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σi2 – variance of returns on asset I = look right
σi – standard deviation of returns on asset i 1 (r it t rit ) 2 /( k 1) Cheryl Mew FINS2624 – Portfolio Management Semester 1, 2011 RISK DIVERSIFICATION
If there is no diversification benefit, SD = SD of constituent assets.
If there is diversification benefit, SD < SD of constituent assets.
A diversification benefit means a proportional change in return, but a disproportionate change in risk. This is
due to the smoothing effect on portfolio return when assets are combined to form a diversified portfolio.
The extent of diversification benefit depends on the correlation of returns between each pair of stocks
included in the portfolio. Correlation is a statistical measure to quantify the relationship between 2 variables.
Its value ranges between -1 and 1. ∑ ( ̅ )(
) pij = correlation coefficient, and σij is the sample covariance between the 2 assets. A pair of highly correlated assets with a large correlation coefficient offers little diversification benefit. Investors
are better off selecting assets that are not highly correlated, or negatively correlated to gain diversification
benefit. On the other hand, covariance cannot be used to reflect their strength of relationship, as it does not
have bounded values. It can only be used to indicate the direction of relationship between 2 variables.
P ORTFOLIO THEORY APPROACH TO MEASURE THE SD OF RETURNS OF A PORTFOLIO
The statistical approach does not explicitly reveal the impact of correlation on diversification benefit, as there
is no correlation involved in the computation of SD.
To highlight the significance of correlation in determining portfolio risk, portfolio theory expresses the SD of
returns of an n-asset portfolio as the square root of the sum of weighted variances and covariances of returns. ∑ ∑∑ As σij = pij x σi x σj, this equation suggests that: A portfolio containing assets which are not highly correlated with one another will have a lower risk
than another portfolio with highly correlated assets.
Assets with a large SD of returns will still provide diversification benefit as long...
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