Currently, I calculate beta, correlation, and covariance measures using daily log normal returns of Security A and Benchmark A. What would it mean if I were to use daily log normal excess returns in these tests? In such a case, I have two hypothetical definitions of excess returns: 1. daily return - average return 2. daily return of security A - daily return of benchmark A

Is there an advantage to doing this?

If I am comparing security A to benchmarks A, B, and C, where there is some correlation between the benchmarks, how could I "clean out" this correlation, so that when I ran the comparison, the correlation I calculate between sec A and the benchmarks is more clear. (E.g. Security A correlates 0.5 to Benchmark A, 0.3 to B, 0.7 to C independently of the benchmarks' correlation to each other).

Note: adding covariance to the list of measurements since it plays a role in beta and port. variance.


1 Answer 1


I'm a bit confused by this.

If "excess returns" = daily - average returns, this shouldn't change any of the beta, correlation or covariance outcomes.

If "excess" = security - market, then the beta should be 1 lower. Correlation and covariance should be commensurately lower, but essentially meaningless.

About "clean" correlations, this is a really tough one. IE easy to ask, but it rapidly gets complicated. Imagine you correlated Apple to the S&P and the NASDAQ: and correlation is ~80% to both indices, that are ~90% correlated to each other. "Cleaning" this to try to say that it's really one more than the other is essentially trying to infer causation from correlation, which is a huge minefield ;-)

But if you insist, you would need to do a Principal Component Analysis of your 3 indices. This would take their returns, and constructs the 3 cross-market signals that explain the returns and are independent of each other. Regressing your security against these three PCs gives you (theoretically) a beta and performance attribution to these different cross-market signals.

  • $\begingroup$ Greatly appreciate the response! $\endgroup$ Aug 25, 2019 at 18:47

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