Portfolio construction
Hierarchical risk parity (HRP)
Groups the tickers into a family tree by correlation and splits the money down the tree, so similar tickers share their risk budget.
用通俗的话解释
Optimisers that invert the covariance matrix become unstable when tickers are highly correlated. HRP never inverts it. It first clusters the tickers (indices with indices, currencies with currencies), orders them so that similar ones sit together, and then divides the money between the two halves of the tree by their risk, again and again down to single tickers.
计算方法
1) Distance between tickers dᵢⱼ = √((1 − ρᵢⱼ) ÷ 2); single-linkage clustering builds the tree. 2) The tree gives an order with similar tickers side by side. 3) Recursive bisection: split the ordered list in two, measure each half's variance with inverse-variance weights inside it, give each half money in inverse proportion to its variance, repeat inside each half.
dᵢⱼ = √((1 − ρᵢⱼ) ÷ 2)
V(half) = w̃ᵀ Σ_half w̃, w̃ ∝ 1 ÷ diag(Σ_half)
α = 1 − V_left ÷ (V_left + V_right); left × α, right × (1 − α)如何使用
- With many tickers, or groups of similar ones (several indices, several currency pairs).
- When other models give unstable weights from one study to the next.
- It is long only and needs no expected returns.
得出结论
- Tickers that cluster together share one budget, so adding a third stock index takes money from the other indices, not from gold.
- The order in the study's notes shows how it grouped the tickers.
示例
Running example (used in every portfolio guide): US500, GER40, gold (XAUUSD) and EURUSD, two years of daily data. Expected returns 8%, 7%, 7% and 1% a year; volatilities 18%, 20%, 15% and 7%. US500 and GER40 move together (correlation about 0.7); gold hardly moves with the indices (about 0.04). HRP orders the tickers US500, GER40 | gold, EURUSD and splits the money between the two pairs by risk: 8% US500, 6% GER40, 15% gold, 70% EURUSD. Return 2.9%, volatility 7.1%. It is more defensive than ERC here because the indices' pair, measured as a block, is very volatile.
示例的输入仅作说明；权重和数据是我们的优化器针对这些输入给出的结果。
注意事项
- Results depend on how the tree splits; with few tickers it can be lopsided.
- It ignores expected returns entirely.
一点历史
Marcos López de Prado, "Building Diversified Portfolios that Outperform Out of Sample" (Journal of Portfolio Management, 2016). It brought machine-learning style clustering into portfolio construction.
仅供学习参考。 没有任何投资组合模型知道未来：每一个都基于对过去的估计，本页内容均不构成投资建议。