# is beta of a portfolio always meaningful?

Consider the following strategies:

• a stat arb strategy with no overnight exposure, but significant market exposure intraday.
• a market timing model which is always long or short the market.
• etc

is it meaningful to consider the betas of strategies like these? Or should we ignore beta when the portfolio returns have low (near zero) correlation to market returns? how do you use beta?

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I would split the question into two sub-questions:

1. Is market beta useful at all?
2. Is market beta useful for high-frequency strategies that are fully hedged EOD?

With regards to the first question, I would summarize the hundreds of papers on the subject as: yes, but not as much as it was initially believed. The reason being that multi-factor models are empirically superior to CAPM and intertemporal CAPM, and in these models the market factor explains relatively little volatility, and in some cases it is entirely omitted, as the volatility is entirely captured by industry factors. Yet, risk models are not universally adopted, especially outside of equities, and moreover market beta can still be useful to assess risk premia (as is usually done in investment banking) or to tactically hedge portfolios.

With regards to the second question: it depends on the time scale. If you estimate beta using daily returns, you cannot use this loading to hedge intraday exposure to market risk, since this risk is not captured by the estimation interval. So you'd have to use 30- or 15- minute returns. This is not trivial however, because asynchroneity effects and induced autocorrelation of returns (Epps' effect). I don't know of commercial high-frequency factor models. I am not sure that statistical arbitrageurs use in house models, but there are many technical hurdles to overcome.

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Could you please elaborate on how investment bankers use beta? This should be interesting.. –  Jase Nov 13 '12 at 2:22

It partly depends on the use case.

If one is taking multiple strategies and assembling a portfolio that includes multiple different strategies and is mixing this with a heavy weighting to an equity index, then this might be a useful measure. Zero or negative beta does have meaning, in the same way that correlation has meaning.

In the more traditional usage of CAPM, a better question might be "which beta to use" in this context. It's still meaningful (in so far as any measure of beta is meaningful) but an active strategy or one which trades different assets should may not be compared to a beta of a long-only stock portfolio. Regarding the specific examples that you give: there are various hedge fund indices which cover statistical arbitrage and long/short equities. These may or may not be good benchmarks, but they are more likely to be useful than a standard equity market index.

Aswath Damodaran has a blog post on this that summarizes some of the issues. Although I really think that it's important to reflect on what $\beta$ is supposed to measure -- market risk -- and ask yourself whether you're definition of "market" is appropriate for the context.

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By William Bernstein, source:

In June of 1992 academicians Eugene Fama and Kenneth French ("F/F") rocked the investing world with a study published in the Journal of Finance, innocuously entitled "The Cross-Section of Expected Stock Returns." The piece is the cognitive equivalent of an enormous hunk of marzipan cake which sits in your freezer for months—there’s no way you’ll get through it in one whack, and is properly consumed only in small sittings. In fact, unless you’ve gotten considerably beyond Stat 101, it’s probably best avoided. So, here’s the short course:

• "Beta," the measure of market exposure of a given stock or portfolio, which was previously thought to be the be-all/end-all measurement of stock risk/return, is of only limited use. F/F convincingly showed that this parameter did not predict the returns of all equity portfolios, although it is still useful in predicting the return of stock/bond and stock/cash mixes.

so it depends on the type of portfolio, more info in the paper in italics.

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Can't see this anywhere in their paper? " F/F convincingly showed that this parameter did not predict the returns of all equity portfolios, although it is still useful in predicting the return of stock/bond and stock/cash mixes." –  user2921 Oct 5 '12 at 17:56

In response to your last question, "how do you use beta?" - I'd say try to as little as possible. Your use seems to be a bit out of the realm of what I'm used to, but whatever beta you get is so prone to observational error, that it may not be meaningful.

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