Portfolio Expected Return and Variance of Return

The expected return on the portfolio $(E(R_p))$ is a weighted average of the expected returns ($R_1\ to\ R_n)$ on the component securities using their respective proportions of the portfolio in currency units as weights $(w_1\ to\ w_2)$:

Portfolio variance is as follows:

Covariance

Given two random variables $R_i$ and $R_j$, the covariance between $R_i$ and $R_j$ is as follows:

Alternative notations are $\sigma(R_i, R_j)$ and $\sigma_{ij}$.

The sample covariance between two random variables $R_i$ and $R_j$, based on a sample of past data of size n is as follows:

Start with the definition of variance for a three-asset portfolio and see how it decomposes into three variance terms and six covariance terms. Dispensing with the derivation, the result is:

Correlation

The correlation between two random variables, $R_i$ and $R_j$, is defined as follows:

Alternative notations are $Corr(R_i,R_j)$ and $\rho_{ij}$.