Only 27.6 per cent of a reported diversification benefit survives a crisis. Four credit sleeves would run at 6.650 per cent volatility in perfect lockstep. Fed the reported correlation matrix, the model returns 5.883 per cent, a benefit of 0.767 of a point and an 11.5 per cent reduction. Re-estimate the same matrix on stressed periods and volatility rises to 6.439 per cent. The ceiling never moves. Value at risk goes from 7,242,456 to 7,925,849 with no position traded.
What four asset classes are worth in points of volatility
Halverton is an open-ended credit fund with 840,000,000 of net assets held in four sleeves: investment-grade credit, high yield, leveraged loans and structured credit. The monthly report calls that four asset classes, and the sentence is true. The question a risk report should answer is narrower. What is the diversification worth, in points of volatility, on the days it is needed?
Start with the portfolio that has no diversification at all. Weight each sleeve's volatility and add the results. That is what the fund would run if every sleeve moved in perfect lockstep with every other.
Sleeve
Weight
Volatility, per cent
Contribution
Investment-grade credit
0.30
4.5
1.35
High yield
0.35
8.0
2.80
Leveraged loans
0.25
6.0
1.50
Structured credit
0.10
10.0
1.00
Undiversified ceiling
1.00
—
6.650
6.650 per cent is the ceiling. Fed the fund's estimated correlation matrix, whose off-diagonal entries lie between 0.45 and 0.80, the model returns a portfolio volatility of 5.883 per cent. The difference is 0.767 of a point, an 11.5 per cent reduction against the undiversified ceiling. That figure is the entire economic content of the four-sleeve structure. It is not a reduction in the chance of loss and it is not protection against any particular event. It is a statement that the dispersion of outcomes around the fund's central expectation is 11.5 per cent narrower than it would be if the four sleeves were one.
The same positions, re-estimated on the months that hurt
The correlations that produced 5.883 per cent were estimated over a full history: good months, bad months, and the great majority of months in which nothing happened. Re-estimate them using only the periods when credit was under pressure and every pairing tightens.
Sleeve pair
Reported
Crisis
Investment grade — high yield
0.75
0.92
Investment grade — loans
0.65
0.88
Investment grade — structured
0.45
0.82
High yield — loans
0.80
0.95
High yield — structured
0.70
0.90
Loans — structured
0.60
0.86
A range of 0.45 to 0.80 becomes a range of 0.82 to 0.95. Nothing has been bought or sold; the positions are identical and only the regime is different. Run the same variance calculation on the second column and portfolio volatility rises from 5.883 to 6.439 per cent. One-day value at risk at 99 per cent rises from 7,242,456 to 7,925,849, a factor of 1.094.
Now look at what that does to the 0.767 of a point. The ceiling is unchanged at 6.650, because the ceiling is a property of the components, not of their relationship. The realised benefit falls to a little over two tenths of a point. Only 27.6 per cent of the reported diversification benefit survives.
The diversification did not fail by half. It failed by nearly three quarters, and it failed on the days it was the only thing standing between the fund and its ceiling. In the calm months, when it was worth 0.767 of a point, nobody needed it.
Four labels, one factor
The reason is structural rather than statistical, and it is visible without any model. Ask what each sleeve is actually exposed to. Investment-grade credit: the price of credit risk at the safest end of the curve. High yield: the price of credit risk further out. Leveraged loans: the price of credit risk, secured, floating, with a different recovery profile. Structured credit: the price of credit risk, tranched and levered. Four sleeves, one factor. They differ in how far each falls, not in whether it falls.
A floating-rate instrument is not uncorrelated with a fixed-rate one. It is the same bet with a smaller position size. That is why the loans barely move in a spread-widening scenario and still move in the same direction as everything else.
So the test is not history. Correlation is a summary of what two things did; diversification is a claim about what two things can do. Four questions settle it without an estimate:
Is there a variable whose movement would hurt both?
Is there a holder who owns both and would sell both to raise cash?
Do both depend on the same financing market staying open?
Would both be marked by reference to the same screens, by the same people, on the same day?
Four sleeves of one risk factor answer yes to all four. That is why the historical estimate was always going to break, and why the breakage was predictable without observing it.
What to do with it
Compute every correlation twice: once on the whole sample, once on the subsample of periods in which the portfolio lost money. Report both, side by side, in the pack. Where the two are close, the diversification is real. Where the conditional figure is materially higher, as it is in every pairing above, the unconditional figure is describing a benefit the fund does not have when it needs one. The conditional sample will be small and the estimate noisy. That objection is correct, and it is not a reason to prefer the wrong number to an imprecise one.
Then run the diagnostic that needs no data at all. For each holding, write down in one line the variable whose movement would cause it to lose money. Sort the holdings by that line rather than by asset class. If the sorted list collapses onto two or three entries, the portfolio has two or three exposures however many sleeves it reports. Halverton's list collapses onto one.
And print the honest version of the figure. The diversification between the four expressions is worth 0.767 of a point when nothing is happening, and a little over two tenths of a point when something is.
The workbooks behind this article
Every figure above is a live formula in the free companion files for
Financial Risk Management. Each workbook ends with a Checks sheet
setting the printed figure beside the computed one. No account and no email address.
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