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Stock Variance

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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

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 = ?2× ?m2+ ?A2 (Daves & Daves, 2012)
= 1.52×0.22+0.32
= 2.25×0.04 + 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.

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Expected Rate of Return and Stock variance and Standard Deviation

1) Given the following data, What is the weight of security 1? Of security 2? 3? What is the expected return on the portfolio?

Security 1 ; $5,000 invested; Expected return 7%
Security 2; $7,000 invested; Expected return 9%
Security 3; $9,000 invested; Expected return 12%

2) The expected possible outcomes for Roxy Stock are below; what is the expected standard deviation of Roxy Stock?

State Probability Return
Super Boom 10% 35%
Boom 15% 20%
Expansion 45% 15%
Recession 30% -5%

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