# Stock Variance

The standard deviation of the market index portfolio is 20%. Stock A has a beta 1.5 and residual standard deviation of 30%.

A) What would make for a larger increase in the stock variance, an increase of 1.5 in its beta or an increase of 3% in its residual standard deviation?

B) An inventor who currently holds the market index portfolio decides to reduce the portfolio allocation to the market index to 90% and to invest 10% in stock A. which of the changes in A, will have greater impact on the portfolio standard deviation?

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Calculation of Stock Variance

Given:

Standard deviation of market index portfolio: (?m) = 20% or 0.2

Beta of stock A: (?) = 1.5

Residual standard deviation of stock A: (?A) = 30% or 0.3

Stock variance at current value: Market risk + Diversifiable risk

Or ?12 = ?2Ã— ?m2+ ?A2 (Daves & Daves, 2012)

= 1.52Ã—0.22+0.32

= 2.25Ã—0.04 + 0.09

=0.09+0.09

=0.18 or 18%

(A): Change in variance, if residual standard deviation increases by 3%:

Standard deviation of market index portfolio: (?m) = 20% or 0.2

Beta of stock A: ...

#### Solution Summary

The expert examines stock variances and standard deviation for market index portfolios.