Track 14 of 25

Correlation and diversification

Why diversification is measured in correlation rather than in count, and why correlations converge in a drawdown so a portfolio that looked diversified in calm markets stops being diversified when it matters.

25 lessons

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Why a count of holdings measures nothing on its ownTwo portfolios of twelve names can carry 13.3 percent volatility and 24.8 percent, and the statement looks the same.6 min
What a correlation coefficient is, computedThe number is a ratio of three sums, and in an eight-month sample one month can move it by fifteen points.7 min
How correlation enters a portfolio's variancePortfolio risk is a grid of pairs, and in a twenty-three holding portfolio 95.65 percent of the grid is pairs of different things.6 min
Two assets, one formula: the variance of a pairTwo of the three terms do not move when correlation moves, which is why the third one decides the whole answer.7 min
Why a second holding at 0.9 changes almost nothingA second position at 0.9 delivers eleven percent of the risk reduction the same position at 0.2 would have delivered.6 min
The effective number of independent betsOne division turns a count and a correlation into the number of separate positions a portfolio actually behaves like.7 min
Why forty holdings can behave like threeThe ceiling on independent bets is one divided by the average correlation, and the ceiling does not move when the count does.6 min
Covariance and correlation, and which one the arithmetic usesThe formula runs on covariance, the number a person can interpret is correlation, and between them sit two volatilities.6 min
What a correlation matrix is, and what it takes to estimate oneTwenty-three holdings need 253 pairwise numbers, and five years of monthly data supplies five observations for each.7 min
Why a matrix estimated in a calm market misleadsThe same nine holdings carried 15.41 percent volatility on one window's matrix and 23.45 percent on another's.6 min
Estimation windows, and the correlation you happen to measureTwo six-month halves each measured about 0.22, and the twelve months containing both measured 0.91.7 min
Rolling correlation, and what it reveals about regimesA six-month window read 0.20, then 0.87, then 0.23, on twelve months in which neither holding changed.7 min
Why correlations converge in a drawdownFifty ordinary months measured 0.29, ten drawdown months measured 0.76, and the sixty containing both measured 0.60.7 min
The mechanism: one common factor dominating everything elseRaise the shared driver's volatility and every pairwise correlation rises, with nothing whatever happening at any company.6 min
Correlation asymmetry: rising markets against falling onesEighteen up months measured about zero and eleven sharply down months measured 0.70, and the sign of the return was not the cause.7 min
Downside correlation, measured on its ownA 0.76 estimated on ten months has an interval running from 0.25 to 0.94, and the two ends differ by a factor of two in bets.7 min
Diversification measured in the tail rather than on averageThirty-six percent of a portfolio's measured risk reduction survives into the window where it is being relied on.6 min
Why the benefit is smallest exactly when it is needed mostAn advance rate prices an ordinary day's diversification, and $402,246 of one line's collateral rested on diversification absent at the call.8 min
What a factor is, and why it explains more than a sector labelTwo holdings in different industries correlated 0.31 because one shared exposure ran through both of them.7 min
Cross-asset correlation, and the sign flip that surprises peopleA 70/30 mix carried 11.48 percent volatility at one correlation and 12.99 percent at another, on identical holdings and weights.7 min
Why a hedge and a holding can correlate positively at the worst momentThe same pairing carried 25.89 percent volatility at minus 0.55 and 30.60 percent at plus 0.30, and one funding event does it.7 min
Correlation is not causation, and it is also not stabilityOne unchanged 0.62 sat above two covariances five times apart, and it is covariance the variance formula consumes.6 min
Joint-distribution modelling, conceptually, and what it was used forTwo holdings both falling past two standard deviations is a 1-in-509-month event at 0.29 and a 1-in-99-month event at 0.81.7 min
Why a lender's grouping rule is a crude correlation modelRounding every entry to zero or one produces a model that cannot be fooled by a calm window, at the cost of never being right.7 min
One portfolio, two correlation regimes, one number that changed$953,600 of unused capacity became a $28,500 deficit, and the only input that moved was an average of twenty-one estimates.7 min

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