Effects of style-based equity portfolio management What happens when investors allocate funds between different investment styles instead of individual stocks? Antti Pirjetä HSE & LTT Research

Three motives for dividing stocks in style portfolios Assigning stocks in categories simplifies the portfolio selection problem Instead of allocating money in Nokia or Stora Enso the decision is made between Telecom and Forest industries In practice the number of alternative stocks is of the magnitude that it is impossible to follow all of them Style investing simplifies the process of diversification It is easier to study the impact of an external shock to (say) ten different sectors instead of 100 individual stocks Creation of categories helps investors to evaluate the performance of money managers Returns to different styles are so divergent that, for instance, value and growth funds should be ranked within their styles 9/19/2018 Antti Pirjetä

Motivation for investigating style returns Market practice is to organise fund management by styles In Finland, large pension funds and life insurance companies are organised so that portfolio managers and analysts look at dedicated sectors. For instance, they might use the sector breakdown of DJ EuroStoxx. Mutual fund managers can also be classified as style investors, with style referring to their benchmark In my opinion, in the near future many fund managers will define themselves in the value-growth axis 9/19/2018 Antti Pirjetä

How to define an investment style? There are a number of approaches to do this Indexing: style is defined as a general (HEX, EuroStoxx) or a subindex (HEX Metals). Main advantage to this approach is, that it gives a clear benchmark Firm-Specific Characteristics:valuation multiples (P/E or P/BV) or by sector Recent performance: buying recent winners and selling losers (feedback trading) 9/19/2018 Antti Pirjetä

Time series of returns to style portfolios Returns to different styles (as well as individual stocks) tend to exhibit positive autocorrelation in the short run Lo & MacKinlay 1988: stocks are sorted in quintiles based on market cap. LM test for random walk using weekly returns and reject H0. They find that all portfolios exhibit positive autocorrelation with coefficients around 0.09 - 0.42. Serial correlation tends to be higher for small cap stocks. This phenomenon (positive autocorrelation of short term returns) is known as momentum in the finance literature 9/19/2018 Antti Pirjetä

Two types of traders Take the model of Barberis and Shleifer (2002, BS model). Investors are sorted in two classes: Switchers (feedback traders, noise traders) invest in styles that have performed well recently. Their behavior triggers momentum in this model. Fundamental traders (or arbitrageurs) buy stocks based on earnings forecasts. They tend to buy recent losers that look cheap based on (estimated) cash flows. Note the difference in decision making: switchers act on past prices, whereas fundamentalists act on forecasts 9/19/2018 Antti Pirjetä

Explaining momentum Behavioral finance explains short-term momentum by the underreaction story (see Shleifer 2000) According to it, investors are quite reluctant to change their beliefs about a firm(Conservatism Bias) Suppose that a company reports surprisingly positive earnings The market fails to appreciate that the news is followed by further positive disclosures and analyses (good news is compounded) As a result the stock will offer above-market returns in the short run (momentum) 9/19/2018 Antti Pirjetä

Return characteristics of portfolios vs. individual stocks A core finding of BS’s model is that given their setting, returns on individual stocks are correlated even if their cash flows are not Therefore, in the short run, style investing breaks the link between expected cash flows and value of the firm This is strictly because investors transfer funds between portfolios and hence not stocks Implication of the core finding: since funds are allocated between styles, stocks in the “shrinking” styles may suffer even if their cash flows are unchanged 9/19/2018 Antti Pirjetä

Covariance structure in the BS model Consider an economy with 2n risky assets, each being a claim to a dividend (D) paid at time T. SD is the covariance matrix of cash flows SD is so defined that all assets have unit variance of cash flows, however, covariances are style-dependent 9/19/2018 Antti Pirjetä

Effect of a cash flow shock (covariance structure) Suppose that there is a CF shock, for example unexpected earnings news A single asset i is affected by three factors: by market-wide factor fM by style-specific factor fS and by company-specific factor fi. Variance of a single asset is scaled to be one, i.e. diagonal elements of D are equal to one 9/19/2018 Antti Pirjetä

Covariance matrix of cash flows, 22 assets We have two styles Each style invests in two assets, hence there are four risky assets and assets 1,2 belong to style X, denote (i,j)  X assets 3,4 belong to style Y, denote (i,j)  Y M and S are constants that determine the relative powers of different factors Submatrix A refers to assets in same style, i.e. Cov(ei,t,ej,t) when (i,j) X or (i,j)  Y. Submatrix B refers to assets in different styles 9/19/2018 Antti Pirjetä

Elements of covariance matrix (cont’d) Submatrix B refers to assets in different styles Since the assets belong to different styles, market effect is the only factor moving them together 9/19/2018 Antti Pirjetä

Covariance matrix with 2n assets Take 2n risky assets divided in two styles assets 1,…,n are part of style X, denote (i,j)  X assets (n+1),…,2n are part of style Y, denote (i,j)  Y D is a (2n2n) matrix 9/19/2018 Antti Pirjetä

Implications of the model Take two assets that belong to the same style As suggested above, the model implies that their returns are less correlated than cash flows (Proposition 1). The opposite is true for two assets in different styles (Proposition 3). Moreover, when an asset is classified, its correlation with other assets (in that style) increases (Proposition 2) Interpretation of Prop 2: when a stock is admitted in an index, it becomes more correlated with the index. This happens regardless of cash flow characteristics. 9/19/2018 Antti Pirjetä

Implications of the model (formally) Proposition 1: For two assets (i,j) in same style, returns exhibit higher correlation than cash flows Proposition 3: For two assets (j,k) in different styles, returns exhibit lower correlation than cash flows Proposition 2: When an asset is classified in a style, correlation with style returns increases 9/19/2018 Antti Pirjetä

References and contact info Barberis & Shleifer (2002): Style Investing, Forthcoming in Journal of Financial Economics Lo & MacKinlay (1988) : Stock Markets Do Not Follow Random Walks, Review of Financial Studies 1: 41-66 Shleifer (2000): Inefficient Markets. Introduction to Behavioral Finance, Oxford University Press Contact info: Antti Pirjetä, LTT Research, tel+ 358 9 4313 8629, email pirjeta@hkkk.fi 9/19/2018 Antti Pirjetä