Strategy #0000000119 · Portfolio optimisation
Minimum-variance portfolio
Enter two volatilities, correlation, long-only constraint, return scenarios and costs.
A minimum-variance portfolio reduces risk using the covariance matrix without forecasting expected returns. Two-asset weights have a closed-form solution; long-only constraints can limit extreme weights and estimation error, but change the solution. Real multi-asset portfolios need robust covariance estimates, constraints and rebalancing costs. This illustration handles two assets only.
A two-asset analytical illustration; other portfolio constraints and robust covariance estimation are omitted.
Three ways in
Understand the story. Then inspect the risk.
Start with a familiar situation, check the payoff, then test how the numbers change.
The idea · in two minutes
How do two assets’ volatilities and correlation determine minimum-variance weights?
A minimum-variance portfolio reduces risk using the covariance matrix without forecasting expected returns. Two-asset weights have a closed-form solution; long-only constraints can limit extreme weights and estimation error, but change the solution. Real multi-asset portfolios need robust covariance estimates, constraints and rebalancing costs. This illustration handles two assets only.
Enter two volatilities, correlation, long-only constraint, return scenarios and costs.
A two-asset analytical illustration; other portfolio constraints and robust covariance estimation are omitted.
- Input assumptionsEnter two volatilities, correlation, long-only constraint, return scenarios and costs.
- Model outputA two-asset analytical illustration; other portfolio constraints and robust covariance estimation are omitted.
Illustrative research examples only. They are not live signals or a recommendation.
The mechanics · payoff and exposure
w_A=\frac{\sigma_B^2-\rho\sigma_A\sigma_B}{\sigma_A^2+\sigma_B^2-2\rho\sigma_A\sigma_B}
Volatility is entered in percent and ρ is correlation; assumed returns display outcomes but do not enter the optimisation.
Greeks: the directional intuition
- 模型
- Measures sensitivity to implied volatility.
- 資料
- Measures sensitivity to implied volatility.
- 執行
- Measures sensitivity to implied volatility.
w_A=\frac{\sigma_B^2-\rho\sigma_A\sigma_B}{\sigma_A^2+\sigma_B^2-2\rho\sigma_A\sigma_B}
Practical context · published observations
Minimum-variance portfolio: read the record with its caveats.
The chart uses the published figures or explicitly labelled study inputs below. A historical index or model replay is not the same as an investor’s realised account return.
A two-asset analytical illustration; other portfolio constraints and robust covariance estimation are omitted. Source ↗ · Methodology ↗
Change assumptions and inspect the scenario
Inputs illustrate the strategy mechanics; they are not live quotes, forecasts or investment advice.
Variants · same family, different risk levers
Data quality, constraints and implementation costs affect results.
Compare modelling and execution assumptions.
| Related strategy | Relationship | What changes | New cost or risk |
|---|---|---|---|
| Base scenario | Manual inputs | A minimum-variance portfolio reduces risk using the covariance matrix without forecasting expected returns. Two-asset weights have a closed-form solution; long-only constraints can limit extreme weights and estimation error, but change the solution. Real multi-asset portfolios need robust covariance estimates, constraints and rebalancing costs. This illustration handles two assets only. | A two-asset analytical illustration; other portfolio constraints and robust covariance estimation are omitted. |
| Conservative version | Lower exposure | Raise cost/risk assumptions and constrain positions. | May reduce participation. |
| Validation version | Out-of-sample test | Freeze the method before evaluation on untouched data. | Needs more clean data. |
A two-asset analytical illustration; other portfolio constraints and robust covariance estimation are omitted.
Read beyond the summary
References
Primary sources and research used to describe the strategy and its limits.