Where Risk Comes From: Component VaR, Concentration, Tail Dependence and HRP

Kuantile Guides · 27.07.2026

"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.