Portfolio expected return and variance

In short

• Portfolio weights are each holding's share of the portfolio's market value; they sum to 1.
• Expected return of the portfolio = weighted average of the holdings' expected returns. Nothing else matters for it.
• Portfolio variance measures expected risk: the expected squared deviation of the portfolio return from its mean.
• Two-asset variance = $w_1^2\sigma_1^2 + w_2^2\sigma_2^2 + 2w_1w_2\text{Cov}_{12}$: two own-risk terms plus a co-movement term.
• Standard deviation is the square root of variance and is quoted in the same units as returns.
• Portfolio standard deviation is at most the weighted average of the holdings' standard deviations; the gap is the benefit of diversification.