Portfolio construction
Minimum correlation algorithm
A fast heuristic that gives more weight to the tickers least correlated with the rest, then evens out their volatility.
The idea in plain words
Instead of solving an optimisation, rank the tickers by how unusual their correlations are: the more a ticker zigs when others zag, the bigger its share. Then divide by volatility so that calm tickers are not drowned out. It reaches much of the diversification of the optimisers with no fragile mathematics.
How it is calculated
1) Standardise each pairwise correlation against the average of all of them and turn it into a score with the normal distribution (low correlation → high score). 2) Rank the tickers by their average score; the ranks are starting weights. 3) Spread those weights through the score matrix, normalise. 4) Divide by each ticker's volatility and normalise again.
aᵢⱼ = 1 − Φ((ρᵢⱼ − ρ̄) ÷ s_ρ)
w₀ ∝ rank(mean_j aᵢⱼ)
w₁ ∝ w₀ᵀA
wᵢ ∝ w₁ᵢ ÷ σᵢHow to use it
- As a quick, stable diversifier for many tickers.
- Compare it with ERC and maximum diversification: when all three agree, the result is robust.
Drawing conclusions
- The ticker with the lowest average correlation gets the top rank.
- Like risk parity it is long only and keeps every ticker.
Example
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). Weights 20% US500, 17% GER40, 21% gold, 42% EURUSD. Return 4.7%, volatility 8.9%: between risk parity and ERC, with slightly more in the indices than ERC.
The example's inputs are illustrative; the weights and figures are what our optimiser returns for them.
Watch out for
- A heuristic: it has no single objective you can point to.
- Rank-based weights change in steps when two tickers swap places.
A little history
David Varadi, Michael Kapler and Corey Rittel, "The Minimum Correlation Algorithm: A Practical Diversification Tool" (2012), written for practitioners who found optimisers too unstable.
Educational content only. No portfolio model knows the future: every one of them works on estimates from the past, and nothing here is investment advice.