Every risk conversation about an alt book eventually reduces to one question, usually asked badly. How many bets is this, really. Position counts do not answer it, sector labels do not answer it, and a full correlation matrix answers it in a form nobody can hold in their head during a meeting. The variance share of the first principal component answers it in one number between zero and one, and it is the single most portable statistic I know for describing a crypto book to someone who does not trade crypto.
The construction is standard. Take daily returns across your universe, standardise them, compute the correlation matrix, take its eigenvalues, and divide the largest by the sum. That fraction is how much of the total cross-sectional variance one common factor accounts for. In equities it is a familiar diagnostic. In crypto it is more useful and less flattering, because the number is higher and moves less.
What the correlations tab supplies and what you compute
Be clear about the boundary. The Correlations tab of the altcoin scorecard prints a Cross-Asset Correlation Matrix over BTC, ETH, SOL, S&P 500, DXY and VIX. It gives you correlations. I cannot confirm that it computes or displays an eigenvalue decomposition, and there is no PC1 share anywhere on the panel. The module describes its correlations dimension as cross-asset correlation matrices and regime detection, but the specific statistic in this article is one you build on your own data.
That is not a serious obstacle, because the decomposition is a few lines of code over a return panel you already have. What the tab is genuinely useful for is a cross-check. If your pipeline's pairwise numbers for the assets shown disagree materially with the panel, one of you has a window or a data problem, and finding that out from a free display beats finding it out in a review.
The arithmetic on the numbers currently printed
You can get a usable estimate without any code at all, using the fact that a matrix with roughly equal pairwise correlations has a closed form. If N assets all correlate at rho, the largest eigenvalue is 1 plus N minus 1 times rho, and the PC1 variance share is that quantity divided by N.
The three crypto correlations on the panel are 0.882, 0.851 and 0.859. Their average is 0.864, and the spread between the highest and lowest is 0.031, which is tight enough that the equicorrelation approximation is fair here rather than lazy.
For those three assets, PC1 share works out at 1 plus 2 times 0.864, divided by 3, which is 0.909. Ninety one percent of the cross-sectional variance across BTC, ETH and SOL is one factor.
Now extend the same rho to a twenty name universe, which is closer to a real alt book. The share becomes 1 plus 19 times 0.864, divided by 20, or 0.871. Adding seventeen more assets moved the number by under four points. That is the result worth internalising. At this level of correlation, breadth does almost nothing, and the inverse of the share is the more brutal way to say it. Twenty positions at rho of 0.864 is about 1.1 independent bets.
Contrast that with what dispersion would look like. At rho of 0.5 across twenty names the share falls to 0.525, and at 0.3 it falls to 0.335. Those are different portfolios in every way that matters to a risk system, and none of them differ in position count.
Universe construction is where this measure dies
The statistic is only as honest as the set you compute it over, and there are four ways to make it say whatever you want.
Membership drift. If your universe is defined by current market capitalisation rank, you are re-selecting survivors every rebalance. Fix the membership as of the start of each window and carry delistings through as terminal observations, or your series will show spurious compression during exactly the periods when weak names died.
Return frequency. Daily and hourly returns give different answers, and crypto trades continuously while your equity comparison does not. Pick one frequency, document it, and never mix them in the same chart.
Window length. The share is an estimate from a finite sample, and a short window over few assets is noisy enough to produce moves that are entirely estimation error. A useful discipline is to compute the share on shuffled or bootstrapped returns and see how much it wobbles with no real change underneath. That noise band is what your alert threshold has to clear.
Stablecoins and wrapped assets. Leave a stablecoin in the universe and you have inserted a near zero variance row that drags the share down for no economic reason. Leave both a token and its wrapped version in and you have inserted a correlation of one, which pushes it up. Both happen in production more often than anyone admits.
Reading the series, and the two ways it misleads
The stylised behaviour is well known in factor risk work and it is what makes the series worth maintaining. The dominant eigenvalue's share rises when markets are stressed and everything moves together, and it compresses when genuine cross-sectional dispersion returns and names start trading on their own news. A rising share means your diversification is evaporating at the moment you need it. A falling share means selection is starting to pay.
Two cautions before you build a trigger on it. First, the level in crypto is high in all regimes, so a threshold imported from equity practice will read as permanent stress and tell you nothing. Calibrate to your own history or the series is useless. Second, and more subtle, the share can fall for a bad reason. A single high volatility name blowing up on idiosyncratic news will reduce the measured share while increasing your actual risk, because variance concentrated in one position is not diversification. Always read the share alongside the dispersion of individual volatilities.
Where it belongs in the risk pack
Report it as a level, a change over the quarter, and a percentile against your own history, on one line. Alongside it put the effective bet count, computed as the reciprocal of the share, because that is the version a non specialist can act on. Telling an investment committee that a twenty position book is worth about one independent bet ends an argument that a correlation heatmap will not.
It also does real work in a post mortem. When a drawdown gets reviewed, the first defensive claim is usually that the book was diversified and the market was exceptional. A PC1 share series stamped monthly settles that. If the share was already at the top of its range going in, the book was not diversified, it was concentrated in a way the position count concealed, and that is a sizing decision to own rather than a market event to blame.