Modern portfolio theory and the efficient frontier

9 minute read · By Krishna Avadhani, Vestora Academy · Updated 18 October 2026

Harry Markowitz (1952) showed that a portfolio's risk depends not only on each asset's risk but on how assets move together (correlation). Combining assets that are not perfectly correlated lowers risk for the same expected return.

The efficient frontier is the set of portfolios with the highest expected return for each level of risk. Adding a risk-free asset gives the capital market line; the best risky portfolio is where that line touches the frontier (the tangency portfolio).

In practice, optimisers are very sensitive to expected-return inputs and can produce extreme portfolios. Practitioners use constraints, shrinkage, Black-Litterman or simple rules like equal weight or risk parity to make the results robust.

Formula

σp² = w1²σ1² + w2²σ2² + 2 w1 w2 ρ σ1 σ2

Key takeaways

Correlation is the key to diversification.
The efficient frontier shows the best return for each risk level.
Optimisers are input-sensitive; constrain them.

Check your understanding

1. Combining two assets with correlation below 1 generally...

Increases risk
Reduces portfolio risk for the same return
Has no effect
Doubles returns

Show the answer

Reduces portfolio risk for the same return. Imperfect correlation is the source of diversification.

2. Why do practitioners constrain mean-variance optimisers?

They are illegal otherwise
Small changes in return estimates cause extreme weights
They are too slow
They ignore risk

Show the answer

Small changes in return estimates cause extreme weights. Estimation error gets amplified.

Go deeper

Practise this in Vestora

Look up real shares, test ideas with paper trading, and track your progress through the course.

Open the app free

General education only, not financial advice. Examples are illustrations. Rules, tax settings and products change; check official sources.