Lesson 4 of 7 · 14 min

Measuring asset and portfolio risk

Portfolio return is a weighted average, but portfolio risk depends on weights, individual risks and how the assets move together.

In short

From historical data: mean = average return; sample variance and sample covariance divide by $n - 1$ ; correlation = Cov ÷ ( $\sigma_1\sigma_2$ ).
Portfolio return: $R_p = \sum w_iR_i$ , weights summing to 1.
Two-asset variance: $\sigma_p^2 = w_1^2\sigma_1^2 + w_2^2\sigma_2^2 + 2w_1w_2\rho_{12}\sigma_1\sigma_2$ .
Correlation runs from −1 to +1: +1 move together always, −1 always opposite, 0 no linear relation.
Adding a riskier asset can raise return and lower risk if correlation is low enough.
A foreign asset is a two-part position: local return and currency return, with $R_D = (1 + R_{lc})(1 + R_{FX}) - 1$ .

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