest
rate (r)
Real
income
Real
income
Π+ve relation
r and (S − I)
Assumption Real money
supply is
constant
 −ve relation
y and (S − I)
Therefore,
−ve relation b/w
r and y
Actual Income = Planned Expenditure
Ÿy Ç = Precautionary & transaction demand Ç
(S − I) = (G − T) + (X − M)
y Ç Fiscal deficit & Trade surplus È = (S −I) È
Real interest
rate (r)
IS
ŸDemand for money Ç = Cost of money Ç
Ÿr Ç = y Ç
Aggregate demand curve
Real money supply ‘Constant’
P Ç = MS/P È
Price
LM2
LM1
If MS/P È then, LM curve
shifts to the left (increases
real interest rate)
Output
(y)
Output
(y)
IS curve - −ve relation (r & y)
LM curve - +ve relation (r & y)
Aggregate demand curve −ve relation (p & y)
ª Marginal propensity to save (MPS) - Proportion of additional income that is saved
ª Marginal propensity to consume (MPC) - Proportion of additional income spent on consumption
ª MPS + MPC = 100%
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LOS g
Aggregate supply curve
Price
LRAS
SRAS
VSRAS
Potential GDP
è VSRAS - Firms adjust output without changing price. VSRAS curve is perfectly
elastic
è SRAS - When prices increase, input costs (such as wages) do not increase as they
are fixed in the short run
è LRAS - All input prices are variable in the long run. LRAS curve is perfectly inelastic
and it shows the level of potential GDP
è Price level has no long run effect on aggregate supply
LOS h
Causes of movements along and shifts in aggregate
demand and supply curves
Price
Price
P2
P1
Q2
Q1
Output
Movement along the curve
Reasons :
Change in price (all other
factors keeping constant)
Aggregate demand curve
ª Increase in consumers’ wealth
ª Optimistic business expectations
ª High future income expectation by
consumer
ª High capacity utilization
ª Expansionary monetary policy
ª Expansionary fiscal policy
ª Home currency depreciation
ª Global economic growth
Output
Shift in curve
Shift in curve
Reasons
Aggregate supply curve
ª Increase in productivity
ª Increase in supply and quality of labor
ª Increase in supply of natural resources
ª Increase in the stock of physical capital
ª Technology improvement
ª Currency appreciation
ª In the long-run the curve shifts because of
ª changes in labor supply, supply of physical
ª and human capital and productivity/
ª technology
ª In the short-run the curve will shift because
ª of changes in potential GDP, nominal wages,
ª input prices, expectations about future
ª prices, business taxes and subsidies, and
ª exchange rate.
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LOS i, j & k
Short-run effects of changes in aggregate demand and supply
Type of change
Ç
È
Ç
È
Ç
È
Ç Aggregate supply
Ç
È
È
È Aggregate supply
È
Ç
Ç
Price
Price
Price
P1
P0
P0
P0
P1
P1
Q0 Q1
Output
Q1 Q0
Price
P1
P0
Output
Output
Q1 Q0
Q1 Q0
Output
Recessionary gap Potential GDP > Real GDP
Inflationary gap Real GDP > Potential GDP
Stagflation High inflation combined with slow economic growth
and high level of unemployment
LOS l
Short-run effects of shifts in both aggregate demand and supply
Aggregate
supply
Ç
Ç
Ç
Ç Or È
È
È
È
Ç Or È
Ç
È
Ç Or È
Ç
È
Ç
Ç Or È
È
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LOS m
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Sources of
economic growth
Sustainability of
economic growth
ª Labor supply
ª Human capital
ª Physical capital stock
ª Technology
ª Natural resources
ª Rate of increase in
the labor force
ª Rate of increase in
labor productivity
Dutch Disease: Even if a country has Natural Resources
Currency appreciates
Which makes other
industries uncompetitive
Govt. focuses only on
one sector
Production function
LOS n & o
Describes relationship between output and labor, capital and total factor productivity
Total factor productivity (TFP) - It is a multiplier that quantifies the amount of output
growth that cannot be explained by the increases in labor and capital. Increase in total
factor productivity can be attributed to advances in technology
∆Y = TFP + α × ∆K + (1 − α) × ∆L
Residual income
that explains
the effect of
technology
Growth
in GDP
Growth of
capital
Share of growth
explained by the
capital
Growth of labor
Growth in potential GDP
Growth in per capita potential GDP
Growth in technology
+ WL (Growth in labor)
+ WC (Growth in capital)
Growth in technology
+ WC (Growth in capital)
Above model is a part neoclassical economics
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Understanding Business Cycles
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Creates upward
Bias
∑(
∑(
)
)
∑(
∑(
)
)
Hedonic pricing - Adjusting price to reflect quantity
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bove potential GDP
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Monetary And Fiscal Policy
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61
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Exchange rate targeting may result in volatily
of money supply as domestic monetary policy
will have to adapt to the necessity of maintaining
stable exchange rate.
Net effect of exchange rate targeting is that the
targeting country will have the same
inflation rate as the targeting currency.
62
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p
●
●
●
Balanced Budget Multiplier
If a government increases G(government expenditure) by the same amount as it
raises taxes, the aggregate output actually rises.
A Balanced Budget lease to a rise in output, which in turn leads to further rise in
output and income via the multiplier effect.
The Balanced Budget Multiplier always take the value unity.
Arguments about being concerned about size of fiscal deficit
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Introduction to Geopolitics
LOS a
Describe geopolitics from a cooperation versus competition
perspective.
»
Geopolitics refers to interactions among nations, including the actions of state
actors (national governments) and non-state actors (corporations, nongovernment organizations, and individuals)
»
One way to examine geopolitics is through analysis of the extent to which
individual countries cooperate with one another
»
In terms of economics, areas of cooperation include freedom of movement across
borders for goods, services, and capital; agreements to harmonize tariffs;
international standardization of rules; and transfers of information and
technology.
»
While a country that engages with other countries on these matters may be
considered cooperative and one that does not may be considered non-cooperative,
the extent of cooperation actually varies along a spectrum
»
We can analyze a country's national interests as a hierarchy, with its top priorities
being those that ensure its survival. A country's geophysical resource endowment
may influence its priorities. For example, a country that has mineral resources but
lacks arable land needs to trade minerals for food, and therefore has an interest in
cooperating with other countries to keep international trade lanes open.
»
To facilitate the flow of resources, state and non-state actors may cooperate on
standardization of regulations and processes. Example - IFRS
»
Cultural factors, such as historical emigration patterns or a shared language, can
be another influence on a country's level of cooperation
»
Strong and stable institutions can make cooperation easier for state and non-state
actors.
»
Cultural exchange is one means through which a country may exercise soft power,
the ability to influence other countries without using or threatening force.
65
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LOS b
Describe geopolitics and its relationship with globalization.
»
Globalization refers to the long-term trend toward worldwide integration of economic
activity and cultures.
»
We may contrast globalization with nationalism, which in this content refers to a nation
pursuing its own economic interests independently
»
We can think of countries' actions along a spectrum from globalization to nationalism
Multilateralism (cooperation and globalization)
refers to countries that engage extensively in
Hegemony (non-cooperation and globalization)
international trade and other forms of
refers to countries that are open to globalization
cooperation with many other countries.
but have the size and scale to influence other
Some countries may exhibit regionalism,
countries without necessarily cooperating.
cooperating multilaterally with nearby
countries but less so with the world at large.
Globalization
Hegemony
Multilateralism
Non-Cooperation
Cooperation
Autarky
Autarky (non-cooperation and nationalism)
refers to a goal of national self-reliance, including
producing most or all necessary goods and
services domestically.
Autarky is often associated with a statedominated society in general, with attributes
such as government control of industry and
media.
Bilateralism
Nationalism/
Anti-Globalization
Bilateralism (cooperation and nationalism) refers
to cooperation between two countries.
A country that engages in bilateralism may have
many such relationships with other countries
while tending not to involve itself in multicountry arrangements.
66
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LOS c
Describe tools of geopolitics and their impact on regions and
economies.
We can consider tools of geopolitics, the means by which (primarily) state actors advance their
interests in the world, as falling into three broad categories of national security, economic,
and financial.
National Security Tools
Include armed conflict,
espionage, or bilateral or
multilateral agreements
designed to reinforce or
prevent armed conflict
LOS d
Economic Tools
•
Can be cooperative or
non-cooperative.
•
Cooperative economic
tools include free trade
areas, common
markets, and economic
and monetary unions
•
Non cooperative
economic tools include
domestic content
requirements,
voluntary export
restraints etc
Financial Tools
•
Foreign investment and
the exchange of
currencies.
•
Sanctions, or
restrictions on a
specific geopolitical
actor’s financial
interest, are a financial
tool that state actors
may use alongside
national security tools.
Describe geopolitical risk and its impact on investments.
Geopolitical risk is the possibility of events that interrupt peaceful international relations.
We can classify geopolitical risk into three types:
»
Event risk refers to events about which we know the timing but not the outcome, such as
national elections.
»
Exogenous risk refers to unanticipated events, such as outbreaks of war or rebellion.
»
Thematic risk refers to known factors that have effects over long periods, such as human
migration patterns or cyber risks.
67
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»
To forecast the effect on investments of a geopolitical risk, we need to consider its
probability (likelihood), the magnitude of its effects on investment outcomes
(impact), and how quickly investment values would reflect these effects (velocity).
»
We can use our framework of cooperation and globalization to help estimate the
likelihood of geopolitical risk.
»
Countries that are more cooperative and globalized tend to have less likelihood of
some geopolitical risks, such as armed conflict, but may have greater likelihood of
other risks, such as the supply chain disruptions that followed the COVID-19
pandemic in 2020.
»
To analyse the velocity of geopolitical risk we can classify risks as high velocity
(short term), medium velocity, or low velocity (long term).
»
Exogenous risks often have high-velocity effects on financial markets and
investment values.
»
To facilitate the flow of resources, state and non-state actors may cooperate on
standardization of regulations and processes. Example - IFRS
»
Black swan risk is a term for the risk of low likelihood exogenous events that have
substantial short-term effects.
»
Investors with longer time horizons typically do not need to react to these kinds of
events, but investors with shorter horizons might find it necessary to react.
»
Medium-velocity risks can potentially damage specific companies or industries by
increasing their costs or disrupting their production processes, while low-velocity
risks tend to affect them in the “environmental, social, and governance” realm.
»
Analysing these kinds of risk is important for investors with long time horizons.
»
Because analysing geopolitical risks requires effort, time, and resources, investors
should consider whether the impact of geopolitical risk is likely to be high or low,
and focus their analysis on risks that could have a high impact.
»
With regard to those risks, investors should determine whether they are likely to
have discrete impacts on a company or industry, or broad impacts on a country, a
region, or the world.
»
Business cycles can affect the impact of geopolitical risk, in that these risks may
have greater impacts on investment values when an economy is in recession than
they would have during an expansion.
»
Investors can use qualitative or quantitative scenario analysis to gauge the
potential effects of geopolitical risks on their portfolios.
68
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International Trade And Capital Flows
69
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Differences in technology is a major
source of comparative advantage but
other countries can close the
technological gap or gain a
technological advantage.
This model assumes that technology in each industry is the same among countries,
but it varies between industries.
(abundant)
70
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71
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Results of customs Union
Trade
Creation
Trade
Diversion
Trade creation occurs when
regional integration results in the
replacement of higher - cost
domestic production by lower cost imports from other
members.
Trade diversion occurs when
lower - cost imports from
nonmember countries are
replaced with higher - cost
imports from members.
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Currency Exchange Rates
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75
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76
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77
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Z- TABLE (COMPLEMENTARY CUMULATIVE)
StandardNormal Distribution
P (Z ::;; z) = N(z) for z ::;; 0
z
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0
0.5000
0.4960
0.4920
0.4880
0.4840
0.4801
0.4761
0.4721
0.4681
0.4641
-0.1
0.4602
0.4562
0.4522
0.4483
0.4443
0.4404
0.4364
0.4325
0.4286
0.4247
-0.2
0.4207
0.4168
0.4129
0.4090
0.4052
0.4013
0.3974
0.3936
0.3897
0.3859
-0.3
0.3821
0.3783
0.3745
0.3707
0.3669
0.3632
0.3594
0.3557
0.3520
0.3483
-0.4
0.3446
0.3409
0.3372
0.3336
0.3300
0.3264
0.3228
0.3192
0.3156
0.3121
-0.5
0.3085
0.3050
0.3015
0.2981
0.2946
0.2912
0.2877
0.2843
0.2810
0.2776
-0.6
0.2743
0.2709
0.2676
0.2643
0.2611
0.2578
0.2546
0.2514
0.2483
0.2451
-0.7
0.2420
0.2389
0.2358
0.2327
0.2296
0.2266
0.2236
0.2206
0.2177
0.2148
-0.8
0.2119
0.2090
0.2061
0.2033
0.2005
0.1977
0.1949
0.1922
0.1894
0.1867
-0.9
0.1841
0.1814
0.1788
0.1762
0.1736
0.1711
0.1685
0.1660
0.1635
0.1611
-1
0.1587
0.1562
0.1539
0.1515
0.1492
0.1469
0.1446
0.1423
0.1401
0.1379
-1.1
0.1357
0.1335
0.1314
0.1292
0.1271
0.1251
0.1230
0.1210
0.1190
0.1170
-1.2
0.1151
0.1131
0.1112
0.1093
0.1075
0.1056
0.1038
0.1020
0.1003
0.0985
-1.3
0.0968
0.095'1
0.0934
0.0918
0.0901
0.0885
0.0869
0.0853
0.0838
0.0823
-1.4
0.0808
0.0793
0.0778
0.0764
0.0749
0.0735
0.0721
0.0708
0.0694
0.0681
-1.5
0.0668
0.0655
0.0643
0.0630
0.0618
0.0606
0.0594
0.0582
0.0571
0.0559
-1.6
0.0548
0.0537
0.0526
0.0516
0.0505
0.0495
0.0485
0.0475
0.0465
0.0455
-1.7
0.0446
0.0436
0.0427
0.0418
0.0409
0.0401
0.0392
0.0384
0.0375
0.0367
-1.8
0.0359
0.0351
0.0344
0.0336
0.0329
0.0322
0.0314
0.0307
0.0301
0.0294
-1.9
0.0287
0.0281
0.0274
0.0268
0.0262
0.0256
0.0250
0.0244
0.0239
0.0233
-2
0.0228
0.0222
0.0217
0.0212
0.0207
0.0202
0.0197
0.0192
0.0188
0.0183
-2.1
0.0179
0.0174
0.0170
0.0166
0.0162
0.0158
0.0154
0.0150
0.0146
0.0143
0.0125
0.0122
0.0119
0.0116
0.0113
0.0110
-2.2
0.0139
0.0136
0.0132
0.0129
-2.3
0.0107
0.0104
0.0102
0.0099
0.0096
0.0094
0.0091
0.0089
0.0087
0.0084
-2.4
0.0082
0.0080
0.0078
0.0075
0.0073
0.0071
0.0069
0.0068
0.0066
0.0064
-2.5
0.0062
0.0060
0.0059
0.0057
0.0055
0.0054
0.0052
0.0051
0.0049
0.0048
-2.6
0.0047
0.0045
0.0044
0.0043
0.0041
0.0040
0.0039
0.0038
0.0037
0.0036
-2.7
0.0035
0.0034
0.0033
0.0032
0.0031
0.0030
0.0029
0.0028
0.0027
0.0026
-2.8
0.0026
0.0025
0.0024
0.0023
0.0023
0.0022
0.0021
0.0021
0.0020
0.0019
-2.9
0.0019
0.0018
0.0018
0.0017
0.0016
0.0016
0.0015
0.0015
0.0014
0.0014
-3.0
0.0013
0.0013
0.0013
0.0012
0.0012
0.0011
0.0011
0.0011
0.0010
0.0010
79
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Z-TABLE (CUMULA TIVE)
StandardNormal Distribution
P (Z :-s; z) = N(z) for z 2 0
z
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0
0.5000
0.5040
0.5080
0.5120
0.5160
0.5199
0.5239
0.5279
0.5319
0.5359
0.1
0.5398
0.5438
0.5478
0.5517
0.5557
0.5596
0.5636
0.5675
0.5714
0.5753
0.2
0.5793
0.5832
0.5871
0.5910
0.5948
0.5987
0.6026
0.6064
0.6103
0.6141
0.3
0.6179
0.6217
0.6255
0.6293
0.6331
0.6368
0.6406
0.6443
0.6480
0.6517
0.4
0.6554
0.6591
0.6628
0.6664
0.6700
0.6736
0.6772
0.6808
0.6844
0.6879
0.5
0.6
0.6915
0.6950
0.6985
0.7019
0.7054
0.7088
0.7123
0.7157
0.7190
0.7224
0.7257
0.7291
0.7324
0.7357
0.7389
0.7422
0.7454
0.7486
0.7517
0.7549
0.7
0.7580
0.7611
0.7642
0.7673
0.7704
0.7734
0.7764
0.7794
0.7823
0.7852
0.8
0.7881
0.7910
0.7939
0.7967
0.7995
0.8023
0.8051
0.8078
0.8106
0.8133
0.9
0.8159
0.8186
0.8212
0.8238
0.8264
0.8289
0.8315
0.8340
0.8365
0.8389
1
0.8413
0.8438
0.8461
0.8485
0.8508
0.8531
0.8554
0.8577
0.8599
0.8621
1.1
0.8643
0.8665
0.8686
0.8708
0.8729
0.8749
0.8770
0.8790
0.8810
0.8830
1.2
0.8849
0.8869
0.8888
0.8907
0.8925
0.8944
0.8962
0.8980
0.8997
0.9015
0.9162
0.9177
1.3
0.9032
0.9049
0.9066
0.9082
0.9099
0.9115
0.9131
0.9147
1. 4
0.9192
0.9207
0.9222
0.9236
0.9251
0.9265
0.9279
0.9292
0.9306
0.9319
1.5
0.9332
0.9345
0.9357
0.9370
0.9382
0.9394
0.9406
0.9418
0.9429
0.9441
1.6
0.9452
0.9463
0.9474
0.9484
0.9495
0.9505
0.9515
0.9525
0.9535
0.9545
1.7
0.9554
0.9564
0.9573
0.9582
0.9591
0.9599
0.9608
0.9616
0.9625
0.9633
1. 8
0.9641
0.9649
0.9656
0.9664
0.9671
0.9678
0.9686
0.9693
0.9699
0.9706
1.9
0.9713
0.9719
0.9726
0.9732
0.9738
0.9744
0.9750
0.9756
0.9761
0.9767
2
0.9772
0.9778
0.9783
0.9788
0.9793
0.9798
0.9803
0.9808
0.9812
0.9817
2. 1
0.9821
0.9826
0.9830
0.9834
0.9838
0.9842
0.9846
0.9850
0.9854
0.9857
2.2
0.9861
0.9864
0.9868
0.9871
0.9875
0.9878
0.9881
0.9884
0.9887
0.9890
2.3
0.9893
0.9896
0.9898
0.9901
0.9904
0.9906
0.9909
0.9911
0.9913
0.9916
0.9931
0.9932
0.9934
0.9936
2.4
0.9918
0.9920
0.9922
0.9925
0.9927
0.9929
2.5
2.6
0.9938
0.9940
0.9941
0.9943
0.9945
0.9946
0.9948
0.9949
0.9951
0.9952
0.9953
0.9955
0.9956
0.9957
0.9959
0.9960
0.9961
0.9962
0.9963
0.9964
2.7
0.9965
0.9966
0.9967
0.9968
0.9969
0.9970
0.9971
0.9972
0.9973
0.9974
2.8
0.9974
0.9975
0.9976
0.9977
0.9977
0.9978
0.9979
0.9979
0.9980
0.9981
2.9
0.9981
0.9982
0.9982
0.9983
0.9984
0.9984
0.9985
0.9985
0.9986
0.9986
3
0.9987
0.9987
0.9987
0.9988
0.9988
0.9989
0.9989
0.9989
0.9990
0.9990
80
© 2023 FinTree Education Pvt. Ltd.
STUDENTS T-DISTRIBUTION
Level of significance for One-Tailed Test
df
l
0.1
1
o.o5
1
o.o25
1
o.o1
1
o.oo5
1
o.ooo5
Level of significance for Two-Tailed Test
df
0.2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
0.1
0.05
0.02
0.01
0.001
3.0777
6.3138
12.7062
31.8205
63.6567
636.6192
1.8856
2.9200
4.3027
6.9646
9.9248
31.5991
1.6377
2.3534
3.1824
4.5407
5.8409
12.9240
1.5332
2.1318
2.7764
3.7469
4.6041
8.6103
1.4759
2.0150
2.5706
3.3649
4.0321
6.8688
1.4398
1.9432
2.4469
3.1427
3.7074
5.9588
1.4149
1.8946
2.3646
2.9980
3.4995
5.4079
1.3968
1.8595
2.3060
2.8965
3.3554
5.0413
1.3830
1.8331
2.2622
2.8214
3.2498
4.7809
1.3722
1.8125
2.2281
2.7638
3.1693
4.5869
1.3634
1.7959
2.2010
2.7181
3.1058
4.4370
1.3562
1.7823
2.1788
2.6810
3.0545
4.3178
1.3502
1.7709
2.1604
2.6503
3.0123
4.2208
1.3450
1.7613
2.1448
2.6245
2.9768
4.1405
1.3406
1.7531
2.1314
2.6025
2.9467
4.0728
1.3368
1.7459
2.1199
2.5835
2.9208
4.0150
1.3334
1.7396
2.1098
2.5669
2.8982
3.9651
1.3304
1.734 1
2.1009
2.5524
2.8784
3.9216
1.3277
1.7291
2.0930
2.5395
2.8609
3.8834
1.3253
1.7247
2.0860
2.5280
2.8453
3.8495
1.3232
1.7207
2.0796
2.5 176
2.8314
3.8193
1.3212
1.7171
2.0739
2.5083
2.8 188
3.7921
1.3195
1.7139
2.0687
2.4999
2.8073
3.7676
1.3178
1.7109
2.0639
2.4922
2.7969
3.7454
1.3163
1.7081
2.0595
2.4851
2.7874
3.7251
26
27
28
29
30
1.3150
1.7056
2.0555
2.4786
2.7787
3.7066
1.3137
40
60
120
200
00
1.7033
2.0518
2.4727
2.7707
3.6896
1.3125
1.7011
2.0484
2.4671
2.7633
3.6739
1.3114
1.6991
2.0452
2.4620
2.7564
3.6594
1.3104
1.6973
2.0423
2.4573
2.7500
3.6460
1.3031
1.6839
2.0211
2.4233
2.7045
3.5510
1.2958
1.6706
2.0003
2.3901
2.6603
3.4602
1.2886
1.6577
1.9799
2.3578
2.6174
3.3735
1.2858
1.6525
1.9719
2.345 1
2.6006
3.3398
1.2816
1.6449
1.9600
2.3264
2.5759
3.2906
81
© 2023 FinTree Education Pvt. Ltd.
F-TABLE AT 5 PERCENT (UPPER TAIL)
Degrees of freedom of numerator along the top most row
Degrees of freedom of denominator along the left most column
df
1
2
3
4
5
6
7
8
9
10
12
15
20
24
30
40
1
161
199
216
225
230
234
237
239
241
242
244
246
248
249
250
251
2
18.5
19.0
19.2
19.2
19.3
19.3
19.4
19.4
19.4
19.4
19.4
19.4
19.4
19.5
19.5
19.5
3
10.1
9.55
9.28
9.12
9.01
8.94
8.89
8.85
8.81
8.79
8.74
8.70
8.66
8.64
8.62
8.59
4
7.71
6.94
6.59
6.39
6.26
6.16
6.09
6.04
6.00
5.96
5.91
5.86
5.80
5.77
5.75
5.72
5
6.61
5.79
5.41
5.19
5.05
4.95
4.88
4.82
4.77
4.74
4.68
4.62
4.56
4.53
4.50
4.46
6
5.99
5.14
4.76
4.53
4.39
4.28
4.21
4.15
4.10
4.06
4.00
3.94
3.87
3.84
3.81
3.77
7
8
5.59
4.74
4.35
4.12
3.97
3.87
3.79
3.73
3.68
3.64
3.57
3.51
3.44
3.41
3.38
3.34
5.32
4.46
4.07
3.84
3.69
3.58
3.50
3.44
3.39
3.35
3.28
3.22
3.15
3.12
3.08
3.04
9
5.12
4.26
3.86
3.63
3.48
3.37
3.29
3.23
3.18
3.14
3.07
3.01
2.94
2.90
2.86
2.83
10
4.96
4.10
3.71
3.48
3.33
3.22
3.14
3.07
3.02
2.98
2.91
2.85
2.77
2.74
2.70
2.66
11
12
4.84
3.98
3.59
3.36
3.20
3.09
3.01
2.95
2.90
2.85
2.79
2.72
2.65
2.61
2.57
2.53
4.75
3.89
3.49
3.26
3.11
3.00
2.91
2.85
2.80
2.75
2.69
2.62
2.54
2.51
2.47
2.43
13
4.67
3.81
3.41
3.18
3.03
2.92
2.83
2.77
2.71
2.67
2.60
2.53
2.46
2.42
2.38
2.34
14
4.60
3.74
3.34
3.11
2.96
2.85
2.76
2.70
2.65
2.60
2.53
2.46
2.39
2.35
2.31
2.27
15
4.54
3.68
3.29
3.06
2.90
2.79
2.71
2.64
2.59
2.54
2.48
2.40
2.33
2.29
2.25
2.20
16
4.49
3.63
3.24
3.01
2.85
2.74
2.66
2.59
2.54
2.49
2.42
2.35
2.28
2.24
2.19
2.15
17
4.45
3.59
3.20
2.96
2.81
2.70
2.61
2.55
2.49
2.45
2.38
2.31
2.23
2.19
2.15
2.10
18
4.41
3.55
3.16
2.93
2.77
2.66
2.58
2.51
2.46
2.41
2.34
2.27
2.19
2.15
2.11
2.06
19
4.38
3.52
3.13
2.90
2.74
2.63
2.54
2.48
2.42
2.38
2.31
2.23
2.16
2.11
2.07
2.03
20
4.35
3.49
3.10
2.87
2.71
2.60
2.51
2.45
2.39
2.35
2.28
2.20
2.12
2.08
2.04
1.99
21
4.32
3.47
3.07
2.84
2.68
2.57
2.49
2.42
2.37
2.32
2.25
2.18
2.10
2.05
2.01
1.96
22
4.30
3.44
3.05
2.82
2.66
2.55
2.46
2.40
2.34
2.30
2.23
2.15
2.07
2.03
1.98
1.94
23
4.28
3.42
3.03
2.80
2.64
2.53
2.44
2.37
2.32
2.27
2.20
2.13
2.05
2.01
1.96
1.91
24
4.26
3.40
3.01
2.78
2.62
2.51
2.42
2.36
2.30
2.25
2.18
2.11
2.03
1.98
1.94
1.89
25
4.24
3.39
2.99
2.76
2.60
2.49
2.40
2.34
2.28
2.24
2.16
2.09
2.01
1.96
1.92
1.87
26
4.23
3.37
2.98
2.74
2.59
2.47
2.39
2.32
2.27
2.22
2.15
2.07
1.99
1.95
1.90
1.85
27
4.21
3.35
2.96
2.73
2.57
2.46
2.37
2.31
2.25
2.20
2.13
2.06
1.97
1.93
1.88
1.84
28
29
4.20
3.34
2.95
2.71
2.56
2.45
2.36
2.29
2.24
2.19
2.12
2.04
1.96
1.91
1.87
1.82
4.18
3.33
2.93
2.70
2.55
2.43
2.35
2.28
2.22
2.18
2.10
2.03
1.94
1.90
1.85
1.81
30
4.17
3.32
2.92
2.69
2.53
2.42
2.33
2.27
2.21
2.16
2.09
2.01
1.93
1.89
1.84
1.79
40
4.08
3.23
2.84
2.61
2.45
2.34
2.25
2. 18
2.12
2.08
2.00
1.92
1.84
1.79
1.74
1.69
60
120
4.00
3.15
2.76
2.53
2.37
2.25
2.17
2.10
2.04
1.99
1.92
1.84
1.75
1.70 . 1.65
1.59
3.92
3.07
2.68
2.45
2.29
2.18
2.09
2.02
1.96
1.91
1.83
1.75
1.66
1.61
1.55
1.50
3.84
3.00
2.60
2.37
2.2 1
2.10
2.01
1.94
1.88
1.83
1.75
1.67
1.57
1.52
1.46
1.39
00
82
© 2023 FinTree Education Pvt. Ltd.
F-TABLE AT 2.5 PERCENT (UPPER TAIL)
Degrees of freedom of numerator along the top most row
Degrees of freedom of denominator along the left most
column
1
2
3
4
5
6
7
8
9
10
12
15
20
24
30
40
1
648
799
864
900
922
937
948
957
963
969
977
985
993
997
1001
1006
2
38.51 39.00 39.17 39.25 39.30 39.33 39.36 39.37 39.39 39.40 39.41 39.43 39.45 39.46 39.46 39.47
3
17.44 16.04 15.44 15.10 14.88 14.73 14.62 14.54 14.47 14.42 14.34 14.25 14.17 14.12 14.08 14.04
df
4
12.22 10.65
9.98
9.60
9.36
9.20
9.07
8.98
8.90
8.84
8.75
8.66
8.56
8.51
8.46
8.41
5
10.01
8.43
7.76
7.39
7.15
6.98
6.85
6.76
6.68
6.62
6.52
6.43
6.33
6.28
6.23
6.18
6
8.81
7.26
6.60
6.23
5.99
5.82
5.70
5.60
5.52
5.46
5.37
5.27
5.17
5.12
5.07
5.01
7
8.07
6.54
5.89
5.52
5.29
5. 12
4.99
4.90
4.82
4.76
4.67
4.57
4.47
4.41
4.36
4.31
8
7.57
6.06
5.42
5.05
4.82
4.65
4.53
4.43
4.36
4.30
4.20
4.10
4.00
3.95
3.89
3.84
9
7.21
5.71
5.08
4.72
4.48
4.32
4.20
4. 10
4.03
3.96
3.87
3.77
3.67
3.61
3.56
3.51
10
6.94
5.46
4.83
4.47
4.24
4.07
3.95
3.85
3.78
3.72
3.62
3.52
3.42
3.37
3.31
3.26
11
6.72
5.26
4.63
4.28
4.04
3.88
3.76
3.66
3.59
3.53
3.43
3.33
3.23
3.17
3.12
3.06
12
6.55
5.10
4.47
4.12
3.89
3.73
3.61
3.51
3.44
3.37
3.28
3.18
3.07
3.02
2.96
2.91
13
6.41
4.97
4.35
4.00
3.77
3.60
3.48
3.39
3.31
3.25
3.15
3.05
2.95
2.89
2.84
2.78
14
6.30
4.86
4.24
3.89
3.66
3.50
3.38
3.29
3.21
3.15
3.05
2.95
2.84
2.79
2.73
2.67
15
6.20
4.77
4.15
3.80
3.58
3.41
3.29
3.20
3.12
3.06
2.96
2.86
2.76
2.70
2.64
2.59
16
6.12
4.69
4.08
3.73
3.50
3.34
3.22
3.12
3.05
2.99
2.89
2.79
2.68
2.63
2.57
2.51
17
6.04
4.62
4.01
3.66
3.44
3.28
3.16
3.06
2.98
2.92
2.82
2.72
2.62
2.56
2.50
2.44
18
5.98
4.56
3.95
3.6 1
3.38
3.22
3.10
3.01
2.93
2.87
2.77
2.67
2.56
2.50
2.44
2.38
19
5.92
4.51
3.90
3.56
3.33
3.17
3.05
2.96
2.88
2.82
2:72
2.62
2.51
2.45
2.39
2.33
20
5.87
4.46
3.86
3.51
3.29
3.13
3.01
2.91
2.84
2.77
2.68
2.57
2.46
2.41
2.35
2.29
21
5.83
4.42
3.82
3.48
3.25
3.09
2.97
2.87
2.80
2.73
2.64
2.53
2.42
2.37
2.31
2.2?
22
. 5.79
4.38
3.78
3.44
3.22
3.05
2.93
2.84
2.76
2.70
2.60
2.50
2.39
2.33
2.27
2.21
23
5.75
4.35
3.75
3.41
3.18
3.02
2.90
2.81
2.73
2.67
2.57
2.47
2.36
2.30
2.24
2.18
24
5.72
4.32
3.72
3.38
3.15
2.99
2.87
2.78
2.70
2.64
2.54
2.44
2.33
2.27
2.21
2.15
25
5.69
4.29
3.69
3.35
3.13
2.97
2.85
2.75
2.68
2.61
2.51
2.41
2.30
2.24
2.18
2.12
26
5.66
4.27
3.67
3.33
3.10
2.94
2.82
2.73
2.65
2.59
2.49
2.39
2.28
2.22
2.16
2.09
27
5.63
4.24
3.65
3.31
3.08
2.92
2.80
2.71
2.63
2.57
2.47
2.36
2.25
2.19
2.13
2.07
28
5.61
4.22
3.63
3.29
3.06
2.90
2.78
2.69
2.61
2.55
2.45
2.34
2.23
2.17
2. 11
2.05
29
5.59
4.20
3.6 1 ·3.27
3.04
2.88
2.76
2.67
2.59
2.53
2.43
2.32
2.21
2.15
2.09
2.03
30
5.57
4.18
3.59
3.25
3.03
2.87
2.75
2.65
2.57
2.51
2.41
2.31
2.20
2.14
2.07
2.01
40
5.42
4.05
3.46
3.13
2.90
2.74
2.62
2.53
2.45
2.39
2.29
2.18
2.07
2.01
1.94
1.88
60
120
5.29
3.93
3.34
3.01
2.79
2.63
2.51
2.41
2.33
2.27
2.17
2.06
1.94
1.88
1.82
1.74
5.15
3.80
3.23
2.89
2.67
2.52
2.39
2.30
2.22
2.16
2.05
1.94
1.82
1.76
1.69
1.61
00
5.02
3.69
3.12
2.79
2.57
2.41
2.29
2. 19
2.11
2.05
1.94
1.83
1.71
1.64
1.57
1.48
83
© 2023 FinTree Education Pvt. Ltd.
CHI -SQUARED TABLE
Values of X 2 (degrees of freedom , level of significance) probability in right tail.
df
0.99
0.975
0.95
0.9
0.1
0.05
0.025
0.01
0.005
1
0.000157
0.000982
0.003932
0.015791
2.705544
3.841459
5.023886
6.634897
7.879439
2
0.020101
0.050636
0.102587
0.210721
4.60517
5.991465
7.377759
9.21034
10.59663
3
0.114832
0.215795
0.351846
0.584374
6.251388
7.814728
9.348404
11.34487
12.83816
4
0.297109
0.484419
0.710723
1.063623
7.77944
9.487729
11.14329
13.2767
14.86026
5
0.554298
0.831212
1.145476
1.610308
9.236357
11.0705
12.8325
15.08627
16.7496
6
0.87209
1.237344
1.635383
2.204131
10.64464
12.59159
14.44938
16.81189
18.54758
7
1.239042
1.689869
2.16735
2.833107
12.01704
14.06714
16.01276
18.47531
20.27774
8
1.646497
2.179731
2.732637
3.489539
13.36157
15.50731
17.53455
20.09024
21.95495
9
2.087901
2.70039
3.325113
4.168159
14.68366
16.91898
19.02277
21.66599
23.58935
10
2.558212
3.246973
3.940299
4.865182
15.98718
18.30704
20.48318
23.20925
25.18818
11
3.053484
3.815748
4.574813
5.577785
17.27501
19.67514
21.92005
24.72497
26.75685
12
3.570569
4.403789
5.226029
6.303796
18.54935
21.02607
23.33666
26.21697
28.29952
13
4.106915
5.008751
5.891864
7.041505
19.81193
22.36203
24.7356
27.68825
29.81947
14
4.660425
5.628726
6.570631
7.789534
21.06414
23.68479
26.11895
29.14124
31.31935
15
5.229349
6.262138
7.260944
8.546756
22.30713
24.99579
27.48839
30.57791
32.80132
16
5.812213
6.907664
7.961646
9.312236
23.54183
26.29623
28 .84535
31.99993
34.26719
17
6.40776
7.564186
8.67176
10.08519
24.76904
27.58711
30.19101
33.40866
35.71847
18
7.014911
8.230746
9.390455
10.86494
25.98942
28.8693
31.52638
34.80531
37.15645
19
7.63273
8.906517
10. 11701
11.65091
27.20357
30.14353
32.85233
36.19087
38.58226
20
8.260398
9.590778
10.85081
12.44261
28.41198
31.41043
34.16961
37.56623
39.99685
21
8.897198
10.2829
11.59131
13.2396
29.61509
32.67057
35.47888
38.93217
41.40106
22
9.542492
10.98232
12.33801
14.04149
30.81328
33.92444
36.78071
40.28936
42.79565
23
10.19572
11.68855
13.09051
14.84796
32.0069
35.17246
38.07563
41.6384
44.18128
24
10.85636
12.40115
13.84843
15.65868
33.19624
36.41503
39.36408
42.97982
45.55851
25
11.52398
13.11972
14.61141
16.47341
34.38159
37.65248
40.64647
44.3141
46.92789
26
12.19815
13.84391
15.37916
17.29189
35.56317
38.88514
41.92317
45.64168
48.28988
27
12.8785
14.57338
16.1514
18.1139
36.74122
40 .11327
43.19451
46.96294
49 .64492
28
13.56471
15.30786
16.92788
18.93924
37.91592
41.33714
44.46079
48.27824
50.99338
29
14.25645
16.04707
17.70837
19.76774
39.08747
42 .55697
45.72229
49.58788
52.33562
30
14.95346
16.79077
18.49266
20.59923
40 .25602
43.77297
46.97924
50.89218
53.67196
50
29.70668
32.35736
34.76425
37.68865
63.16712
67.50481
71.4202
76.15389
79.48998
60
37.48485
40.48175
43 .18796
46.45889
74.39701
79.08194
83.29768
88.37942
91.9517
80
53.54008
57.15317
60.39148
64.27785
96.5782
101.8795
106.6286
112.3288
116.3211
100
70.0649
74.22193
77.92947
82.35814
118.498
124.3421
129.5612
135.8067
140.1695
84
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FinTree Education Pvt. Ltd.
1 Muktali Building, First floor,
Lane 16, Bhandarkar Rd, near
by TVS Showroom, Pune,
Maharashtra,
India - 411004
148, 3rd Floor, 60 Feet Rd,
KHB Colony, 5th Block,
Koramangala, Bengaluru,
Karnataka
India 560034
Disclaimer: CFA Institute does not endorse, promote, review, or warrant the accuracy or quality of the
products or services offered by FinTree Education Pvt. Ltd. CFA Institute, CFA®, and Chartered Financial
Analyst® are trademarks owned by CFA Institute.
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