**1. The portfolio volatility formula**

Consider a portfolio of three assets X, Y and Z with portfolio weights of a, b and c respectively. The portfolio volatility is:

Variance (X) = Variance in asset X’s returns, i.e. X’s returns volatility squared (σ

_{x}

^{2})

Variance (Y) = Variance in asset Y’s returns, i.e. Y’s returns volatility squared (σ

_{y}

^{2})

Variance (Z) = Variance in asset Z’s returns, i.e. Z’s returns volatility squared (σ

_{Z}

^{2})

_{ρxy}= correlation coefficient of X and Y returns

_{ρxz}= correlation coefficient of X and Z returns

_{ρyz}= correlation coefficient of Y and Z returns

If the assets in the portfolio are independent of each other the correlation coefficient terms in the equation above would be zero. If the assets in the portfolio are perfectly correlated with each other then the volatility of the portfolio would simply be the weighted average sum of the asset return volatility.

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