What is the formula for portfolio standard deviation of returns for two assets?

The formula for calculating the portfolio standard deviation of returns for two assets takes into account not just the individual standard deviations of the two assets, but also their correlation, which reflects how the returns of the two assets move in relation to each other.

In the correct formula, the standard deviation of the portfolio is computed as the square root of the weighted variances of the individual assets plus two times the product of their weights, their individual standard deviations, and their correlation coefficient. This captures the diversification effect and the risk that arises from the relationship between the assets.

When both assets are equally weighted at 0.5 each, the formula becomes:

[

\sqrt{(0.5)^2 \times (\sigma_a)^2 + (0.5)^2 \times (\sigma_b)^2 + 2 \times (0.5) \times (0.5) \times \sigma_a \times \sigma_b \times \text{correlation}(a,b)}

]

This formula is essential in portfolio theory, as it helps investors understand the overall risk of the portfolio, taking into account both the individual assets' risks and how they interact with one another through their correlation.

This understanding is crucial for effective risk management