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Unformatted text preview: Individual Investment Risk
Measure
Variance • – It is a measure of the variation of possible
rates of return Ri, from the expected rate of
n
return [E(Ri)] 2
2 Variance (σ ) = ∑[R i  E(R i )] Pi
i =1 where Pi is the probability of the possible
rate of return, Ri
• Standard Deviation (σ)
– It is simply the square root of the variance
7 1 Individual Investment Risk
Measure
Exhibit 7.3
Possible Rate Expected of Return (Ri) Return E(Ri) Ri  E(Ri) [Ri  E(Ri)] 0.08
0.10
0.12
0.14 0.103
0.103
0.103
0.103 0.023
0.003
0.017
0.037 0.0005
0.0000
0.0003
0.0014 2 Pi
0.35
0.30
0.20
0.15 σ2) = 0.000451
Standard Deviation ( σ ) = 0.021237
Variance ( 7 2 2 [Ri  E(Ri)] Pi
0.000185
0.000003
0.000058
0.000205
0.000451 Covariance of Returns
• • A measure of the degree to which two
variables “move together” relative to their
individual mean values over time
For two assets, i and j, the covariance of
rates of return is defined as:
Covij = E{[Ri  E(Ri)] [Rj  E(Rj)]} • Example
– – The Wilshire 5000 Stock Index and Lehman
Brothers Treasury Bond Index during 2007
See Exhibits 7.4 and 7.7 7 3 Exhibit 7.4 7 4 Exhibit 7.7 7 5 Covariance and Correlation
• • The correlation coefficient is obtained by
standardizing (dividing) the covariance
by the product of the individual standard
deviations Cov
Computing correlation from covariance
ij
r =σ σ
ij
ij r = the correlatio n coefficien t of returns
ij
σi = the standard deviation of R it
σ j = the standard deviation of R jt
7 6 Correlation Coefficient
• • • The coefficient can vary in the range +1
to 1.
A value of +1 would indicate perfect
positive correlation. This means that
returns for the two assets move together
in a positively and completely linear
manner.
A value of –1 would indicate perfect
negative correlation. This means that the
returns for two assets move together in a
7 7 Exhibit 7.8 7 8 ...
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 Spring '12
 DAVIDBRAY
 Standard Deviation, Mean, Ri, Individual Investment Risk

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