1. 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

2. 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

3. 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

4. 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

5. 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 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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 ,
9/19/2018
Antti Pirjetä