explain the assertion that the relationship between deviation on a portfolio and standard deviations of the...

explain the assertion that the relationship between deviation on a portfolio and standard deviations of the assets in the portfolio is not a simple one

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Expert Solution

The Portfolio return is the weighted average of the return of assets in the portfolio, i.e.

Return on Portfolio = Wa*Return(a) + Wb*Return(b)

where the Wa is the percentage of portfolio funds invested in stock A and Wb is the percentage of portfolio funds invested in stock B. Howvever the Standard Devaition of the portfolio is not the weighted avergae of individual stocks. The risk of portfolio (standard Deviation ) depends upon the degree of correlation between the returns of the securities. If it is -1, the risk of posrtfolio can be eliminated (i.e 0). However even if the correlation is negative, the total risk of portfolio can be reduced. On the other hand, if the correlation is perfect positive (+1), then SD of the portfolio will be the weighted average of SD of individual stocks.

Portfolio standard deviation will be calculated as

Example

Portfolio Return = 9%

Assuming Correlation = -1

Portfolio Risk (SD) =

= 0.

Thus the Portfolio standard deviation is not a weighted average of individual stock SD but depends upon the correlation coefficient.

jeff jeffy answered 1 year ago

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