= Portfolio diversification
= Diversification
{synonym}
Spreading a <portfolio> across assets can reduce risk that is not shared by them. For centered asset risks with <covariance matrix> $\Gamma$, the <variance> of the weighted risk is $w^T\Gamma w$. Equal weights across $n$ independent risks with common <variance> $s^2$ give <variance> $s^2/n$, whereas equal weights across risks that are all the same <random variable> leave <variance> $s^2$. Thus small individual weights do not by themselves remove common risk; the <covariance criterion for diversification of factor residuals> identifies sufficient dependence and weight conditions.
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