Active vs Passive Investment Strategies

Dr. Roberto Garrone

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Summary

1. Introduction

2. An historical perspective on alpha and management strategies

2.1. Developments from the Markowitz paradigm

2.2. The relation between alpha and management strategies

3. Performance evaluation for portfolio management

3.1. The active side of indexing strategies

3.2. The alpha side of beta

3.3. The biased-ness of traditional performance measurement

3.4. Stock picking and market timing skills

4. Final considerations

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1. Introduction

Active management is characterised as concerned with expectations of price movements, asset allocation, security selection and market timing while passive strategies are dominated by risk aversion. The evaluation of outcomes traditionally involves cap-weighted policy benchmarking. Actually, the nature of active and passive management is interrelated and historically bound to the evolution of portfolio theory.

2. An historical perspective on alpha and management strategies

In its simplicity, the MV paradigm is the most common framework amidst many alternatives praising more realistic descriptions of returns (Fama 1965, Elton and Gruber 1974, Kraus and Litzenberger 1976, Lee 1977, Elton and Gruber 1997), even if the extension to the multi period version of the problem rests over, among the others, the arduous assumption of independence of returns between periods (Campbell and Shiller 1988, Fama and French 1989).

2.1. Developments from the Markowitz paradigm

The extensive research is characterised by covariance matrixes estimation with index models: from the early single index market model popularised by (Sharpe 1963) to the various multi index versions with a pre-specified structure (Cohen and Pogue 1967, Chen, Roll et al. 1986, Fama and French 1992) and the ones based on factor and principal component analysis to extract indexes from the variance-covariance matrix (Roll and Ross 1980, Brown and Weinstein 1983, Cho, Elton et al. 1984, Dhrymes, Friend et al. 1984). Recent research widened the scope of the variance-covariance matrix introducing the copula extension.

2.2. The relation between alpha and management strategies

From an historical perspective active and passive management appear to be twins divided after the birth. Researchers provided a functional definition of Jensen’s alpha as either “the abnormal return above what would be earned if the CAPM held, and thus the non-equilibrium return the manager earned” or “the return the manager earned over a combination of an index fund (the market portfolio) and Treasury bills, where the combination is selected to have the same risk as the managed portfolio” (Elton and Gruber 1997). The main issue turned to be the identification of an efficient index. Some suggested a single index model assuming the CAPM (Treynor and Black 1973) and ignoring Fama results on the serial correlation of residuals (Fama 1968), thus proposing that “the investment in any stock should be proportional to the ratio of alpha to the variance of residual risk” (Elton and Gruber 1997). Instead, the arbitrage pricing theory “postulated that expected returns can be expressed as a linear function of sensitivities to more than one index” (Elton and Gruber 1997), in fact the multi index alternative of Ross (Ross 1978) determines a multi-dimensional space for the optimal solution with respect to expected return, betas and, whenever it occurs, residual risk for mis-priced securities.

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3. Performance evaluation for portfolio management

The earliest study on performance’s assessment for active and passive portfolios is attributed to Cowles (1933), its conclusions favoured active management but completely ignored risk. Later studies instead assumed the superiority of passive portfolios and adjusted the performance’s evaluation for risk either using total risk (Sharpe 1966, Friend 1970) or beta (Treynor 1965, Jensen 1969, Friend 1970). In fact, assuming perfectly efficient markets any active strategy should randomly outperform or underperform an adjusted passive strategy because abnormal returns are strictly random. Consequently, an active strategy outperforming net of fees should exhibit persistence and thus some managers may have superior information that can take advantage of modern portfolio theory (Elton and Gruber 1997).

3.1. The active side of indexing strategies

Therefore, indexing strategies are historically and theoretically grounded with the market efficiency theory. Empirical research summarized and pointed out that even weakly efficient markets (Malkiel 2003) that occasionally show anomalies (Fama and French 2008), predictability (Ferson 2002, Campbell, Lo et al. 2012), momentum (Barroso and Santa-Clara 2015) and irrational behaviours (De Bondt and Thaler 1995, Fama 1998, Edenfield 2003) do not provide any ex ante arbitrage opportunity. Others investigated the role of information and its managing agents (Dang, Moshirian et al. 2015) confirming to some extent the efficiency of markets. Another branch of research reconsidered the commonalities between the two strategies with respect to the arbitrary choices behind index building and re-balancement, as well as to the motivations indices as Dow Jones, Frank Russel and Standard & Poor’s have been built to the extent that he redefines them as paper indices (Fuller, Bing et al. 2010). Substantially, the practice of benchmarking against an index to replicate passive strategies is a form of active management because the difference in performance has been ascertained to originate from the selection-exclusion rule of the index; moreover, all-inclusive index are difficult and expensive to obtain (Roll 1977) thus any kind of selective index is applying to some extent active techniques that may correspond, for instance, to momentum strategies (Ranaldo and Häberle 2008). Empirical evidence confirmed the influence of the benchmark on the evaluated performance of mutual funds (Lehmann and Modest 1987).

3.2. The alpha side of beta

Further empirical studies (Chen, Roll et al. 1986, Fama and French 1993, Fama and French 2015) confirmed a multi-factor (value, size, momentum, liquidity, etc.) representation of assets returns capturing multiple sources of systematic risk rewarded by the relative risk premia. In other terms, passive management optimizes exposures to various sources of beta while active management optimizes sources of alpha unrelated to systematic beta risks. Interestingly, “certain returns that were once considered alpha are now recognized as newly isolated forms of beta” (Bender, Hammond et al. 2014). Renewed interest in this new type of (smart) beta or implicit alpha (Leibowitz and Bova 2007) fostered research, documenting the performance of naïve portfolios based on risk parity, equally weighted and minimum volatility strategies but without providing extensive theoretical support (Clarke, De Silva et al. 2006, Choueifaty and Coignard 2008, Martellini 2008, DeMiguel, Garlappi et al. 2011, Lee 2011). Essentially, either

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risk-based or return-based strategies exhibit higher returns but extensive time variation because the underlying risk premia do not guarantee long term portfolio performance, although minimum volatility (Scherer 2011) and value-weighted indices have shown long term correlations that may permit a rewarding diversification. For such reasons, risk premia are reported as substitutes for cap-weighted allocations, but also for active allocations on the ground that the performance of active managers seldom consists of persistent and substantial alpha (Malkiel 1995, Gruber 1996, Carhart 1997, Jones and Wermers 2011, Bender, Hammond et al. 2014) although interesting evidence highlights that constraints (corporate governance and regulations restricting fund managers’ choice of instruments, liabilities and strategies) strongly influence performance (Clarke, de Silva et al. 2002).

3.3. The biased-ness of traditional performance measures

The performance’s measurement based on normal distributed returns does not appear to be the best choice to assess the diatribe (Francis 2013). Some studies evidenced that traditional benchmarking procedures may not detect abnormal returns (Cornell 1979, Grinblatt and Titman 1989, Kothari and Warner 2001) arguing the underperformance is influenced by survivorship bias; thus, alternative benchmarks better explaining active performances have been developed (Petajisto 2013, Hunter, Kandel et al. 2014). But acceptance appears to be far, the general academic opinion arguments that value subsists (Jacobsen 2011) but it may not destined to shareholders (Shukla 2004). However, empirical exceptions confirming the existence of alpha occur, for instance when accounting for selected asset class (like institutional equity funds in EM) (Wenling 2013) and market movements (Aglietta, Briere et al. 2012). Specifically, the theoretical grounds of abnormal returns estimation with Jensen’s alpha require a correctly specified K-factor model (the joint hypothesis) and, accordingly, literature investigated omitted or wrong factors and incorrect betas. Using only the assumption of no-arbitrage, some argued that whenever money managers produce abnormal returns they also generate true arbitrage opportunities, as well as that nonzero Jensen’s alpha may appear with mis-specifications whenever an underlying asset price bubble is present (the illusion of arbitrage) (Jarrow and Protter 2013): indeed, such bubbles in incomplete markets are assessed with the study of relevant derivatives (Jarrow, Protter et al. 2010). 1

3.4. Stock picking and market timing skills

Researchers documented the superior hedge funds performance (Chung, Fung et al. 2015) , and showed its persistence, attributable to long-equity selections (the classic stock picking skill) (Yen, Hsu et al. , Fung and Hsieh 1999, Fung and Hsieh 2001, Mitchell and Pulvino 2001, Kosowski, Naik et al. 2007, Aggarwal and Jorion 2010, Avramov, Kosowski et al. 2011), compared to other institutional classes of funds which performed as predicted by classical results (Fama and French 2010); moreover such studies hold against contrasting results (Capocci and Hübner 2004, Griffin and Xu 2009) but the measure of risk is seldom clear. Substantially, few managers achieve the required performance (Cuthbertson, Nitzsche et al. 2010), despite previous results recognized significant evidence for market timing ability

The possibly equivalent presumption of creating real or apparent arbitrage opportunities may constitute a strand of research in order to 1assess past and present performance of actively managed funds, although beyond the scope of this assignment.

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(Avramov and Wermers 2006, Jiang, Yao et al. 2007, Kacperczyk, van Nieuwerburgh et al. 2014, Pástor, Stambaugh et al. 2015), which alone does not explain the point.

4. Final considerations

While I cannot argue in favour of one strategy or the other, I may suggest with confidence that a careful assessment of the performance of active funds cannot except from taking in consideration the price paid (Chung, Fung et al. 2007, French 2008, Kritzman 2012, Gennaioli, Shleifer et al. 2015) for management services that are expensive in nature and that may require considerable funds to be invested. Thus, active management does not appear a feasible strategy for retail investors while it may appeal to the wealthier, in substance and liquidity, which are traditionally hedge funds customers; but it is in this sense the funds performances must be categorised and analysed in order to possibly include the information “un-efficiently” available to elites that may reconcile the different strands of research.

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