# Portfolio Theory is Dead, Now What?

Readers often ask what Quantivity thinks of *long-term* quantitative strategies, and thus corresponding relevance of modern portfolio theory and asset allocation (strategic and tactical). In short, Quantivity is *not a fan*.

That said, holistic understanding of *how* and *why* these theories are wrong is insightful and relevant for both short- and long-term quantitative strategies. This perspective is informed by standard institutional and retail portfolio management as exemplified by Grinold and Kahn and Faber, along with academic background in both economics and finance.

Despite intellectual tradition, the mountain of contrary evidence is simply too overwhelming:

- Decades of counterexamples to CAPM
- Increasing cross-asset correlations worldwide, dramatically reducing diversification efficacy
- Two market bubbles, amply validating behavioral finance to those working in tech and finance
- Quantification across many marketplaces, rapidly accelerating since 2007
- Rise of “volatility” as a proposed asset class, going back to Derman in 2003

Even Kahn was moved to comment last year in Quantitative Equity Investing: Out of Style?

All these speak to arguably the fundamental conjecture of financial economics: accepting incremental “risk” demands compensation by commensurately higher return. Or, in jargon: the risk premium is non-negative and increasing. This conjecture underlies justification for mean-variance optimization, diversification, benchmarking, index investing, and thus much of modern retail investing.

Yet, *evidence strongly indicates this conjecture is false*.

Given that, the pertinent question is what are the *relevant practical implications* for quantitative strategies due to falsity of this conjecture. Several aspects to consider, depending upon your horizon:

- Long-term: portfolio optimization, bubbles, envy utility functions, and lottery stocks
- Short-term: volatility bias, variance minimization, symmetric loss, and regime indicators

Follow-on posts will expand upon these considerations, beginning with minimum variance portfolios (MVPs).

To motivate this topic, both Falkenblog and Estimation Risk are outspoken advocates from the blogosphere. On the institutional side, Clarke and de Silva from Analytic Investors and Pim van Vliet from Robeco are actively publishing. MSCI Barra is offering indices on global minimum volatility.

This topic also speaks to the ongoing Quantivity theme of market regimes, as exemplified by Scherer (2010, p. 6):

Evidence for the existence of two equity market regimes. Both are normally distributed on their own, but non-normal in combination. Sharpe ratios for this period are close to zero because of the negative impact of the credit crisis on both time series.

If indeed true, then *past* performance of MVPs hold interesting potential as an *ex-ante* market *regime indicator*. Again, from Scherer (2010, p. 5):

The following articles are worth consideration by readers interested in the refuting literature, which recently converged onto minimum variance as a guiding principle for portfolio composition preferential to Markowitz-derived models:

- The Efficient Market Inefficiency of Capitalization–Weighted Stock Portfolios, by Haugen and Baker (1991)
- Mutual Funds, Idiosyncratic Variance, and Asset Returns, by Falkenstein (1994)
- Asymmetric Volatility and Risk in Equity Markets, by Bekaert and Wu (1997)
- On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model, by Karceski
*et al.*(1999) - Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps, by Jagannathan and Ma (2002)
- The Cross-Section of Volatility and Expected Returns, by Ang
*et al.*(2004) - Minimum-Variance Portfolios in the U.S. Equity Market, by Clarke, De Silva, and Thorley (2006)
- The Cross-Section of Volatility and Expected Returns, by Ang
*et al.*(2006) - Aggregate Idiosyncratic Risk and Market Returns, by Bali and Cakici (2006)
- Estimating the Global Minimum Variance Portfolio, by Memmel and Kempf (2006)
- The Volatility Effect: Lower Risk Without Lower Return, by Blitz and van Vliet (2007)
- Risk and Return in General: Theory and Evidence, by Falkenstein (2010)
- Optimal versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy, by DeMiguel
*et al*(2009) - Portfolio Selection with Robust Estimation, by DeMiguel and Nogales (2009)
- A Generalized Approach to Portfolio Optimization: Improving Performance By Constraining Portfolio Norms, by DeMiguel
*et al.*(2009) - The Pricing of Volatility and Skewness: A New Interpretation, by Bradford (2009)
- The Properties of Equally Weighted Risk Contribution Portfolios, by Maillard, Roncalli , and Teïletche (2010)
- Minimum Variance Portfolio Composition, by Clarke, De Silva, and Thorley (2010)
- A New Look at Minimum Variance Investing, by Scherer (2010)
- Stock Return Serial Dependence and Out-of-Sample Portfolio Performance, by DeMiguel
*et al*(2010) - Betting Against Beta, by Frazzini and Pedersen (2010)
- Variations on Minimum Variance, by Falk (2011)
- Expected Idiosyncratic Skewness , by Boyer, Mitton, and Vorkink
- The Puzzling Relationship Between Risk and Return, by Luo
*et al.*(2011) - Minimum Variance: Exposing the “Magic”, by Alvarez
*et al.*(2011) - Improving Portfolio Selection Using Option-Implied Volatility and Skewness, by DeMiguel
*et al.*(2011) - Benchmarks as Limits to Arbitrage: Understanding the Low-Volatility Anomaly, by Baker (2011)

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Nice post and very good review. Congrats!

What do you mean, decades of counterexamples to CAPM?

@Lao: read any of Fama’s recent papers, which provide illustrative counterexample over longitudinal panels. Similarly, both his and French participation in DFA is arguably an implicit acknowledgment.