Multi-Alpha Equity Porfolios

1. Multi-Alpha Equity Porfolios R. Leote de Carvalho, X. Lu, P. Moulin Inquire Europe – October 2013, Munich, Germany

2. Smart Beta indexes • Smart Beta indexes have gained huge popularity • Risk-based Indexes: Minimum Variance, Maximum Diversification, Risk Parity • Fundamental Indexation: stock weights determined by company fundamental data • Back-tests show that Smart Beta indexes would have performed better than market-cap • More performance • Less risk • Or both • The buzz of the moment

3. What is new in Smart Beta indexes • “Demystifying Equity Risk-Based Strategies: an alpha plus beta description” Seminar Inquire Europe, Autumn 2012, 28 - 30 October, Pera Palace Hotel Istanbul, Turkey • Risk-based Smart Beta indexation relies on alpha from Low Volatility and Small Cap stocks • Others have since shown: • Fundamental Indexation relies on alpha from Value stocks • Perhaps not that much new… clumsy approaches exposed to market anomalies? Smart Beta indexes are a new form of systematic active strategies where stock selection is based on a formula that determines how portfolios deviate from the market cap index. Despite being transparent with the formula made public, many can be quite complex. And finally, Smart Beta seems to rely on well known market anomalies but in a somewhat clumsy way.

4. How to build a multi-alpha portfolio? Objective: Build an active portfolio invested in equities Combine different sources of alpha Make sure the portfolio complies with constraints Make sure that constraints have the least possible impact on your alpha • Let’s step back and reconsider the problem again

5. How to build a multi-alpha portfolio? Identify your sources of alpha Allocate a risk budget to each source of alpha Build an unconstrained target portfolio Get implied returns for unconstrained target portfolio Optimise from implied returns applying constraints R Leote de Carvalho, X. Lu, P. Moulin Multi-Alpha Equity Portfolios: An Integrated Risk Budgeting Approach for Robust Constrained Portfolios. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2173230 • The steps required

6. Identify your sources of alpha Allocate a risk budget to each source of alpha Build an unconstrained target portfolio Get implied returns for unconstrained target portfolio Optimise from implied returns applying constraints

7. Identify sources of alpha • Where to find sources of alpha? • In any strategy that can generate returns higher than predicted by beta • Examples of quantitative sources of alpha: • 1972: Low Risk anomaly (Haugen & Stein, Wiscosin University) • 1977: Value anomaly (Basu, Journal of Finance) • 1979: Earnings Revisions anomaly (Lakonishok and Givoly, Journal of Acc. and Economics) • 1981: Small Cap stocks anomaly (Banz, Journal of Financials Economics) • 1990: Short-term reversal anomaly (Jagadeesh, Journal of Finance) • 1993: Momentum anomaly (Jagadeesh and Titman, Journal of Finance) • 1996: Accruals anomaly (Sloan, The Accounting Review)

8. Identify your sources of alpha Allocate a risk budget to each source of alpha Build an unconstrained target portfolio Get implied returns for unconstrained target portfolio Optimise from implied returns applying constraints

9. Allocate a risk budget to each source of alpha • Given expected information ratios and strategy variance-covariance matrix • Markowitz if correlations not too large • Re-sampling from history (bootstrapping optimisation) • Uncorrelated alpha strategies • Risk budget allocate to each alpha strategy is proportional to expected information ratio • Same expected Information Ratio for each alpha strategy but different correlations • Maximum diversification allocation of alpha strategies • No accurate forecast of returns or correlations • Equal risk budget allocation to each alpha strategy • How much do you know? How accurately?

10. Identify your sources of alpha Allocate a risk budget to each source of alpha Build an unconstrained target portfolio Get implied returns for unconstrained target portfolio Optimise from implied returns applying constraints

11. Build an unconstrained target portfolio • How much alpha? • Low Volatility and Value Sector Neutral • Correlation of low volatility and value alpha by sector

12. Build an unconstrained target portfolio • How much alpha? • Low Volatility and Value Sector Neutral • Correlation of low volatility and value alpha by sector Average = 30% Average = 0% Average = 30%

13. Build an unconstrained target portfolio • Alpha Capture strategy based on long-short portfolios • long stocks with expected positive alpha • short stocks with expected negative alpha • Quantitative sources of alpha: • Exposure to factors predicts stock alpha • Value • Low Volatility • Momentum • Small cap • Etc

14. Build an unconstrained target portfolio • Quantitative alpha can be captured using the set of selected of factors: • Each factor contributes to the final stock tilts via a long/short portfolio. • Long-short factor tilts = active stock deviations from benchmark: • Leverage to each long-short factor tilt to meet assigned risk budget • Leverage to combination of long-short factor tilts to meet target tracking error risk budget • Add tilts to Benchmark Market Capitalisation Index • Target constant level of ex-ante portfolio tracking error risk • Keep constant he contribution of each alpha factor to portfolio tracking error • Target portfolio = Benchmark Market Capitalisation Index + Long-Short factor tilts

15. Build an unconstrained active target portfolio • Combine the different systematic alpha portfolios

16. Identify your sources of alpha Allocate a risk budget to each source of alpha Build an unconstrained target portfolio Get implied returns for unconstrained target portfolio Optimise from implied returns applying constraints

17. Get implied returns for unconstrained active target portfolio • The implied return of each stock are return which renders the portfolio efficient • Implied returns are obtained through reverse optimisation of the unconstrained portfolio • What are implied returns?

18. Identify your sources of alpha Allocate a risk budget to each source of alpha Build an unconstrained target portfolio Get implied returns for unconstrained target portfolio Optimise from implied returns applying constraints

19. Optimise from implied returns applying constraints • The efficient portfolio obtained from the implied returns using constrained optimisation will: • respect the constraints while minimizing their impact! • represent as much as possible the views in the original unconstrained portfolio • Robust optimisation

20. Robust framework for model portfolio construction Starting unconstrained portfolio • How are constraints handled? Do not apply constraints Implied returns Apply constraints Target same TE as in unconstrained portfolio Target same risk aversion as in unconstrained portfolio Target same TE as in unconstrained portfolio Starting unconstrained portfolio Portfolio with the lowest tracking error against unconstrained portfolio Portfolio with the largest correlation against unconstrained portfolio Constraints impact specific risk exposures. Exposures to risk factors are mimicked as much as possible.

21. 1. Combine Value, Low Volatility, Momentum and Small Cap • Build a benchmarked long-only constrained portfolio Jan-95 through Dec-11. USD. MSCI World index stock universe. Source http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2173230

22. 1. Combine Value, Low Volatility, Momentum and Small Cap • Build a benchmarked long-only constrained portfolio Almost indistinguishable performance for different portfolios, whether constrained or unconstrained! Jan-95 through Dec-11. USD. MSCI World index stock universe. Source http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2173230

23. 1. Combine Value, Low Volatility, Momentum and Small Cap 3 approaches to ex-ante risk budgeting Ex-post, risk budgets are in line with ex-ante, even with constraints. First achievement of the framework! • Build a benchmarked long-only constrained portfolio Jan-95 through Dec-11. USD. MSCI World index stock universe. Source http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2173230

24. 1. Combine Value, Low Volatility, Momentum and Small Cap • Build a benchmarked long-only constrained portfolio Performance and risk are little impacted by constraints. Long only implementation with much smaller number of stocks still achieves comparable results. Second achievement of the framework! Capturing alpha around constraints is possible if the portfolio is constructed thoughtfully. Jan-95 through Dec-11. USD. MSCI World index stock universe. Source http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2173230

25. 2. Combine Value, Low Volatility, Momentum and Profitability • Long-only • Max 200 stocks • Max 2% weight for each stock • 5% tracking error risk against the benchmark index • Turnover constrained to max 150% annual • Build a benchmarked long-only constrained portfolio

26. 2. Combine Value, Low Volatility, Momentum and Profitability • Build a benchmarked long-only constrained portfolio Source: Theam, BNP Paribas Investment Partners

27. 2. Combine Value, Low Volatility, Momentum and Profitability • Attribution analysis Based on monthly returns Source: Theam, BNP Paribas Investment Partners

28. 2. Combine Value, Low Volatility, Momentum and Profitability • Performance breakdown of 1995-2013: contributions to excess returns Profitability Value Momentum Low Volatility Source: Theam, BNP Paribas Investment Partners

29. 2. Combine Value, Low Volatility, Momentum and Profitability Constraints • Decomposition of ex-post active risk allocation compared to ex-ante target Profitability (15% ex-ante unconstrained target) Value (20% ex-ante unconstrained target) Momentum (30% ex-ante unconstrained target) Low Volatility (35% ex-ante unconstrained target) Final portfolio, all constraints including turnover constraint Source: Theam, BNP Paribas Investment Partners

30. Conclusions • Separates the process of mixing unconstrained views from managing of constraints • Different approaches to mixing unconstrained views depending of information available • In any case, at stock level, all boils down to • weighted average of portfolios representing views to form unconstrained target portfolio • Back-test results show application to real portfolios • Intuition confirmed • Large correlation between unconstrained and constrained results • Management of portfolio constraints and risk while keeping simplicity • Achieves similar results to “Index + Long-Short hedge fund” while staying long-only • Intuitive but robust approach to portfolio construction

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