Question

The standard deviation of the market-index portfolio is 15%. Stock A has a beta of 2.2 and residual standard deviation of 25%.

a) What would make a for a larger increase in the stock’s variance: an increase of 0.2 in its beta or an increase of 3.84% in its standard deviation?

b) An investor who currently holds the market-index portfolio decides to reduce the portfolio allocation to the market index 90% and to invest 10% in stock. Which of the changes in (a) will have a greater impact on the portfolio’s standard deviation?

Please not to solve with excel!!

Answer 1

Use the following formula

Total variance = Systematic variance + Residual Variance

Given Beta = 2.2, Residual standard deviation = 25%

Standard Deviation market = 15%

A.

SDM	SDe	Beta	Total Variance
0.15	0.25	2.4	2.42*0.152+0.252= 0.1921
0.15	0.2884	2.2	2.22*0.152+0.28842= 0.1921

When Beta increases by 0.2 then Total Variance = 0.1921

When SD increases by 3.84% then Total Variance = 0.1921

B. Increase of 0.2 of Beta has greater impact on the portfolios standard deviation.

Beta will have direct impact on the portfolio because it increases the systematic risk. We cannot reduce the systematic risk.

In case of residual standard deviation it will not have significant impact on the portfolio since it can be reduced through diversification. Thus, Residual standard deviation has less or no impact on investment portfolio.

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