Modern portfolio theory and risk management: assumptions and unintended consequences

Abstract

This article presents an overview of the assumptions and unintended consequences of the widespread adoption of modern portfolio theory (MPT) in the context of the growth of large institutional investors. We examine the many so-called risk management practices and financial products that have been built on MPT since its inception in the 1950s. We argue that the very success due to its initial insights had the unintended consequence, given its widespread adoption, of contributing to the undermining the foundation of the financial system in a variety of ways. This study has relevance for both the ongoing analyses of the recent financial crisis, as well as for various existing and proposed financial reforms.

Keywords:

• benchmarking
• contagion
• efficient market hypothesis
• financial crisis
• financial reforms
• investor herding
• modern portfolio theory
• risk management
• systemic risk

Acknowledgements

The authors thank Mark Ansen, Andreas Hoepner, Keith Johnson, Jon Lukumnik, Lynn Stout and Ed Waitzer, for their helpful feedback and commentary. In particular, they wish to thank Andrew Williams for his especially close reading, his tough but important questions and as always his close editing. They acknowledge a grant from the International Centre for Pension Management at the University of Toronto for their generous assistance. Any errors and omissions remain solely those of the authors.

Notes

Indeed, the expansion of asset class investments is parallel to the move from bonds into equities in the 1950s and 1960s: both are logical outcomes of MPT.

The Conference Board. The 2010 Institutional Investment Report, 2010, New York, 9, 11.

Ibid. (22, 27).

While the numbers appear small in relation to total holdings (the largest 200 DC funds’ hedge fund assets were 1.6% of their total assets) this is an important change in the last decade as the inflow of funds is typically magnified through hedge funds’ use of significant leverage, a point we examine below (Ibid, 5).

Additional factors have also changed the context of investment, most importantly an increasing short-term investment horizon in practice which is often at odds with long-term value creation and retirement horizons. The average holding period currently stands at less than 1 year on the New York Stock Exchange, while the impact of high-frequency trading has increased dramatically. The Conference Board, ‘Commission on Public Trust and Private Enterprise, Part 2 – Corporate Governance,’ January 2003; New York Stock Exchange. http://www.nyxdata/com/nysedata/asp/factbook.

While fiduciary duty to DB plan participants is clearer to some observers, DC retirement plans and more generally mutual funds have equally clear fiduciary obligations to investors as well.

http://www.arnoldporter.com/resources/documents/Advisory-Dodd-Frank_Act_Addresses_Systemic_Risk_071610.pdf, accessed 10 March 2011.

Bhidé (2010, 118–119) suggests that one reason most financial theory adopted normal distributions is that they were able to have, in Fama's word, ‘traction’. That is, Lévy distributions (based on Mandelbrot's work) made ‘no headway’ as predictions could not be done in a systematic way, leading Bhidé ton concludes that ‘… flawed, but mathematically convenient assumptions of normal distributions … shaped the practice of finance’.

In statistics risk is associated with undetermined outcomes when the probability distribution of outcomes is known. The word ‘uncertainty’, however, is used when the probability distribution of outcomes is not known.

For example, Monte Carlo simulations’ and scenario tests’ accuracy depend on both the number of simulations and how the analysis view outliers.

Investor's irrational behaviour and preferences, herding and cascading and seasonal habits will be discussed later.

This formulation was originally proposed by Louis Bachelier in the early 20th century. It was strongly criticized by Henri Poincaré who argued that the independence assumption is empirically false, that investors watch each others’ actions, which causes both feedback loops and under some conditions herding effects. See, for example, ‘Non-normality of market returns’, J.P. Morgan Asset Management (available at www.jpmorgan.com/insight), and Taleb (2007,  20, 150). A good example of this is the ‘pack mentality’ of hedge funds (correlations of returns) from 2004 to 2010. Jenny Strasburg and Susan Pulliam, ‘Pack mentality grips hedge funds’ The Wall Street Journal.  online.wsj.com/article (accessed, January 14, 2011).

The concepts of relative and absolute risk aversion are introduced in the seminal work of Arrow (1965).

These axioms are part of a more general framework, known as expected utility theory. The seminal work of Von Neumann and Morgenstern (1944) provide a through explanation. Later on in this paper a more psychologically realistic alternative to this theory (prospect theory) will be discussed it is under von Neumann (not Neumann).

CAPM assumes that only one source of risk (market risk) is common to everyone. Instead of finding correlation between two assets in your portfolio separately, you only need to find the correlation between each asset to the market.

Note that a fundamental difference between CAPM, as a single-factor model, and multifactor models is that CAPM is based on an equilibrium model under conditions of risk, while multifactor models, are based on likely systematic risk candidates, economists identify using intuition.

In a significant set of variations of increasing complexity, Fama and French's model show that two empirically determined variables, size and book-to-market equity do a very good job explaining the cross-section of average returns. They argue that if stocks are priced rationally, systematic differences in average returns are due to differences in risk. So size and book-to-market must proxy for sensitivity to common risk factors in returns. Fama and French (1993) use the cross-section regressions of Fama and MacBeth (1973) where the cross-section of stock returns is regressed on the interested variables. However, they use time-series analysis in which a well-specified asset-pricing model must produce intercepts (alphas) that are not significantly differently from 0. In their study, the returns to be explained are 25 stock portfolios formed on the basis of size and book-to-market equity. Testing intercepts are jointly equal to zero is based on Gibbons, Ross and Shanken (1989) who suggest an F-test under the assumption that the returns and explanatory variables are normal and the true intercepts are 0. Over the years different factors have been added to Fama and French (1992, 1993) model by different researchers. As a famous example, Carhart (1997) suggests momentum factor in his study. Also market microstructure factors including liquidity and information asymmetry costs are suggested to be included in the asset-pricing models (e.g. Brennan, Chordia and Subrahmanyam 1998; Easley, Havildkjaer and O'Hara 2002; Amihud 2002).

A portfolio can be benchmarked against a market index for instance Standard and Poor's 500 index or Russell 1000 index to see if it has performed better than a market or not. The idea is that a good performance of a portfolio may not essentially be based on the portfolio manager's ability rather it might be due to desirable market conditions. Therefore, the excess return on a benchmark will represent the component of the portfolio's return that was generated by the portfolio manager (this excess return after adjustment for risk is called alpha).

For more discussion see Roll (1977). A market should represent all possible investment choices an investor can make. Therefore, one can argue that the reason that financial models fail in practice, is not because of their inaccuracy but it is because of choosing the wrong proxy for market (a.k.a. market identification problem).

Some of these conditions are relaxed or eliminated in more recent models, for example models that assume volatility is not constant but rather follow a different stochastic process.

As we argue below, widespread adoption has led to tipping points and feedback loops which have paradoxically led the practice of risk management itself to contribute to increased risk.

She notes that Sharpe and Litner (originators of CAPM) published subsequent work on investor heterogeneity.

Among this anecdotal evidence, large number of legal cases relating to insider trading can be counted. This evidence per se is a proof against (at least) the strong form of market efficiency.

Not only do economic agents not make the essentially optimal decisions based on the information they received, but their decisions are affected by the mechanism with which the information is presented to them. More on this will be discussed below.

Grossman and Stiglitz (1980), also Fama (1991) provide a thorough analysis of the difficulties in using market efficiency tests and some abnormalities that cannot be explained through EMH. For instance, the positive autocorrelation of daily or weekly returns, price swings from fundamental values, reversals in winners and losers (overreactions) also known as momentum and firm size effects that are frequently observed in data are not consistent with the EMH.

Levy's theorem (for more information see Shreve 2004, 158).

Ibid (153–158); the original is in Black and Scholes (1973).

Also known as Expected Utility Theory (see Kahneman and Tversky, 1979).

Examples that include predictable transaction volume or price changes are weekend effects on stock returns (French 1980, etc.), on exchange rates (Levi 1988) and in money markets (Eisemann and Timme 1984; Flannery and Protopapadakis 1988). Also December and January effects (turn-of-the-year effect) have been observed continuously over time (Rozeff and Kinney 1976). Kamstra, Kramer, and Levi (2000) also provide evidence that a repetitive anomaly can be detected around daylight saving time changes.

Keynes (1936) refers to a newspaper promotion in which the object was to select the contestant that most other participants would choose as the most beautiful. Thus, the ‘beauty contest’ was not about which woman was in each individual's opinion the most beautiful, but rather a wager on what the average opinion was of who was most beautiful. In an iterative game (e.g. the stock market) this can become the average opinion of the average opinion ad infinitum, in short, a cascading and/or herding effect.

When cost of obtaining information is low, more likely, people collect information themselves. When it is high, most likely they herd.

Cascading effects are dynamic over time and condition dependent, making measurement extremely difficult. As conditions evolve (e.g. innovations in communications and financial instruments; changes in politics regimes) they feedback into cascading tendencies.

Even if real-time comprehensive data could be collected, its analysis would need to have perfect understandings both of present conditions and those likely to occur in the future.

Myron Scholes, speech at NYU/IXIS conference on hedge funds, New York, September 2005.

One reason that there has been correlation among asset classes is due to model standardization among major market actors, which makes investments that were previously less correlated, more correlated, increasing downside risk and negating to some degree the whole point of diversification.

Including but not limited to the European Union (Capital Requirements Directive), United States (Dodd-frank Wall Street Reform and Consumer Protection Act) and G-20 (Basel III Accord).

Under Bank of International Settlement's Financial Stability Board's ‘Guidance to Assess the Systemic Importance of Financial Institutions, Markets and Instruments: Initial Considerations’ reported to G20 Finance Ministers and Governors in October 2009, A SIFI is defined as a financial institution who's ‘failure or malfunction causes widespread distress, either as a direct impact or as a trigger for broader contagion’.

That is when stakeholders of a SIFI believe that the government will bail it out at the time of non-viability they do not have an incentive anymore to incur the cost of monitoring the SIFI. As a result there is no effective market mechanism to prevent SIFI's managers from excessive risk taking.

For more information see Basel Committee on Banking Supervision's ‘Proposal to Ensure the Loss Absorbency of Regulatory Capital at the Point of Non-Viability’, August 2010.

a.k.a. market discipline, see Flannery and Sorescu (1996) for a detailed definition. Balasubramnian and Cyree (2011) show that market discipline has weakened after the US government started to bail-out financial institutions such as Long-term Capital Management in 1998.