Individual Investment Risk Measure

Individual Investment Risk Measure - Individual Investment...

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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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Individual Investment Risk Measure - Individual Investment...

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