Why the common expression “all correlations go to one” may be overstated

CAPM / Alpha Theory 28 Feb 2008

In his book A Demon of Our Own Design Richard Bookstaber describes how the breakdown of basic market physics during Black Monday meant that “all stocks moved together” (see related posting):

“The huge volatility of the market broke down all but the most fundamental relationships between markets and securities.  The usual day-to-day world where investors cared about subtleties like corporate earnings or analysts’ forecasts dissolved as the energy of the market was turned up.  All stocks moved together; if it was a stock, it was soldit was like plasma physics: as matter becomes hotter, it becomes less differentiated.  The forces that bond atoms together in the form of molecules are overwhelmed, so that rather than having a myriad of different substances, we have the elemental building blocks of the atoms.  Turn up the heat even more and the atoms themselves are melded into plasma, positively charged ions and negatively charged free electrons; matter in its most uniform and non-differentiated state, no longer hydrogen atoms and oxygen atoms, just a seething white-hot blur of matter.”

Since 1987, the term “correlations go to one in times of stress” has become axiomatic in financial markets.  But does research actually back up his common assumption?

In a January research note to clients (Stress Risks within Asset and Surplus Frameworks) available here at AllAboutAlpha.com with free registration), Morgan Stanley’s Marty Leibowitz and Anthony Bova take a good hard look at this phenomenon.  According to their report:

“one often hears the comment that, under such adverse conditions, ‘all correlations go to one’.  However, there is rarely any serious analysis of the covariance and volatility effects implied by such extreme extrapolations.

“The concept of ‘correlation tightening’ provides a more measured way to gain insight into these effects.”

“Correlation tightening can cover a wide range of processes with very different outcomesA literal interpretation of the expression ‘all correlations go to one’ would generally lead to an unrealistic covariance matrix.  A more coherent interpretation is that each asset class volatility becomes totally loaded on a primary risk factor such as U.S. equities.”

The authors create what they call a “beta response curve” to explain the effect of this correlation tightening (illustrated below).  The straight black line in the chart represents the volatility of a passive portfolio containing the market portfolio (U.S. equities) and cash.  A 0% allocation to the market produces a volatility of 0% while a 100% allocation to the market produces the market’s volatility (16.5%).

The curved lines represent the volatility of a diversified portfolio containing several asset classes (e.g., emerging market equities, private equity etc.).  Even under normal circumstances, these other asset classes introduce a healthy measure of US equity exposure to the portfolio since they tend to have a significant correlation to US equities.  But as the US equity beta of these diversified portfolios is reduced (through, for example, a negative beta overlay), the idiosyncratic volatility of these other asset classes begins to dominate.  When the entire US equity beta is removed from these diversified portfolios, idiosyncratic volatility (of approximately 5%) remains.  Conversely, as beta increases, the idiosyncratic risk in the portfolio drops due to the benefits of diversification between the market portfolio and the additional asset classes.

The authors use this framework to prove the counter-intuitive notion that the gap between expected and ‘stress point’ risk levels will – ironically – be worse for the more highly diversified funds.

While ironic, this assertion makes intuitive sense when you think about it.  Diversification can be a temporary mirage that is only visible under so-called normal market conditions.  Thus, a heavy reliance on diversification exposes the investor to a larger downside if the mirage disappears.  Succinctly stated, more diversification benefits equals more to lose when those benefits evaporate.

Technically speaking, Leibowitz’s and Bova’s stress point risk levels are defined as those which occur during periods of correlation tightening as described above.  Such stress points mean that previously low-correlation assets begin to deliver more market beta to the portfolio.  In other words, what was idiosyncratic risk now becomes mostly systematic (beta) risk.

The report then extends this analysis from the volatility of assets in a pension plan to the volatility of a pension plan’s surplus (the difference between its assets and its liabilities).   As they point out, the present value of future payments to pensioners is determined by a number of factors including the discount rate used to calculate that present value of those liabilities.  When long term rates change, the present value of these future liabilities changes.  As a result, these liabilities are also volatile.

Thus, the volatility of the plan’s surplus is a combination of the volatilities of the assets and of the liabilities (reduced slightly due to the benefits of diversification between these two components).

This is graphically depicted in the following chart from the report (which assumes a 10% volatility for liabilities):

As you can see, getting the surplus volatility below 10% is impossible by simply removing the beta (U.S. equity) exposure of the assets.  Instead, the authors advocate a liability hedge (i.e., hedging out swings in the discount rate used to calculate the present value of liabilities).  This would drop the entire beta response curve of the plan’s surplus back down (the upper curves in the Exhibit 6).

Unfortunately, such a liability hedge would also raise the beta response curve of the plan’s assets (the lower curves in Exhibit 6) since the liability hedge itself would constitute an additional risky asset.

The report concludes:

Beta reduction can act as a de-risking agent in both asset-based and surplus terms. However, a liability hedge alone can only be said to transfer or ‘re-risk’ the interest rate component from surplus to an asset-based framework.

The basic point is that some balanced combination of beta reduction AND liability hedging may be needed to attain comfortable levels of risk that address a fund’s overall concerns.

Of course, not investing in risky assets at all would also reduce beta to zero (no beta hedge required).  But the report cautions that pensions’ long term time horizons allow them “to enjoy certain competitive advantages in pursuing long term investment returns”. Therefore, they should probably not avoid risky assets altogether.

In other words, don’t throw out the baby with the bath water.

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  1. Brent Wheeler
    March 2, 2008 at 5:18 am

    Back in 1987 working in the NZ Treasury I and another colleague did a study of how correlations altered over the before / after the 87 equities crash. NZ was stung very hard with this and did not recover as the US did.

    Results were just as reported here. Our correlation with the US tightened. In fact we still have this kind of analyst jargon here that talks of “coupling” and “decoupling” with the US markets. The US futures market used to appear to lock step our every move before we even got out of bed.

    So we should not assume, good fund manager excuse as it sounds, all correlations move to “one” necessarily. They didn’t. One should also bear in mind that in trying not to infer cause from correlations that the square root of these things tells you how much a linear equation is explaining… and even with high correlations the answer is… not always that much.

    Conclusion – before incurring the vast transaction costs trying to chase changes in correlations think very carefully – and as Liebowitz and Bova suggest, try actually studying them rather than getting the cocktail party version.

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