Research finds most equity indices actually contain alpha

CAPM / Alpha Theory 28 Jan 2008

When Credit Suisse and S&P both recently announced 130/30 “indices”, we struck a note of skepticism.  Wasn’t such an active index an oxymoron?  Doesn’t a short-extension simply leverage a manager’s pre-existing alpha?  And if so, isn’t such an index just an arbitrary benchmark based upon the underlying alpha-generation model?

Andrew Lo provided some arguments in favour of such an index in his December 2007 paper “130/30: The New Long-Only“.  In it, he acknowledges:

“our proposal to put forward an algorithm or dynamic portfolio as an index is a significant departure from the norm. Existing indexes such as the S&P 500 are defined as baskets of securities that change only occasionally, not dynamic trading strategies requiring monthly rebalancing.  Indeed, the very idea of monthly rebalancing seems at odds with the passive buy-and-hold ethos of indexation.”

According to a paper published in the January 2008 edition of the Journal European Financial Management, the “passive buy and hold ethos of indexation” ain’t so passive after all.  The paper (earlier version available here), finds that most indices are chalked full of active biases – making a truly passive index a rare animal indeed.  This, of course, is the central argument made by proponents of fundamental indexation (see related posting, “Arnott: Does My Beta Produce Alpha?”)

Angelo Ranaldo of the Swiss National Bank and Rainer Haberle of UBS divide indices into two broad classes: “inclusive” (e.g. the Wilshire 5000) and “exclusive” (e.g. the DJIA).  They argue that the Wilshire is a more passive index because it does not require as much rebalancing.  However, they acknowledge that indices which exclude large numbers of stocks in order to focus on a representative sample do serve a solid purpose.  Index replication is a critical prerequisite to a healthy index derivatives market, they point out.  And since a large chunk of the Wilshire 5000 are relatively illiquid, replicating it in real time would be next to impossible.

Notwithstanding these operational advantages however, the authors spend most of the paper showing why “exclusive” indices need to be treated as containing both a passive and an active component.  Since the active component might result from technical factors (e.g. mergers) affecting both inclusive and exclusive indices, the focus their attention on the discretionary elements of index creation (the most obvious being the subjective method used by the DJIA board).  They analyze several countries and find that such discretionary factors represent anywhere from 12% to 75% of all exclusions of specific stocks from an index.

Then, to isolate the active component, they compare what they call “index twins” – pairs of different sized indices based on the same underlying equity market.  They look for mathematical evidence of market timing that might results from the discretionary component of index management.

They find that the exclusive twins perform better that their larger “inclusive” twins during bull markets…

…and usually worse during bear markets…

Given that the exclusive indices tend to have a large cap bias, this seems to run contrary to the (Fama French) assumption that small caps outperform large caps ceteris paribus.  Explain the authors:

“We argue instead that the outperformance of exclusive indices – which are admittedly large cap-type indices – is not due to a large cap effect but to the selection and exclusion rules behind the constitution of these indices.”

In other words, these “selection and exclusion rules” constitute active management (much to the delight, we’re guessing of Fundamental Indexation proponents).  In fact, the authors say these rules have an effect remarkable similar to recognized trading strategies “such as momentum, autocorrelation and the limitation of tail risks.”

Perhaps not surprisingly, the outperformance of the exclusive indices is highest in equity markets where the index is most dynamic (i.e., the least buy-and-hold).  In other words, the more active an index, the better the performance.

So what?  The authors explain…

“The first implication for an asset manager is that he or she has to be aware of the implicit trading strategy behind index construction. This is a simple but important consequence. The asset manager can then consciously decide whether to accept – and how to handle – the implicit trading strategy hidden in some market indices.

“All the main aspects of the investment process are affected by the implicit index strategy: client analysis (determination of risk-return profile, investment horizon, and other investment guidelines such as liquidity requirements, currency, tax aspects), benchmark construction (or strategic asset allocation), timing (or tactical asset allocation), selection (or stock picking), performance measurement and attribution, and risk management.

“The hidden but implicit active strategy of some indices can also pose agency problems in the asset manager – client relationship. A vague definition of a benchmark may have a significant impact on the final performance. As shown above, index twins may provide different performances, depending on which index twin is used.”

To this list we would add that the delineation of active and passive elements of a return stream may need to account for the fact that the “embedded ETF” within every actively managed fund itself contains an active and passive component.  Similarly, the distillation of equity betas out of hedge fund returns may need to account for this – meaning the residual alpha component may end up being different that what we assumed.

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  1. moom
    January 29, 2008 at 1:02 am

    How is a 130/30 index different to all the various hedge fund indices out there?

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