Transcript IPM Chp01 Risk and Return Concept

Basics: Risk and Return
Investors are concerned with two principal
properties inherent in securities:
• The return that can be expected from
holding a security.
• The risk i.e. the return that is achieved
will be less than the return that was
expected.
Investors want to maximize expected
returns subject to their tolerance risk.
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Realized Return Vs Expected Return
Realized returns are after the fact return that
was earned. It is a historical data.
1
ri 
n
n
r
t 1
it
rit = Realized Return generated by the ith stock in
time period t.
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Realized Return Vs Expected Return
Expected Return on the other hand is our expectation
from future. It is the return from an asset that
investors anticipate they will earn over future period.
It is a predicted return. It may or may not occur.
n
E (r )i   pi ri
i 1
E (r ) i = Expected Return on asset i
P(i ) = Probability of ith state to occur.
r(i )
= Expected Return for the ith stock
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Arithmetic Mean Vs Geometric Mean
Arithmetic Mean
The arithmetic average, customarily designated by
the symbol X-bar ( X )
X

X 
n
or the sum of each the values being considered
divided by the total number of values.
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Geometric Mean
The geometric average return measures compound,
cumulative returns over time. It is used in
investments to reflect the realized change in wealth
over multiple periods.
The geometric average is defined as the nth root of
the product resulting from multiplying a series of
returns together
1
n
G  [(1  R1 )(1  R2 )......(1  Rn )]  1
where:
R = total return
n = number of periods
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RISK
(Variability in Returns)
Systematic Risk
Unsystematic Risk
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Measurement of Risk
Standard Deviation
The formula for Expected (ex-ante)
Where
n=
X=
P=

2
P
(
n

X
)

a possible outcome
the expected outcome.
the probability (or likelihood)
of the difference between n
and X occurring.
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Historical (ex-post) 
n
=
1
2
(
r

r
)

it
i
n
t 1
rit
= Realized Return generated by the ith
stock in time period t.
ri
= Average Return of ith stock.
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COEFFICIENT OF VARIATION

CV =
r
The coefficient of variation shows the risk per
unit of
return, and it provides a more
meaningful basis for comparison when the
expected returns on two alternatives are not
the same.
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COEFFICIENT OF VARIATION
Projects
X
Expected Return
60%
Risk
15%
CV
25.00%
Y
8%
3%
37.50%
If we calculate the Coefficient of Variation here, then
we find Project Y actually has more risk per unit of
return than Project X, in spite of the fact that X's
standard deviation is larger. Therefore, even though
Project Y has the lower standard deviation,
according to the coefficient of variation it is riskier
than Project X.
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BETA
Beta is a measure of the systematic risk of a
security that cannot be avoided through
diversification. Therefore, Beta measures nondiversifiable risk.
 IM 
Covim
 m2
where
 IM = Beta of security with market
Covim = Covariance between security and market

2
= Variance of market returns
m
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