Hierarchical Risk Parity

Also seen as: HRP, hierarchical clustering allocation

How does Hierarchical Risk Parity build the tree?

The tree comes from correlation: two instruments whose returns move closely together sit on neighbouring branches, and groups of such instruments join into larger branches the less alike they are. Six utility stocks that rise and fall together form one branch; a bond fund that moves on its own sits far from them. The instruments are then reordered so that relatives are side by side, and the capital is split by halving that ordered list — first into two halves, then each half into two, and so on down to single instruments. The cut falls at the middle of the list, not necessarily where one group ends and the next begins; following the groups exactly is what Hierarchical Equal Risk Contribution does differently.

At each split the capital is divided between the two halves in inverse proportion to their variance:

where: $\sigma^2_{\text{left}}$ and $\sigma^2_{\text{right}}$ are the variances (the squared volatility) of the two halves, and $w$ is the share of that branch's capital each half receives. In words: the riskier half gets the smaller share, and the split repeats inside each half until every instrument has its weight.

Why use Hierarchical Risk Parity instead of MPT?

Because it never has to invert the covariance matrix, which is where MPT turns small estimation errors into extreme weights. With many instruments and a short history, MPT can load most of the capital onto the one instrument whose past correlation happened to look low; Hierarchical Risk Parity cannot, because it only ever compares two halves at a time. The trade-off is that its splits follow a rule rather than an optimisation, so it does not claim to find the best risk-and-return mix.

How does Fincanva handle it?

• Hierarchical Risk Parity is offered inside a single strategy only, across its instruments; a Combined does not offer it when it splits capital across strategies.
• It has no settings of its own. It reads the calculation window (In-sample, 12 months by default) and the Risk estimation choice, which decides how volatilities and correlations are measured — see Risk estimation.
• Weights are never negative: every instrument receives a share of the capital, and none is held short.
• With most risk estimates — including the recommended Ledoit-Wolf · constant correlation — every instrument must have moved in price at some point inside the window: an instrument whose price stayed flat for the whole window, such as a suspended listing, stops the backtest rather than receiving a weight. Two estimates are the exception; Risk estimation names them.
• Weights are recomputed at every rebalance from the window ending on that date.

Which plan includes Hierarchical Risk Parity?

Included from Advanced upwards. See what each plan includes.

What does it look like in practice?

A strategy holds four instruments that fall into two pairs: two equity funds that move together, and two bond funds that move together. The equity pair, held as a pair, has a volatility of 20% (variance 0.04); the bond pair has 10% (variance 0.01).

• First split, equities against bonds: the equity side receives 0.01 ÷ (0.04 + 0.01) = 20% of the capital and the bond side 80%.
• Second split, inside each pair: the same rule shares each pair's slice between its two members by their own variances. With two equity funds of equal risk, each gets 10%; with two bond funds of equal risk, each gets 40%.

The result is 10% / 10% / 40% / 40%. Compare Equal Weights, which gives each 25% and so lets the equity pair supply most of the risk, and Hierarchical Equal Risk Contribution, which splits the same tree by volatility rather than variance.