Jan 07

FAJ Study about stock returns within industry groups (an example of using correlation)

by David Harper, CFA, FRM, CIPM

FRM | CFA |

Today's video tutorial introduced the correlation coefficient (rho). Of course, correlation is an essential risk building block. To diversify is to add imperfectly correlated assets. At the same time, recent events show that correlation (or the correlation matrix), while a vital model input, can be a notoriously elusive parameter (e.g., the correlation structure that underpins credit derivative basket instruments is notoriously time-varying, or we might say less generously, unstable).

Covariance is the relationship between variables but it is not intuitive; it is hard to understand what the covariance says. So we translate covariance into correlation, which is "standardized covariance." Specifically, correlation is covariance divided by the product of volatilities. Where covariance is not natural to us, correlation is unit-less, running from -1.0 to 1.0. Correlation, therefore, is a function of volatility in addition to co-movement (covariance). Volatility impacts correlation. (This excellent New York Fed study showed why apparently high correlations among hedge funds, for a recent study period, were really due to low volatilities).

The latest Financial Analyst Journal (FAJ) contains an interesting study by Louis Chan, Josef Lakonishok and Bhaskaran Swaminathan. They use correlation to test the cohesion of industry group definitions. Specifically, they looked at different industry group classifications to see to what extent stocks within the industry classifications are correlated. Under this idea, from an investment perspective, you'd prefer to classify companies into industry groups that tend to exhibit strong within-industry correlation. To perform this analysis, they performed a straightforward test. They computed the average pair-wise correlation between each stock within an industry group and its industry peers (other stocks within the same industry classification):

pairwisecorrel1


Where rho is the time-series correlation coefficient between two the returns on two stocks:

correl_plain1

They looked at three industry classifications:

They found industry groups to be cohesive: stocks within industry grouping showed higher pair-wise correlations. Specifically,

  • The average correlation within the ten GICS sectors (two digit codes) was 0.38. That was 0.13 higher than outside the sector.
  • The Fama and French correlations were similarly strong: within group correlations were 0.40 which was also 0.13 higher than outside the sector
  • The correlations improved, but modestly, as the industry/sector definitions become more granular. In other words, narrower industry definitions were modestly associated with tighter within-group correlations

In short, they showed that "industry groups correspond to collections of of economically similar companies in two respects." First, as discussed, they showed stock returns tend to covary more with their industry/sector peers than with outside-the-group stocks. Second, they also found (not surprisingly) that underlying operating performance tends to show a greater covary within group.

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