The part of a portfolio's total volatility that comes from one holding. It depends on the holding's weight, its own volatility and how it moves with the other holdings.
Risk contribution measures how much of a portfolio's Volatility comes from each holding. The contributions of all holdings add up to the volatility of the whole portfolio, so each one can also be shown as a percentage: the holding's risk share.
A holding's risk share is often different from its value share. A stock that is 10% of the money can carry 20% of the risk when it moves more than the other holdings, or when it moves with them. A stock that moves against the rest of the portfolio can carry less risk than its weight, and its contribution can even be negative.
The calculation follows from Euler's theorem. Portfolio volatility is σ = √(wᵀΣw), where w holds the weights and Σ is the covariance matrix of the returns. The contribution of holding i is wᵢ × (Σw)ᵢ / σ. The marginal contribution, (Σw)ᵢ / σ, shows how much the portfolio volatility changes for a small change in that weight.
For an Indian investor, risk contribution makes Diversification visible. A book of five private banks can look spread across five names, but the five stocks move together, so a large part of the risk comes from one sector. A gold or debt holding with a low correlation to equity often carries a much smaller risk share than value share.
Risk contribution describes the past. It is measured over a window of daily returns, and a different window gives different shares. It does not say which holding to buy or sell.
Formula
Contribution of holding i = wᵢ × (Σw)ᵢ / σ, where σ = √(wᵀΣw); risk share = contribution / σIndia Context
Artha shows each holding's risk share beside its value share in the portfolio holdings table and in Deep Analysis, over the past year of daily NSE/BSE prices and AMFI NAVs.