Portfolio theory
A portfolio isn't made good by its best individual pieces, but by how they interact. What matters is the return earned per unit of risk taken.
The central insight is unassuming and far-reaching: two investments that are risky on their own can combine into a less volatile portfolio, if they don't fall at the same time.
It follows that you should never judge an investment alone. The question isn't whether it's good, it's what it adds to what you already hold.
The second insight: for every level of risk, there's a best possible mix. Anything below that is waste, since you're carrying the same risk and getting less for it.
In practice, none of this requires math. A broad world stock ETF plus safe assets in the desired ratio captures the core of what the theory recommends, with nothing to calculate.
Portfolio variance follows from σ²_p = Σ Σ w_i w_j σ_i σ_j ρ_ij. Alongside individual volatilities, it depends on pairwise correlations, which is why the diversification effect grows larger as those fall. At a correlation below one, portfolio volatility always sits below the weighted average of individual volatilities.
The set of portfolios with maximum return per unit of risk forms the efficient frontier. Adding a risk-free asset produces the capital market line, and every efficient portfolio can be represented as a mix of the risk-free asset and a single tangency portfolio. This separation is the theoretical reason why the split between equity share and safe share matters more than stock selection within the equity portion.
The practical weakness lies in estimation. Expected returns can only be estimated very imprecisely from historical data, and optimization procedures react extremely sensitively to these estimation errors, producing extreme and unstable weights. That's why simple rules like equal weighting or market-cap weighting often perform as well as or better than formal optimization in comparative studies.
Summary
- Judge an investment by its contribution, not on its own.
- The split between risky and safe matters more than stock selection.
- Formal optimization often fails on estimation errors; simple rules suffice.
Did you get it?
When does adding a holding lower portfolio volatility?
As soon as its correlation to the rest of the holdings sits below one.
What does the capital market line's separation tell us?
That efficient portfolios can be represented as a mix of the risk-free asset and a single tangency portfolio.
Why do simple rules often beat formal optimization?
Because optimizers react extremely sensitively to estimation errors in expected returns.
Related
- Hedging with optionsStage 4
- What return actually meansStage 0
- Risk and return are linkedStage 0