投資組合配置優化工具

分類： Uncategorized
- August 31, 2026
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Optimize your investment portfolio allocation based on Modern Portfolio Theory (MPT). Balance risk and return by finding the optimal asset weights for maximum Sharpe ratio or minimum volatility.

Portfolio Assets

Asset
Expected Return (%)
Volatility (%)
Action
%
%
%
%

相關性矩陣

Enter the correlation coefficients between assets (values between -1 and 1).

S&P 500
US Bonds
S&P 500
1.00
US Bonds
1.00

Optimization Parameters

%
一般採用相同年期的國債孳息率

Portfolio Tools

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Presets Library

Load common asset allocation models to start your optimization.

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Import/Export Data

Save your work or import data from external sources.

Modern Portfolio Theory & Efficient Frontier

Modern Portfolio Theory (MPT) is a mathematical framework for constructing a portfolio of assets such that the expected return is maximized for a given level of risk. It was pioneered by Harry Markowitz in 1952 and is centered on the concept that an investment's risk and return should not be assessed by itself, but by how it affects the portfolio's overall risk and return.

主要概念

  • Efficient Frontier: The set of optimal portfolios that offer the highest expected return for a defined level of risk.
  • Sharpe Ratio: A measure of risk-adjusted return, calculated as (portfolio return - risk-free rate) / portfolio standard deviation.
  • 分散程度： Combining assets with different return patterns to reduce overall portfolio risk.
  • Correlation: How assets move in relation to each other. Lower correlation increases diversification benefits.

Optimization Goals

  • Maximize Sharpe Ratio: Find the portfolio with the highest risk-adjusted return.
  • Minimize Volatility: Construct the lowest-risk portfolio possible.
  • Maximize Return: Find the highest return portfolio (usually results in a single-asset portfolio).
  • Target Return: Construct the lowest-risk portfolio for a specified return.
  • Target Risk: Construct the highest-return portfolio for a specified risk level.

主要公式

Portfolio Return
E(Rp) = ∑ wi × E(Ri)

The weighted sum of individual asset returns, where wi is the weight of asset i and E(Ri) is its expected return.

Portfolio Variance
σp2 = ∑∑ wiwjσiσjρij

Where wi and wj are the weights, σi and σj are the volatilities, and ρij is the correlation between assets i and j.

夏普比率
Sp = (E(Rp) - Rf) / σp

The excess return (over the risk-free rate Rf) per unit of risk (standard deviation σp).

Diversification Ratio
DR = σp(weighted) / σp

Measures diversification benefit as the ratio of weighted average of individual asset volatilities to actual portfolio volatility.

Limitations of MPT

  • Assumes Normal Distribution: Returns may not follow a normal distribution, especially during market stress.
  • Historical Inputs: Optimization relies on historical data that may not predict future performance.
  • Constant Correlations: Asset correlations tend to increase during market crises.
  • Single-Period Model: MPT optimizes for a single time horizon and doesn't account for changing market conditions.

Despite these limitations, MPT remains a fundamental framework for portfolio construction and risk management.

本工具計算什麼

在既定風險水平下，尋求最佳回報的資產配置比重。

公式
組合方差 = ΣΣ wᵢwⱼσᵢσⱼρᵢⱼ，在權重總和為 1 的條件下求最小值
計算示例
兩項資產波幅各 20%、相關系數 0.3，各佔一半，組合波幅約 16.1%，低於任何單一資產。
何時使用
決定資金如何在多個持倉之間分配，而非逐一考慮。
常見錯誤
結果的質素完全取決於輸入的相關性與回報估算，而兩者皆源自未必重演的過去。