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CFA® level 1 Quantitative Methods - Soleadea Summary

This is a summary of CFA® Quantitative Methods created by Soleadea (www.soleadea.com).
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Soleadea Team

on 16 February 2015

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Transcript of CFA® level 1 Quantitative Methods - Soleadea Summary

CFA® Quantitative Methods
Tools for valuation
and
the basics of statistics

CFA level 1 Quantitative Methods can be divided into two parts:
Time Value of Money
Probability and Statistics
Generally, after covering readings concerned with the concepts of time value of money,
CFA level 1 candidates should understand and master problems of calculating present and future values for particular cases:
TVM principles by Khan Academy:
Central Limit Theorem by Khan Academy
Time value of money
Probability and Statistics
TVM techniques are tools that help financial specialists:
financial instruments and investments
1
3
value
make financial decisions
2
value
a company or an equity
about whether to invest in a project or not
TVM is
for a financial analyst
like
addition and subtraction
for a primary school pupil.

It is essential to master TVM before moving to more complex issues!
To solve TVM questions you can use:
direct formulas,
TVM functions on your calculator,
cash flow, NPVand IRR sheets on your calculator.
Useful Formulas
Normal Distribution
Chebyshev's Inequality
or
or
Draw a
time line
Example:
John is planning to set aside $100.000 today. He is also planning to take $7.000 from this account at the beginning of every year for the nearest 10 years. Additionally, as a happy father of a newborn daughter, he has decided to give her on her 17 birthday a sum of money. How much will he be able to give
to his daughter if the account pays an interest rate of
8 percent a year for all this time.
Future Value
Present Value
Uneven Cash Flows
use time line
Ordinary Annuity
Annuity Due
Future Value of a single sum of money
Although most prep providers show mainly how to make calculations using TVM sheet on your calculator, we strongly encourage you to become familiar with other methods mentioned above, as well.
Future Value of

and
Present Value of
a single sum of money
Present Value of a perpetuity
FV
PV
A
PV
A
A
A
...
FV
PV
Ordinary Annuity
Annuity Due
Present Value of
ordinary annuity
and
annuity due
ordinary annuity
annuity

due
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
For more complicated questions, you sometimes have to calculate the present value or future value
of uneven cash flows.
To manage such questions...
-100
+7
+7
+7
+7
+7
+7
+7
+7
+7
+7
+X
Solution
(using cash flow sheet and NPV sheet
on TiBA II Plus Professional)
=>CF
[2nd][CE/C]
clear cash flow sheet
CF0= -100+7=-93
[Enter]

->
CF1= +7

[Enter]

->
F01= 9 (because first 7 is added at the beginning)
[Enter]
=>NPV
I=8
[Enter]
->
NPV
[CPT]
NPV=-49.27 (this is the present value of the last payment=X)
X=49.27*1.08^17
X=182.31
Contest
The first person who will write on
our Facebook site (
http://www.facebook.com/soleadea
)
will get free access to
Soleadea Mock Exam
for Contributors
how to prove, using cash flow sheet and NPV sheet on TiBA II Plus (Professional), that X=182.31 is the correct answer for this question
for CFA level 1 Candidates
This part of the presentation covers 3 topics:
1. measures of central tendency

2. measures of dispersion

3. skewness

4. kurtosis
Properties of Return Distributions
TVM on the exam
Why does QM matter?
1.
Properties of Return Distributions
2.
3.
Chebyshev's Inequality
Normal Distribution and
Central Limit Theorem
Positively skewed
mode < median < mean
Negatively skewed
mean < median < mode


For all k>1, the proportion of the observations within k standard deviations of the arithmetic mean is at least:
Chebyshev’s inequality is valid for any distribution with finite variance!
It states that:
Key properties
is described by two parameters: mean and standard deviation,
a linear combination of normal random variables is normally distributed,
is symmetric (skewness=0),
its kurtosis is equal to 3.
Normal distribution
1
2
both are used as tools that help financial specialists
describe and estimate risk.
For a set of numbers, three basic
measures of central tendency
are distinguished:
the mean
the median
the mode
There are different types of means and they are used in different situations.
Remember that:
the harmonic mean (
h
) is always less or equal to the geometric mean(
g
)
the geometric mean(
g
) is always less or equal to the arithmetic mean(
a
)
h
<
g
<
a
For an ordered set of elements, the value for which the number of elements higher than the value is equal to the number of elements lower than the value is called the median.
Depending on the number of elements in a given set, the median is calculated differently:
The mode is the element of the set repeated most frequently.
The median
If the set contains an odd number of elements, n, then the median is equal to the value of the element occupying the position:
If the set contains an even number of elements, n, then the median is equal to the value calculated as the mean of the elements occupying positions:
{inverse alphabetical order}
The mean
The mode
Remember

If a unimodal distribution is symmetric,
the mean
=
the median
=
the mode!
Kurtosis
is the measure of the peakedness of the return distribution.
Kurtosis
of a normal distribution equals 3.
Excess kurtosis
(by definition) of a normal distribution equals 0.
and
=
=

D
ispersion
is the variability around the central tendency.
The common measures of dispersion are:
the range
the Mean Absolute Deviation (MAD)
the variance
the standard deviation
range
= maximum value – minimum value

Mean Absolute Variation
(MAD):
Population variance:



Sample variance:
Standard deviation is the positive square root of variance.
Time value of money (TVM) is extremely important
because:
are important because:
and use it to mark all significant data used in the question.
copyright by Soleadea
Visit our site: http://www.soleadea.com

Khan Academy videos can be found at:
www.youtube.com/watch?v=As1QpFGlGbg
www.youtube.com/watch?v=JNm3M9cqWyc
Full transcript