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.