Strategy #0000000025 · Portfolio construction and allocation
Mean-variance portfolio optimisation
Change expected return, volatility, weight and risk aversion to recalculate the objective.
Mean-variance portfolio optimisation converts defined inputs into a rule or allocation. Its scenario illustrates the arithmetic, not validated excess returns.
The objective follows assumed inputs; it is not a return forecast.
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
Mean-variance portfolio optimisation
Rose frames allocation with expected returns, volatility and covariance. Diversification comes from co-movement, not the number of holdings; equal expected returns can still produce different weights when correlations differ.
They find that both μ and Σ must be estimated, and an optimiser can magnify small errors. Jack shrinks expected returns, caps positions and turnover, and includes costs in the objective.
Weights depend on the window, shrinkage, constraints and risk aversion. A rolling out-of-sample evaluation is needed; the same data should not estimate inputs and report performance.
- Assumed expected returnAssumed expected return: assumed scenario 5; no historical observation is implied.
- Risk penalty at default weightRisk penalty at default weight: assumed scenario 3.75; no historical observation is implied.
- Illustrative objective after costIllustrative objective after cost: assumed scenario 3.65; no historical observation is implied.
Illustrative research examples only. They are not live signals or a recommendation.
The mechanics · payoff and exposure
Change expected return, volatility, weight and risk aversion to recalculate the objective.
w denotes asset weights, μ expected returns, Σ the return covariance matrix and λ risk aversion. TC represents turnover costs relative to prior weights w₀. Long-only, leverage, sector and position constraints can be added.
Greeks: the directional intuition
- Input quality
- Measures sensitivity to implied volatility.
- Constraints
- Measures sensitivity to implied volatility.
- Execution
- Measures sensitivity to implied volatility.
- Validation
- Measures sensitivity to implied volatility.
Change expected return, volatility, weight and risk aversion to recalculate the objective.
Practical context · published observations
Mean-variance portfolio optimisation: 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.
互動工具計算單資產的簡化效用尺度，不是最佳化器或歷史回測。真實配置要使用點時估計、完整協方差、約束、交易成本和樣本外檢查；小幅輸入誤差可能造成大幅權重變化。 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
Model settings and execution rules change the result.
These methods share a broad idea, but their estimates and trading assumptions are not interchangeable.
| Related strategy | Relationship | What changes | New cost or risk |
|---|---|---|---|
| Global minimum variance | Covariance-only allocation | Minimises estimated portfolio variance. | Can concentrate in assets with understated volatility. |
| Tangency portfolio | Risk-free benchmark | Maximises estimated Sharpe ratio. | Highly sensitive to expected-return errors. |
| Black–Litterman | Views plus equilibrium prior | Combines market-implied returns with investor views. | Results depend on prior and view-confidence choices. |
| Constrained optimisation | Practical portfolio limits | Adds leverage, sector, turnover or position bounds. | Constraints can bind and shift exposures materially. |
The interactive tool calculates a simplified single-asset utility, not an optimiser or backtest. Real allocation needs point-in-time estimates, full covariance, constraints, costs and out-of-sample checks; small input errors can cause large weight changes.
Read beyond the summary
References
Primary sources and research used to describe the strategy and its limits.