Portfolio Inputs

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Total portfolio market value
Asset Allocations
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Correlation Matrix
Ryan O'Connell, CFA
Calculator by Ryan O'Connell, CFA

Portfolio Risk Summary

Portfolio VaR (Annual) $1,922,825 19.23% of portfolio
Portfolio Volatility 8.27%
Undiversified VaR $2,419,352
Diversification Benefit $496,527

Component VaR Breakdown

Asset Component VaR % of Total Budget Utilization
Asset 1 $1,317,157 68.5% $600,000 219.5%
Asset 2 $227,407 11.8% $200,000 113.7%
Asset 3 $378,261 19.7% $300,000 126.1%
Total $1,922,825 100% $1,100,000 174.8%

Risk Allocation Charts

Component VaR vs Budget
VaR Contribution (%)
Model Assumptions
  • Annual volatility inputs - VaR is expressed as annual
  • Normal distribution assumed for asset returns
  • Component VaRs sum exactly to total Portfolio VaR (Euler decomposition property)
  • Single-period analysis - correlations and weights assumed constant
  • Risk budgets are in dollar terms for the same confidence level and horizon

For educational purposes only. Not financial advice.

Understanding Risk Budgeting

What is Risk Budgeting?

Risk budgeting is a portfolio management technique that allocates risk (rather than capital) across different assets or strategies. Instead of asking "how much money should I put in each asset?", risk budgeting asks "how much risk should each asset contribute to the portfolio?"

Component VaR Formula
Component VaRi = wi x betai x Portfolio VaR
where betai = Cov(Ri, Rp) / Var(Rp)

Component VaR vs Individual VaR

Component VaR

Risk contribution in context
Measures how much each asset contributes to total portfolio VaR, accounting for diversification. Sum of all component VaRs = Portfolio VaR.

Individual VaR

Standalone risk
Measures each asset's risk in isolation, ignoring correlations. Sum of individual VaRs is higher than Portfolio VaR (the gap is the diversification benefit).

The Diversification Benefit

The diversification benefit represents the risk reduction achieved by combining assets that are not perfectly correlated. It equals the sum of individual (standalone) VaRs minus the actual portfolio VaR:

  • Higher diversification benefit: Assets have low or negative correlations - combining them reduces overall risk significantly
  • Lower diversification benefit: Assets have high correlations - combining them provides less risk reduction
  • Zero diversification benefit: All correlations equal 1 - no diversification effect at all
Key Insight: Risk budgeting allows risk managers to set limits on how much risk each asset or strategy can contribute, ensuring that no single position dominates the portfolio's risk profile.
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Frequently Asked Questions

Individual VaR measures an asset's standalone risk without considering correlations with other assets. Component VaR measures the asset's contribution to total portfolio risk, accounting for diversification effects. The sum of component VaRs equals total portfolio VaR exactly, while the sum of individual VaRs is typically higher. The difference between these sums is the diversification benefit.

This is a mathematical property called Euler's theorem for homogeneous functions. Portfolio VaR is homogeneous of degree 1 in the weights, meaning if you scale all weights by a factor k, the VaR scales by k. Euler's theorem guarantees that the weighted sum of partial derivatives (which defines component VaR) equals the total function value. This property makes component VaR the only valid way to decompose portfolio risk.

Utilization above 100% means the asset's actual risk contribution (Component VaR) exceeds its allocated risk budget. This signals the asset is consuming more than its "fair share" of portfolio risk. Risk managers may need to reduce the position, implement hedges, or reallocate the risk budget. Consistently over-budget positions may indicate that the risk budget was set too low or that market conditions have changed.

Lower correlations increase diversification benefit and reduce total portfolio VaR. However, the effect on individual component VaRs is more nuanced - some may decrease while others increase depending on the specific correlation structure. Higher correlations (approaching 1) reduce diversification benefit, increasing portfolio VaR and typically pushing all assets closer to their individual (undiversified) VaR contributions.
Disclaimer

This calculator is for educational purposes only and assumes normally distributed returns with constant correlations. Actual risk budgeting involves additional factors like fat tails, changing correlations during market stress, and liquidity constraints. This tool should not be used for actual investment decisions without professional risk management oversight.

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Course by Ryan O'Connell, CFA, FRM

Value at Risk (VaR) Course

Master Value at Risk from theory to practice. Covers parametric, historical, and Monte Carlo VaR methods with hands-on Excel implementations.

  • Parametric, Historical, and Monte Carlo VaR
  • Marginal, Component, and Incremental VaR
  • Backtesting and stress testing techniques
  • Real-world risk management applications
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