FINA 3332
Exam 2: Chapter Review
Spring 2011
Chapter 6: Analysis of Risk and Return
•
Risk
o
The possibility that actual returns, or cash flows, will be different from expected
returns
o
Refers to the potential variability of returns from an asset or a portfolio of assets
o
Returns reflect cash flows
o
Riskfree returns are known with certainty
•
Outcomes and Probability
o
Outcome
—different possible events that may occur
o
Probability
—the likelihood of each outcome
o
Return outcomes and their probabilities are used to obtain statistical measures of
risk and return.
•
Two data types
o
Subjective or personal determination
Forward projections
Uses ex ante data
o
Historical
Actual past observations
Uses ex post data
•
Expected Return
r
=
j=1nrjpj
•
r
= Expected return
r
j
= return outcome j
p
j
= probability of the j
th
outcome
n = number of possible
outcomes
o
o
Mean, or average, value of possible return outcomes
o
Weighted average of the possible return outcomes
•
Standard Deviation of Returns
σ=j=1n(rjr2pj
)
r = Expected return
r
j
= return outcome j
p
j
= probability of the j
th
outcome
n = number of possible
outcomes
σ = standard deviation
σ
2
= variance
o
o
Measures variability of returns from the mean
o
Indicates risk of an asset
1
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•
Normal Probability Distribution
o
Mean
o
Standard Deviation
o
Daily stock returns follow this
•
ZTables
=
z
Target Value –Expected ValueStandard Deviation
•
Historical Data
o
Find Expected Return
o
Find Standard Deviation
•
Subjective Data
o
Find Expected Return
o
Find Standard Deviation
•
Coefficient of Variation
o
Measures Relative Risk
o
Measures total risk per unit of expected return
CV= σr
o
Appropriate measure of total risk when comparing two investment projects or assets
of different size
•
Covariance
o
Measures the degree of comovements of returns between pairs of assets
(+)  on average, the asset prices move in the same direction
()  on average, the asset prices move in opposite directions
(0) – on average, there is no relationship between asset returns
,
σA B
=
=
(
, 
)(
, 
)(
)
j 1n rA j rA rB j rB pj
o
First Calculate mean returns of each
Expected return
o
Second, Calculate Covariance
•
Correlation
o
Measures degree of comovement of returns
o
Unitless number between 1 and +1 inclusive
o
, = +
ρA B
1
Perfectly positive correlation
o
, = 
ρA B
1
Perfectly negative correlation
o
, =
ρA B
0
No relationship
o
,
=
,
ρA B
σA BσAσB
o
•
RiskReturn Relationship
o
Required Rate of Return
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 Spring '08
 DARLACHISHOLM
 Capital Asset Pricing Model, Financial Markets, Modern portfolio theory

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