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Statistics for finance · level 1

Weighted mean (portfolio return)

A portfolio return is a weighted mean: each weight times its return, added up. Do it as percentage blocks — 60% of 9 is 5.4 — never as a plain average of the returns.

Theory: Describing Data

Worked example: Portfolio: 60% at 9%, 40% at 3%. Portfolio return?

60% weight9% → 5.4%
40% weight3% → 1.2%
portfolio6.6%

Step by step

  1. 1

    Weighted mean, not a plain average

    r_p = Σ wᵢ rᵢ

  2. 2

    Sleeve 1

    60% × 9% = 5.4%

  3. 3

    Sleeve 2

    40% × 3% = 1.2%

  4. 4

    Add the contributions

    6.6%

Portfolio: 60% at 9%, 40% at 3%. Portfolio return? = 6.6

The theory behind it

Intuition

A weighted mean is the only correct average when the items differ in size — portfolio return is weights times returns, never a simple average.

Common pitfalls

  • ×Averaging percentages of differently sized bases.
  • ×Weights that do not sum to one.

In the interview

Blended margin, blended price and portfolio-return rounds.