Kuantile
Where Risk Comes From: Component VaR, Concentration, Tail Dependence and HRP
"Your portfolio VaR is 3.2%" does not translate into action. "ASELS is 15% of your money but 41% of your risk" does. Kuantile's risk attribution and concentration cards break the single risk figure into parts and show what each position really carries.
Component VaR: risk with an address
The Euler decomposition splits total VaR across positions so that the parts sum exactly to the total — nothing is left over, nothing is double-counted. Each position's share comes from its own volatility and its correlation with the rest: a small but volatile position that moves with the portfolio can carry more risk than a large, quiet one. The table shows money share next to risk share; when risk share is clearly higher, that position is the true source of your risk.
Incremental VaR: "what if I close it?"
This is usually the question investors actually ask. Incremental VaR computes how VaR changes if you close a position entirely and spread the money across the rest. Negative means less risk; near zero means the position sits in your portfolio almost for free thanks to diversification.
Concentration: how many independent bets?
Owning twenty stocks does not mean making twenty independent decisions — if they all watch the same index, the same currency and the same interest rate, you effectively hold one or two bets. Three measures quantify this:
- HHI and effective positions: the sum of squared weights. Four equal-weighted assets give HHI 0.25 and 4 effective positions; put half your money in one asset and the effective count collapses.
- Diversification ratio: the weighted sum of individual volatilities divided by portfolio volatility. Near 1, diversification is doing nothing; the higher it goes, the harder correlations work for you.
- Effective independent bets (PCA): an entropy measure derived from the eigenvalues of the correlation matrix. "You own 20 assets but effectively hold 2.8 independent bets" comes from here — the number that stops everyone who thinks they are diversified.
Tail dependence: crisis-day correlation
Pearson correlation describes average days; in a crisis, correlations "break" and assets that looked unrelated crash together. Empirical tail dependence (λ) measures this directly: how often two assets land in their own worst 5% on the same day. Independent assets give ~0.05; a pair showing 0.4-0.5 behaves like a single asset on crisis days. For the BIST-crypto-FX triangle, this metric confirms with daily data what stress tests suggest with scenarios.
HRP: allocation without inverting the covariance matrix
Classical mean-variance optimization inverts the covariance matrix; when the matrix is noisy (and with 250 observations and 30 assets it always is), the output is extreme, fragile weights. López de Prado's Hierarchical Risk Parity never inverts: it clusters assets by correlation distance, then splits the risk budget recursively down the cluster tree. The HRP weights Kuantile shows are a reference frame: large gaps between them and your current weights reveal where you are taking deliberate bets — or concentrating without noticing. A suggestion, not advice.
Weight ≠ risk contribution
Your portfolio pie shows how many dollars you hold in an asset; it does not show how much that asset contributes to risk. A volatile asset can produce a large share of risk even at a small weight. Component VaR makes exactly this distinction: it measures each asset's contribution to total portfolio VaR, accounting for correlations. Summed together it equals the entire portfolio VaR — a true breakdown of your risk budget.
How to read component VaR
Kuantile computes this with an Euler decomposition and a noise-reducing Ledoit-Wolf covariance estimate. If an asset's risk contribution is markedly larger than its weight, that position is your portfolio's "risk engine"; if smaller, it is providing diversification; it can even be negative — a buffer that lowers overall risk (often gold or negatively correlated assets). This table is a direct answer to "where do I cut to reduce my risk the most?"
Measuring concentration
Concentration is risk piling into a few positions, and it is the hidden enemy of diversification. Even a 20-asset portfolio is concentrated if 70% of its risk comes from two positions. That means one asset's bad day can drag the whole portfolio down. Kuantile makes this concentration visible by looking at the distribution of risk contributions; experienced investors look not at the count but at how evenly the risk is spread.
See where your risk comes from →