# Alpha - the most abused term in Finance. Jason MacQueen Alpha Strategies & R-Squared Ltd

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1 Alpha - the most abused term in Finance Jason MacQueen Alpha Strategies & R-Squared Ltd

2 Delusional Active Management Almost all active managers claim to add Alpha with their investment process This Alpha is usually attributed to their Stock Selection skills This is nearly always Just Plain Wrong Slide 2

3 Some Common Examples Value Managers Screening on B/P, E/P, D/P, C/P, S/P, etc. Growth Managers Screening on EGR, EMOM, EVOL, DGR, etc. Large Cap / Small Cap Managers Diversified within Cap-delimited universes Socially Responsible Investment (SRI) Slide 3

4 Active Management Styles All of these are actually examples of common factor approaches to investment Each of them could be represented by a multi-factor model of stock returns Indeed, managers who use these type of approaches will often claim to be using a Multi-factor Model Slide 4

5 A Multi-factor Model of Stock Return K R it = β R + f =1 if ft α it Slide 5

6 How are these Models used? Most managers follow a standard process : Define a Followed List of investable stocks Identify a set of attributes linked to returns Screen the universe for stocks with attribute values above (or below) certain limit values Alternatively, sort the universe into N-tiles Convert the screen or sort into Buy/Hold/Sell Slide 6

7 How are the Attributes chosen? Typically, run cross-sectional regressions of stock attributes at the end of month t against stock returns over month t+1 Repeat over a number of months, and then select attributes with consistently positive (or negative) Information Coefficients (N.B. don t forget to convince yourself that this is not just data-mining) Slide 7

8 Multi-factor Model for Stock Selection The forecasting form of the model is : K E[ R + 1 ] = it βifte[ R ft+ 1] + ( E[ ai] + E[ ε it+ 1]) f = 1 Since the expected value of the error term is zero, this becomes : K E [ R ] = β E[ R ] + it+ ift ft+ 1 E[ a 1 i f = 1 ] Slide 8

9 Consequences - Betas If we relate the standard stock selection process back to the form of the underlying multi-factor model, we can see that : The attributes are being treated as proxies for the underlying stock betas ß if While the true stock betas are dimensionless scalars, the attributes may be in any arbitrary units (such as B/P or Capitalisation) Slide 9

10 Consequences - Factors Note that nothing is being said explicitly about the SIZE of the factor returns However, by implication, the SIGN of each factor return is presumed to be known Thus, screening for high B/P implies that the Value factor return is POSITIVE Screening for Small Capitalisation implies the Size factor return is NEGATIVE Slide 10

11 Consequences - Weighting? This overly-simplistic implementation of a multi-factor model for stock selection leads to an entirely artificial problem : How to weight the attributes? This arises simply because nothing is being said about the SIZE of the factor returns Slide 11

12 Consequences - Persistence? Whatever weights are used will be proxies for the SIZE of the missing factor returns In most multi-factor models, these weights add up to one, implying that the factors always work just as well In reality, factors sometimes work well and sometimes don t work at all (and sometimes even go into reverse!) Slide 12

13 Consequences - Alpha?! Nowhere in the standard process is there any attempt to forecast stock Alphas Instead, the focus is entirely on selecting stocks that have desirable Attributes Each stock is being treated simply as a set of exposures to a limited set of factors Slide 13

14 Multi-factor Model for Stock Selection? In a typical implementation this equation : K E [ R ] = β E[ R ] + it + ift ft + 1 E[ a 1 i f = 1 effectively becomes transformed into this one : ] E[ R K 1 ] = AttriftE[( S * W ) ] + it+ f f = 1 0 Slide 14

15 Features of this Implementation The Alpha term has disappeared, since no stock Alphas are actually being forecast Attribute values are being used instead of Betas The factor returns are replaced by a dummy sign variable S (+1 or-1) and an arbitrary weighting W Note that these returns are no longer in return units, but will be return per Attribute unit Slide 15

16 A Simple Example Suppose we follow a Small Cap/Value strategy, equally weighted Buy list is the top quintile of Small Cap, high B/P ratio stocks Sell list is the bottom quintile of not-small (Large) Cap, not-high (low) B/P ratio stocks The model is equally-weighted, so we assume that the SIZE of the two factor returns are equal Slide 16

17 Comments It seems highly unlikely that : Small Cap is always better than Large Cap Value stocks always do better than the market The Return to Value is always the same as the Return to Small Cap In reality, we know that while Value and Small Cap do often work, sometimes they don t Slide 17

18 Oh, Yes - the Scaling Problem If stock A has half the Capitalisation of stock B is it twice as attractive? What if its B/P ratio is twice as large? These scaling issues are often addressed by simply normalising the attributes However, this simply makes the attributes LOOK the same it doesn t necessarily make them equally significant Slide 18

19 Comment on IC analysis The conclusions we can draw from the IC analysis are actually quite limited We may be confident that higher B/P stocks tend to outperform lower B/P stocks, but we have no reason to believe that all stocks will react the same way to a given increase in their B/P ratio In fact, different stocks may well react in different ways to the same change in B/P ratio Attributes may not be good proxies for betas Slide 19

20 A Better Way K + f = 1 E[ R ] = β E[ R it 1 ift ft + 1 ] Derive estimates of the true betas by assuming a linear relationship between the attribute and the underlying beta (Return-Space Rescaling - RSR) Model the (time-varying) factor returns and make actual forecasts of factor returns Slide 20

21 Features and Benefits - Betas RSR produces true dimensionless betas RSR recognises that not all stocks returns react to changes in attribute values to the same extent RSR also copes with different accounting conventions and investor perceptions RSR also deals with the scaling problem Slide 21

22 Features and Benefits - Factors Modeling the factor returns with FMPs recognises that they are time-varying in size and sign Various methods can be used to forecast factor returns, including Vector Auto-Regression, moving averages, and/or exogenous variables Forecasting the factor returns eliminates the (artificial) weighting problem, and allows for the possibility that factors sometimes stop working (i.e. factor returns become close to zero) Slide 22

23 Features and Benefits - Risk Turning a stock selection process into a true multi-factor model also has other advantages : A corresponding risk model can be developed This can be used to ensure that portfolio risk consists mainly of the factor bets that are expected to be rewarded Performance attribution will provide useful feedback on the value and consistency of the Stock Selection Model Slide 23

24 Back to Alpha True Alphas are stock specific returns Assume a simple CAPM risk model in which Market risk = 18% p.a. Specific risk = 32% p.a. (on average) The model has an average stock R 2 of 24% Even so, stock risk diversifies away quickly Slide 24

25 Number of Holdings Problem For a portfolio s performance to contain a meaningful Alpha, it would probably need to have less than 20 holdings Note, however, that the CAPM is not normally used as a risk model, for the simple reason that there are actually many more sources of co-variation in stock returns than the market Slide 25

26 Adding factors makes it harder In a more realistic multi-factor risk model, the average R 2 would be more like 35-40%, and the average Specific risk around 24% Such a model would identify a larger part of the portfolio risk as factor-related, and leave an even smaller part to generate true Alpha The number of holdings in a true (long-only) Alpha portfolio would need to be even smaller Slide 26

27 Portfolio Diversification 100% Multi-factor model CAPM 90% Portfolio R-squared 80% 70% 60% 50% Number of stocks held in portfolio Slide 27

28 Choose your analysis! Systematic risk in a CAPM framework is likely to seem lower than in a multi-factor risk model This offers obvious possibilities for a manager to be able to report a higher Portfolio Alpha This can be done by simply deducting from the portfolio return the market/benchmark-related return, and claiming everything else as Alpha This Alpha is risk-adjusted portfolio return, but using an inappropriate risk model Slide 28

29 Summary 1 the Strategies Alpha is properly defined as factor-riskadjusted stock specific return Most active investment strategies are based on common factor approaches These strategies may well generate outperformance, but this is not Alpha True Alphas are very rarely forecast Slide 29

30 Summary 2 - the Holdings Most institutional portfolios are diversified to the point that their stock specific risk is a very small proportion of their total risk Such high diversification is inconsistent with achieving portfolio Alpha, but is consistent with pursuing a common factor active strategy True Alpha portfolio managers would only have a very small number of holdings (Warren Buffet?) Slide 30

31 Summary 3 - the Analysis Most claims of portfolio Alpha are based on an inappropriate analysis of return, such as only recognising the portfolio s beta to the benchmark (the CAPM) To demonstrate genuine Alpha, the risk model should include all the common factors used in the investment strategy Slide 31

32 Postscript Managers rarely consider more than a dozen factors, although there are clearly many other common factor effects at work It would be possible to eliminate Alpha altogether, by simply having enough factors in the risk model The degree to which stock return is factorrelated or Alpha is essentially arbitrary Slide 32

33 ALPHA!! The most abused term in Finance Slide 33

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