A correlation cell gives you one number per pair, and that number is an average over every kind of day in the sample. Quiet Tuesdays where nothing happened, grinding rallies, and the four or five sessions in the period where everything fell at once are all in there together, weighted the same.
That is a problem, because the days you own diversification for are not average days. You hold two things instead of one so that when the first falls the second does something else. The coefficient on the panel cannot tell you whether that is true, because it has already mixed the falling days back in with the rest.
The fix is to compute the correlation twice, once on days the market rose and once on days it fell, and compare. It is a spreadsheet job and it takes twenty minutes. The part almost everyone gets wrong is the comparison, and getting it wrong produces a confident conclusion that is entirely an artefact of the arithmetic.
What one coefficient hides
At the time of writing the Cross-Asset Correlation Matrix was on its MONTHLY window with 500 periods analyzed, and the populated cells sat in the recession-model block. M6 (LEI) against M7 (Combined) read 0.88, M1 (BC Labs) against M7 read 0.80, and the S&P 500 row read 0.30, 0.45 and 0.46 against those three models.
Each of those is a single blended number. The panel is not hiding anything from you, it is doing exactly what a correlation matrix does. But a reading of 0.45 is consistent with a pair that sits at 0.45 in every state of the world, and equally consistent with a pair that runs at 0.30 on the way up and 0.65 on the way down. Those are very different things to own and the cell cannot distinguish them.
Building the split in a spreadsheet
Pull daily closes for both assets over the same dates. Compute daily percentage returns for each. Then add one column that flags whether the first asset, or a market benchmark if you prefer to condition on the market, closed down that day.
Now compute the correlation of the two return columns twice. Once filtered to the down-flagged rows and once to the up-flagged rows. Two numbers. That is the whole calculation, and any spreadsheet does it with a correlation function and a filter.
The temptation at this point is to compare the down-day number against the full-sample coefficient and declare that correlation rises in drawdowns. Do not do that. It will be true almost every time you check, and it will be true for pairs that have no asymmetry in them whatsoever.
The benchmark that stops you fooling yourself
Here is the thing that changed how I read these splits. I generated two return series with a true correlation of exactly 0.50, symmetric, no asymmetry built in at all, four million paired observations. Then I kept only the days where both series fell and measured the correlation on that subset.
It came back at 0.27, not 0.50. Filtering to the down days on the up days gave 0.27 as well. The subsample correlation is roughly half the true one, in both directions, purely because filtering on the returns themselves throws away part of the variation the coefficient is computed from.
Push the filter further out and it falls further. Keeping only days the first series fell more than one standard deviation gave 0.25, and beyond one and a half standard deviations, 0.22. The pattern is the opposite of the intuition. Under a plain symmetric relationship, conditioning on bad days makes the measured correlation go down, not up.
So the correct comparison is never the down-day number against the full-sample number. It is the down-day number against the up-day number, on the same filter, with the same number of observations. If your pair reads 0.27 down and 0.27 up, you have found nothing, however far both sit below the headline cell. If it reads 0.55 down and 0.27 up, you have found real asymmetry, and it is worth more than the headline coefficient ever was.
How much of this is just a small sample
The other honest constraint is that you are now estimating from a fraction of your data, and correlation estimates on small samples are far less precise than they look printed to two decimals.
In a year of daily data there are around 250 observations. Roughly a third of days will have both assets falling, which leaves about 83 rows in the down bucket. A correlation of 0.50 measured on 83 observations carries a 95 percent range of roughly 0.32 to 0.65. On the same 83 rows a reading of 0.27 ranges from about 0.06 to 0.46.
Those two ranges overlap heavily. Which means a single year of data comparing 0.55 down against 0.27 up is suggestive and nothing more. Two or three years gets you to where the difference is worth acting on. Anyone showing you a down-day correlation from a few months of data and calling it a regime is showing you noise.
What to actually do with an asymmetric pair
Assume you have run this over a few years and found a real gap. The practical response is not to sell the position. It is to stop counting it as diversification and to size the pair off the down-day number instead of the blended one.
On a $10,000 pair split evenly between two holdings that each swing about 20 percent a year, believing 0.30 puts your two standard deviation year at roughly $3,225 of movement. Believing 0.85 puts it at about $3,847. The pair does not care what you believed. Sizing off the wrong half of the split means the position is about 20 percent larger than you intended precisely on the days it hurts.
The second thing worth doing is checking whether your hedge is a hedge. The pairs where this test matters most are the ones you hold specifically for protection, because a hedge whose correlation to the thing it hedges goes positive in a fall is not doing the job it was bought for, and the blended coefficient will keep telling you it is fine right up until the week it matters.
Run the split on your two largest positions and on anything you describe to yourself as a hedge. Four pairs, an afternoon, and you will know which of your diversification stories survives contact with the down days.