Risk parity allocates by risk contribution rather than by rupees. Each holding’s marginal contribution to portfolio volatility is calculated, and weights are solved so those contributions are equal.
The risk contribution of position i is:
RC_i = w_i * (Σ w)_i / σ_p
where Σ is the covariance matrix, w the weight vector and σ_p the portfolio volatility. Risk parity finds the w that makes every RC_i equal to σ_p / N. Unlike equal weight or inverse volatility, there is no closed form; the weights come from an optimiser.
The difference from inverse volatility is correlation. Inverse volatility uses only the diagonal of the covariance matrix and treats every pair of stocks as independent. Risk parity sees that HDFCBANK and ICICIBANK move together and cuts the combined banking allocation accordingly. When all pairwise correlations happen to be identical, the two schemes give the same answer.
Illustrative allocation
A three-asset portfolio where two holdings are correlated and one is not.
| Holding | Volatility | Correlation with peer | Inverse-vol weight | Risk-parity weight |
|---|---|---|---|---|
| Bank A | 25% | 0.85 | 30% | 22% |
| Bank B | 25% | 0.85 | 30% | 22% |
| Pharma | 19% | 0.10 | 40% | 56% |
Illustrative arithmetic. The correlated pair is treated as closer to one risk source, so the uncorrelated holding absorbs the difference.
The covariance estimate is the weak point
A portfolio of N stocks needs N (N + 1) / 2 covariance parameters. For a 100-stock universe that is 5,050 numbers estimated from a few hundred daily observations each. The estimate is noisy, and optimisers amplify noise: a spuriously low correlation looks like free diversification, so the optimiser leans into it.
Shrinkage is the standard defence. Ledoit and Wolf (2004) showed that blending the sample covariance matrix toward a structured target materially improves out-of-sample behaviour. Hierarchical risk parity, introduced by Lopez de Prado in 2016, sidesteps matrix inversion entirely by clustering assets first and allocating down the tree.
Honest caveats
Correlations are unstable and rise in crashes, which is when diversification is supposed to pay. During March 2020 nearly everything on the NSE fell together, and a risk-parity book calibrated on calm-period correlations was more concentrated in practice than it looked on paper.
Equalising risk contribution also loads the portfolio into whatever was recently quiet, which pushes weight toward low-beta and defensive names. That is a factor bet, and it should be a deliberate one. Institutional risk-parity funds add leverage to lift expected return back up; a long-only retail portfolio cannot, so accept the lower volatility and the lower expected return together.