相關性及協方差矩陣工具

分類： Uncategorized
- August 31, 2026
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Analyze relationships between multiple assets to optimize portfolio diversification and understand risk factors

Input Data

Asset Returns

Analysis Options

Correlation (-1 to 1) or Covariance
Linear vs Rank-based correlation
How to visualize relationships
Data period to include in calculations

Correlation & Covariance Results

相關性矩陣

-1.0 0 +1.0

Key Insights

Strongest Correlations

  • S&P 500 — Nasdaq: 0.89
  • EUR/USD — GBP/USD: 0.78
  • Gold — US 10Y Treasury: 0.72

Weakest Correlations

  • S&P 500 — Gold: -0.45
  • US Dollar — EUR/USD: -0.82
  • VIX — S&P 500: -0.76

Asset Clusters

Equity Markets
S&P 500, Nasdaq, Dow Jones
Safe Havens
Gold, US 10Y Treasury, Japanese Yen

Diversification Opportunities

Assets with low correlation to your portfolio can provide diversification benefits. Consider adding 黃金 or US 10Y Treasury to a portfolio heavy in equities, as they show negative to low correlation with stock indices.

Understanding Correlation & Covariance

Correlation and covariance measure the relationship between different assets, helping traders and investors understand how prices move together. These metrics are essential for portfolio construction, risk management, and identifying trading opportunities.

Correlation Basics

  • Range: Correlation coefficients range from -1.0 to +1.0
  • Positive Correlation: Assets tend to move in the same direction
  • Negative Correlation: Assets tend to move in opposite directions
  • Zero Correlation: No linear relationship between asset movements
  • Perfect Correlation (±1.0): Exact linear relationship between returns

Covariance Explained

  • Measurement: Covariance measures how two variables change together
  • Units: Expressed in units that are the product of the two variables
  • Interpretation: Positive values indicate variables move together; negative values indicate opposite movement
  • Limitation: Scale-dependent and harder to interpret than correlation
  • Relationship: Correlation = Covariance / (Standard Deviation of X × Standard Deviation of Y)

Mathematical Definitions

Correlation Formula
ρX,Y = Cov(X,Y) / (σX × σY)

Where ρX,Y is the correlation coefficient, Cov(X,Y) is the covariance, and σX and σY are the standard deviations of X and Y.

Covariance Formula
Cov(X,Y) = E[(X - μX)(Y - μY)]

Where E is the expected value operator, μX and μY are the means of X and Y.

Applications in Trading and Investing

Portfolio Diversification

Combining assets with low or negative correlations can reduce overall portfolio risk without sacrificing expected returns.

Pairs Trading

Identifying highly correlated securities that temporarily diverge can create mean-reversion trading opportunities.

Hedging Strategies

Understanding correlations helps identify effective hedges to protect against specific risks in your portfolio.

Market Regime Analysis

Changes in correlation patterns can signal shifts in market regimes and macroeconomic conditions.

本工具計算什麼

衡量一組工具之間的同步走勢程度。

公式
相關系數 = 協方差(x, y) ÷（σx × σy），數值介乎 −1 至 +1
計算示例
EUR/USD 與 GBP/USD 的相關系數常在 +0.8 左右。同時持有兩者，實際更接近一個大倉位而非兩個獨立倉位。
何時使用
加倉前檢查，確認是在分散風險而非重複押注。
常見錯誤
相關性並不穩定。危機時原本走勢各異的資產往往同步下跌，而那正是最需要分散的時候。