預期虧損（CVaR）計算器

分類： Uncategorized
- August 31, 2026
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Calculate Expected Shortfall (Conditional Value at Risk) to better understand and manage extreme market risks beyond traditional VaR measures

組合參數

$

風險參數

Higher confidence levels capture more extreme risks
Timeframe for risk measurement

Distribution Parameters

Distribution model for returns
%
預期回報的年度標準差

Risk Metrics Results

預期虧損（CVaR）
$8,752.14
Average loss in 95% worst-case scenarios
Value at Risk (VaR)
$6,480.25
Expected Shortfall
$8,752.14
Value at Risk (VaR)
$6,480.25
Maximum loss with 95% confidence
VaR as Percentage
6.48%
Of portfolio value
ES as Percentage
8.75%
Of portfolio value
ES to VaR Ratio
1.35
Higher ratios indicate more tail risk
Maximum Loss
$15,243.62
Worst case in simulations

Return Distribution & Risk Measures

Expected Shortfall by Confidence Level

Risk Measure Comparison

信心水平 Value at Risk (VaR) Expected Shortfall (ES) ES/VaR Ratio 風險水平

Stress Test Scenarios

Market Crash Scenario

Expected Loss $28,452.10
VaR (95%) $19,564.32
Expected Shortfall $32,741.88

Based on historical market crash patterns (2008 Financial Crisis), this scenario simulates a severe market downturn with increased volatility and correlation.

Volatility Spike Scenario

Expected Loss $15,832.65
VaR (95%) $12,960.50
Expected Shortfall $17,504.28

This scenario models a sudden spike in market volatility (similar to the 2020 COVID crash) with 2x the normal volatility but without sustained directional movement.

Liquidity Crisis Scenario

Expected Loss $21,345.78
VaR (95%) $16,243.19
Expected Shortfall $24,863.42

Models the impact of a liquidity crisis where market depth decreases significantly and slippage increases, causing more severe losses than normal market conditions would suggest.

風險管理建議

Portfolio Allocation

Your Expected Shortfall is 8.75% of portfolio value, which is moderately high. Consider reducing exposure to more volatile assets or implementing tighter stop-loss levels.

Tail Risk Management

With an ES/VaR ratio of 1.35, your portfolio shows significant tail risk. Consider tail risk hedging strategies like out-of-the-money put options or volatility instruments.

分散投資策略

Based on your risk profile, consider adding negatively correlated assets to reduce overall portfolio risk without necessarily sacrificing return potential.

Risk Monitoring

Monitor ES/VaR ratio regularly. If it exceeds 1.5, it indicates that tail risk is increasing, which may require adjusting your portfolio allocation or hedging strategies.

Understanding Expected Shortfall (CVaR)

Expected Shortfall (ES), also known as Conditional Value at Risk (CVaR), measures the average loss in the worst cases of a distribution beyond the Value at Risk (VaR) threshold. While VaR tells you the maximum loss with a given confidence level, ES tells you how bad that loss could be when VaR is exceeded.

Expected Shortfall vs. VaR

  • Value at Risk (VaR): Maximum loss at a given confidence level (e.g., 95% VaR is the loss that won't be exceeded 95% of the time)
  • Expected Shortfall (ES): Average loss in the worst cases beyond the VaR threshold (e.g., 95% ES is the average loss in the worst 5% of cases)
  • Key Difference: ES accounts for the severity of the worst losses, not just their probability
  • Coherent Risk Measure: Unlike VaR, ES is a coherent risk measure that satisfies mathematical properties important for risk management

Interpreting ES/VaR Ratio

  • Ratio ≈ 1.2-1.3: Normal distribution with typical tail behavior
  • Ratio ≈ 1.3-1.5: Moderate tail risk, slightly heavier tails than normal
  • Ratio ≈ 1.5-2.0: Significant tail risk, fat-tailed distribution
  • Ratio > 2.0: Extreme tail risk, very fat-tailed distribution with potential for severe losses
  • Higher ratios indicate that when losses exceed VaR, they tend to be much larger than expected

Mathematical Definition

Expected Shortfall (ES) at confidence level α is defined as:

ESα = E[X | X > VaRα]

Where E[X | X > VaRα] denotes the expected value of the loss X, given that X exceeds the VaR at confidence level α.

Applications in Trading and Risk Management

倉位管理

Use ES to determine conservative position sizes that account for tail risk. Positions can be sized inversely to ES to maintain consistent risk exposure.

Risk Budgeting

Allocate risk across different strategies or assets based on their contribution to total ES, rather than just using standard deviation or VaR.

壓力測試

ES provides a natural framework for stress testing by focusing on the severity of tail events rather than just their probability.

Regulatory Compliance

Banking regulations like Basel III have shifted from VaR to ES as the primary risk measure for determining capital requirements.

本工具計算什麼

突破 VaR 門檻當日的平均虧損——即 VaR 所忽略的尾部風險。

公式
CVaR = 所有超出 VaR 門檻的虧損之平均值
計算示例
若最差 5% 日子的平均虧損為 32,000 港元，而 VaR 為 19,740，則 CVaR 為 32,000——出事時真正相關的數字。
何時使用
與 VaR 並用，了解最壞情況實際有多壞。
常見錯誤
CVaR 需要足夠的尾部樣本才有意義。以短期數據計算，只是估算之上的估算。