Where’s my free lunch?

Ever since Harry Markowitz published his June 1953 paper on portfolio selection, investors both institutional and retail have subscribed to the theory that diversification – and its use in combination with mean-variance optimized allocations – universally widens and almost always improves the possibilities of risk and return.

At its core, the theory states that an investor should consider including assets with a) positive return expectations and b) low correlations to existing investments.  Faithfull acolytes of Markowitz as many of us have now become, the years subsequent to the financial crisis have challenged if not the theory, then at least the practice of expecting diversification to provide a “free lunch”: macro-economics dominated performance as condition b) above remained persistently obstinate in its absence.

Average strength of multi-asset correlations, based on 12-months returns*.

Multi-asset Corr

Sources: S&P Dow Jones, Barclays, JP Morgan, HFRI. Charts and graphs are provided for illustrative purposes. Past performance is no guarantee of future results.

And in due course, the great minds of investment and allocation have bent their efforts into ever-more esoteric assets.

But it’s not just about correlation, which measures the strength of linear relationships. It’s also about differing market betas, and about conditional relationships between financial assets. It’s about how disperse the returns are, this month and next. In an environment of high dispersion, not only does it matter more which allocations you make, it also – at least in theory – implies a greater benefit from diversification. If you’re wondering whether it’s worth expanding your investment footprint beyond a core set of exposures, or even how much difference your decisions really make, that’s a particularly useful concept to keep in mind.

We recently offered some thoughts to define, examine and to some extent publicize dispersion. Not only because we think it’s an under-celebrated and remarkably useful measure of market opportunity, but also because it has much to say about the current diversification of existing portfolios (like the S&P 500®) and – in tandem – can provide a useful guide to the factors that are most important in understanding Index returns.

* Average of absolute values of 12-month correlations between the S&P GSCI Commodities, S&P 500®, S&P Europe 350®, S&P Emerging Market BMI, JP Morgan Core EMBI, Barclays Aggregate U.S. Corporate High Yield, S&P 7-10 year U.S. Treasuries and HFR Global Investable Indices. Note that negative correlations are counted as positive – it is the strength not the sign of the relationship that we wish to emphasize.

The posts on this blog are opinions, not advice. Please read our disclaimers.

4 thoughts on “Where’s my free lunch?

    1. Tim EdwardsTimothy Edwards Post author

      Perhaps they did. But I would say that they identified situations where for behavioural reasons there are be free lunches to be had, certainly in doing so providing a challenge to the efficient market hypothesis. Neither challenged the theory that the process of diversification can improve the risk/return ratio beyond what was previously available (which is rather independent of efficient markets). I hoped, with my post, to argue that this process of diversification – while still theoretically valid – has been hard to benefit from in practice recently, at least if you use correlations and dispersion as the measure of how much opportunity there is to add value.

  1. Paul Jacoby

    In reference to the linked piece titled “Dispersion: Measuring Market Opportunity”… I wonder if the dispersion measure adopted is the most appropriate – specifically the use of ‘w’ in the dispersion formula. It would seem that the effect of ‘w’ is double counted – once in the construction of ‘P’ and then again in the weighting of the squared deviation. Consider a market comprising 100 stocks where a single stock accounts for 99% of the capitalization. P will then very closely reflect the ‘r’ for that stock, so (r – P) will be close to zero. The formula will apply a 99% weighting to this close-to-zero deviation and reveal that there is practically no dispersion in the market, even if the other 99 stock returns diverge widely. While the measure that you employ may have value, I suspect that is not as useful as the same formula sans the ‘w’. Did you test this alternative formulation, and if so, what where the results?

    1. Tim EdwardsTimothy Edwards Post author

      Thanks for your thoughts Paul. It’s a valid objection – there is clearly a choice to be made on whether to weight or not.

      Firstly, conveniently, the dispersion of an equal-weight index recovers close to what you were looking for, close but not exactly because this compares differences to the unweighted the average stock performance represented by the equal-weight index return.

      We do have that equal-weight dispersion for the S&P 500. It’s slightly larger, showing the greater variability among smaller stocks, but characteristically similar to the weighted version. The impact of size can be seen in dispersion of mid-cap and small-cap indices, shown next the the S&P 500 dispersion here. I should imagine a more concentrated index might have greater discrepancy. Related – and perhaps to you your point – equal weight indices and their dispersion are perhaps more appropriate measures of average performance and opportunity, respectively, for security selection strategies. I think both provide useful information.

      Secondly, we wanted a measure that could be compared with market (index) volatility as fairly as possible, which also double counts in the same sense: a low volalatity stock comprising 99% of the market will cause a low reading for market volatility and a potential underestimation of how much risk there is “out there”. It is because we wanted to compare dispersion with characteristics of the market portfolio (such as volatility or internal correlation) that a index-weighted average was ultimately preferred over other alternatives.


Leave a Comment

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>