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Worrying about Correlation

Everybody likes diversification. But how do you achieve it in a world that's increasingly correlated?

By J.C. Louis

Since the creation of portfolio theory in the 1950's, the sacred edict of investing has been diversify, diversify, diversify. Lately, however, some forward-thinking quants at both dealers and software boutiques have been rethinking this fundamental wisdom. They are faced with an increasingly difficult challenge: how to conceptualize and strategize in the face of a rising synergy between intermarket correlations and volatility. "Correlations are the key to asset allocation and Value-at-Risk," says John Zerolis, director and global head of risk control analytics for Swiss Bank Corp.

Markets are positively correlated when, say, the German and Japanese stock markets decline in lock step with the American market. The Australian pound tends to appreciate against the U.S. dollar in lock step with the British pound. Negative correlation is the tendency for assets to move consistently in opposite directions. The critical point is that rising correlation reduces the protection provided by diversification.

In the recent past, markets were much less interdependent. Volatility in U.S. interest rates, for example, had relatively little effect on foreign interest rates. That's no longer the case. A number of systemic causes-hyperefficient capital markets, sophisticated globalization of trade and investment, and shifts in the aggregation of industries within broad economic sectors-appear to have contributed to an environment in which volatility and correlation go hand in hand.

"When markets are in stressful situations, volatility skyrockets and correlations tend to go to 100 percent," explains Lance Smith, a managing director at Imagine Software. "That presents problems, because risk management cannot just look at averages. It must also look at extremes. On average, you might be OK, but the exception could wipe you out."

Smith's concerns have been echoed by a number of market observers who note that, during extreme market moves, increases in market correlations are greatly magnified by spikes in volatility. A market that shows very little correlation with other markets experiences an abrupt shock that triggers rapid increases in correlation and volatility. During the 1979 Mexican oil crisis and the 1982 default, correlation between the Mexican markets and U.S. and international markets increased dramatically. When times got better, however, those correlations fell off just as dramatically.

Is classical diversification theory a dead end? One set of thinkers tends to favor adapting and extending the classical theory, while another group is bent on coming up with the next new paradigm.

According to the first group, the goal of portfolio composition should remain the same: constructing a diversified portfolio to maximize return per unit of risk from a number of different asset classes that are not well-correlated. But institutional investors need to understand that traditional asset diversification, which is suitable in low correlation, low volatility market environments needs to be retooled in high-correlation, high-volatility environments.

According to this theory, the best course of action is to launch a renewed search for new assets noncorrelated with traditional ones. Some industry watchers believe that it is still possible for small- to medium-sized funds to buck the volatility-correlation spike with broad diversification across a wide geographic swath and a selective blend of alternative assets, such as Brady bonds, restructured loans along with local equities, fixed income and currencies. "If you are diversified equally across 40 to 50 countries and misallocate or miss a major devaluation, you are only 5-percent exposed," says a market-advisory company president. "Let straight diversification hedge all the risk while the rest of the portfolio gets the total returns."

Others, however, believe that alternative asset classes like emerging markets no longer provide the diversification they may have in recent years. "As markets become more global, players are increasingly active at emerging markets desks," observes Jay Smith, president of Leading Market Technologies. "From London to Tokyo, everyone is trading in everyone else's markets. The big money-makers and movers execute strategies in regional markets in more uniform fashions. Instruments become more predictably correlated as markets become more efficient. Increased exports and reduced trade barriers have a globalization and correlating effect that make certain industries move together more than they did in the past."

Although a generation of risk managers since the 1950s has recognized that the process of portfolio construction must include an expected return, an expected risk (expressed as a volatility) and a correlation measure, the full impact of correlation is underappreciated. "Experience with options has given people intuition about volatility," explains Joseph Mezrich, director of quantitative research of Salomon Bros. "Correlation, however, is a little more subtle. It's the glue that connects the assets. It's of fundamental importance in characterizing portfolio risk. People say 'the correlations are not stable' and throw up their hands. They want to think about correlation differently from volatility because they have less experience with it, but it is not fundamentally different. Properly modeled, correlation and volatility are very similar."

"If you do not understand your exposure to correlation, at the end of the day you won't understand the rate at which you are coming unhedged," echoes Amy Strickland, vice-president of First National Bank of Chicago. "You can derive correlation directly from market-implied volatilities. Typically, there is a mismatch between what the market is saying about correlations and volatility and what a historical model is saying. Often, a longer-term portfolio must be risk-managed with day-traded instruments." As a result, she says, "the risk manager needs to come up with a strategy to reconcile the historical correlation levels with the available traded instruments."

One approach is to spend less time dissecting the correlations between returns and spend more time on measuring the correlation between volatilities. "Because volatility moves all over the place," says Alan Kaufman, president of Trilogy Investments, "we must look at risk in a different way. We need to ask how correlated volatilities are within different markets. Looking at the correlation of prices between two assets is one measure of risk. But our research indicates that returns have correlations with changes in volatility, and that a much better lever to examine diversification is the correlation between market volatilities, rather than just between returns."

Take, for example, the correlation between stocks and bonds. By correlating the returns of stocks and bonds, it would be possible to come up with an allocation strategy that would minimize the overall portfolio variance. "That is the classic way, but that may not be a good picture of the risk," cautions Kaufman. "If stocks and bonds are noncorrelated, then stocks may be up, maybe bonds are down. But if their volatility is linked-stock volatility and bond volatility are high-even if they are noncorrelated by return, you still might find that they are risky assets to hold because of their linkage in volatility." In October 1987, he points out, stocks and bonds were noncorrelated, but both were extremely volatile-and extremely risky assets by any measure.

Eric Sorenson, head of quantitative research at Salomon Bros., also prefers measuring the correlation of historical volatilities over that of returns. "Forecasts of the correlation of volatility can be modeled more easily than forecasts of the rate of return," he says. "If we improve from 50- to 55-percent accuracy of our forecasting of S&P returns, then we can forecast volatility and correlation at 60- or 70-percent accuracy."

Classical portfolio theory's assumption that volatilities are fixed causes its own problems in the interest rate market. "The shape of the volatility curve has been more stable than the interest rate curve itself," observes Emmanuel Frushard, head of financial engineering at Summit Systems. "The correlation between short- and long-term rate volatilities will generally be positive but do not approach 100 percent. Correlation between forex and interest-rate volatility, however, may be negative or close to zero. In a big crisis, volatilities will all go up, and therefore the correlation of volatilities will approach 100 percent."


The market is quickly developing a number of solutions to the correlation problem. The recent use of VAR calculations represent only the beginning. VAR, along with classical theory, assumes that the variance of a portfolio's value is fully represented by a normal distribution curve. But other statistical properties of the returns, including skewness and kurtosis, are essential to the analysis.

William Ferrell, president of Ferrell Capital Management, notes that a number of variations on standard VAR calculations are now being used to address the major impact of volatility and correlation on bottom-line performance. Because of the enormous computational effort involved in measuring the covariance of every possible pair of instruments in the portfolio, he suggests using a simplification of market factors, or what he calls key drivers.

Key drivers are the correlated risk factors having the greatest impact on changes in net asset value. Ferrell observes that managers often benefit from their shift in focus from the portfolio's largest positions to the factors governing the largest risk exposures. "We do not worry about the 3 percent of performance arising from obscure market exposures," adds Ferrell. "We spend a lot of time stress testing those markets that have significant impact on the bottom line."

After identifying the largest risk exposures, managers should go on to define worst-case market scenarios by shocking the key drivers. These stress tests create what Ferrell calls "heat maps," which accurately foretell the impact of concurrent changes in volatility and correlation on the portfolio.

Other extensions of VAR often involve tracking essential market factors with sophisticated statistical tools. One method employed by Bankers Trust is Bayesian regression, which provides a robust means of measuring the market factors' varying effects over time. While standard regression coefficients remain fixed, Bayesian coefficients change through the method's use of a rolling time window that continually estimates the coefficients with data from a new time window. The method helps weigh the degree over time to which each variable contributes to returns.

Historical simulation models also do not assume that portfolio variance or any other parameter is sufficient for measuring risk, and, for this reason, they are termed "non- parametric." This technique reprices portfolios using data from different days in the past. "The weakness of historical simulation is that it is a 'weak form' market-efficiency-based measure, and that has its attendant problems", says Ranjon Chakravary, vice president of market risk management at BancBoston. "This weakness is shared to a great extent by the variance-covariance method."

Weak-form market efficiency assumes that the past contains all the information necessary to predict the future. To overcome this weakness, various forms of Monte Carlo simulation, such as structured Monte Carlo (which includes all observed information, including correlations), are becoming more popular in the risk-management market.

The solution to the correlation problem is not around the corner. Although correlation poses a potentially lethal threat to classical portfolio theory, investors who want to track the true risk in their portfolios have an increasingly complex set of alternatives to choose from.