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.
Die Idee in einfachen Worten
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.
So wird gerechnet
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 ÷ σᵢAnwendung
- As a quick, stable diversifier for many tickers.
- Compare it with ERC and maximum diversification: when all three agree, the result is robust.
Schlüsse ziehen
- The ticker with the lowest average correlation gets the top rank.
- Like risk parity it is long only and keeps every ticker.
Beispiel
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.
Die Eingaben des Beispiels dienen der Veranschaulichung; die Gewichte und Zahlen sind das, was unser Optimierer dafür liefert.
Worauf man achten sollte
- A heuristic: it has no single objective you can point to.
- Rank-based weights change in steps when two tickers swap places.
Ein wenig Geschichte
David Varadi, Michael Kapler and Corey Rittel, "The Minimum Correlation Algorithm: A Practical Diversification Tool" (2012), written for practitioners who found optimisers too unstable.
Nur Bildungsinhalte. Kein Portfoliomodell kennt die Zukunft: Jedes arbeitet mit Schätzungen aus der Vergangenheit, und nichts hier ist eine Anlageberatung.