COMBINING FACTORS IN A PORTFOLIO Thierry Roncalli Head of Quantitative Research François Millet Head of Product Line Manager ETF & Indexing There s rapidly growing interest in constructing equity portfolios by risk factors, rather than by individual geographical markets and sectors. But how should factors be combined? François Millet, Product Line Manager for ETFs and Indexing at Lyxor Asset Management and Thierry Roncalli, Head of Quantitative Research, explore the origins of factor investing and argue that a dynamic tactical allocation approach using factors promises attractive risk-adjusted returns. THE LIMITS OF ALPHA Excess returns collectively referred to as alpha are earned by a portfolio manager in return for taking idiosyncratic risk: in other words, picking stocks. But the more diversified an equity portfolio becomes, the more difficult it is to generate alpha. In practice, many portfolio managers own too many stocks as they are reluctant to risk too large a gap in performance against their index benchmark. By doing this, they severely reduce their chances of adding value. There is plenty of evidence to support this claim. As long ago as 1986, Brinson, Hood and Beebower calculated that less than 10% of the average institutional portfolio s return is explained by security selection and market timing. In a report published in 2009 on the performance of the active managers of Norway s Government Pension Fund Global, Professors Ang, Goetzmann and Schaefer stated that exposure to common risk factors contributed over 99% of the fund s past variation in returns, with active risk contributing a tiny proportion. More anecdotally, Warren Buffett famously said, «if you can identify six wonderful businesses, that is all the diversification you need. So the greater the number of stocks you hold, the less chance you have of generating alpha. If you use more than one factor to measure shared risks, the possibilities for alpha are even slimmer. Alpha Falls as Number of Holdings Increases Alpha (in%) 30 20 10 0 0 10 20 30 Number of stocks in the portofolio *4F: Carhart s Four Factor model (market beta, low size, value, momentum). Source: Cazalet and Roncalli (2014) >> IN BRIEF >> Much of the past performance of active managers can be explained by exposure to common risk factors >> Factors have played a key role in the evolution of investment theory since the 19s >> Diversification across factors offers an alternative to traditional portfolio approaches. >> A dynamic tactical allocation exploits the tendency for short-term persistence in factor returns. 4F
THE RISE OF SMART BETA Over the last ten years, the way investors perceive the equity markets has changed. Before, following the theoretical framework of the Capital Asset Pricing Model (CAPM), many viewed investing as a simple dichotomy between beta and alpha. An investor would allocate part of his or her portfolio to an index-tracking fund to capture beta, the equity market risk premium. The remainder of the portfolio would be delegated to active managers in search of alpha. But with the accumulation of evidence that much of the historical performance of active managers can be explained by exposure to alternative risk premia, there is growing demand to access these premia by new, rules-based investment strategies. These are commonly referred to as smart beta. By contrast with CAPM, a portfolio construction approach that combines traditional beta, new betas and alpha can be described as a risk factor asset allocation framework 1. Incorporating New s Alpha Idiosyncratic Risk Other Risk premia Alpha New FACTORS HELP US UNDERSTAND PORTFOLIOS PERFORMANCE We view smart beta as any rules-based strategy that does not rely on the traditional approach of weighting portfolio constituents by their market capitalisation. There has been a sharp rise in inflows into smart beta funds in recent years: European smart beta ETF assets quadrupled between the end of 2013 and April 2015, for example. Factor strategies are an important sub-category of smart beta. As we mentioned earlier, there is a great deal of evidence that much of the historical performance of active managers can be explained by their exposure to common risk factors, such as value, low size, momentum and quality. Factor strategies aim to capture such risk premia in a transparent, rules-based manner. But it s also important to remember that the idea of factors is not new. Since CAPM was first published by Treynor, Sharpe, Lintner and Mossin in the early 19s, academics have introduced a number of theoretical modifications to better explain the empirical performance of investment portfolios. Common risk factors have played an important role in these explanations for over twenty years. Factors in the Evolution of Investment Theory 1961-1964 - Treynor/Sharpe/Lintner/Mossin introduce CAPM - Share performance = market risk + idiosyncratic risk The Equity Risk Premium 1968 - Jensen s alpha - Average risk-adjusted mutual fund return is negative after fees CAPM Source: Lyxor Asset Management Risk Factor framework We don t want to downplay the role of alpha as it hasn t disappeared. But alpha should be seen as the preserve of portfolio managers who take truly idiosyncratic risks. Those active managers who hold too many stocks and who are reluctant to take bets will end up being displaced by smart beta approaches, including factor portfolios. 1973 1992 1997 - Malkiel s «Random Walk down Wall Street» - Asset prices follow a random walk: persistent outperformance is impossible - Fama/French three-factor model - Stock returns explained by value and size factors in addition to market beta - Carhart s «On Persistence in Mutual Fund Performance» - Alpha of equity managers is not persistent if it is measured with respect to risk factors Source: Lyxor Asset Management (1) See the Lyxor Expert Opinions: Risk Factor Investing Explained (October 2014); Combining Active and Passive Management in a Portfolio (March 2015); Smart : Broader Than you Think (May 2015).
LYXOR S FACTOR FRAMEWORK Lyxor s equity market factor framework focuses on those alternative risk premia that have solid theoretical support and which are backed by empirical evidence. In addition to the market risk factor, the framework has five additional risk factors: the Fama-French factors of value and size, plus momentum, low beta and quality. The factor definitions we use are: Value: a composite of book-to-price, earnings yield and free cash flow yield Low size: market capitalisation Momentum: total return (with dividends reinvested) over the last 12 months Low beta: beta of the stock relative to its local market Quality: a composite of total equity/net debt, return on equity and net income/sales Each Lyxor JP Morgan single factor index is constructed using a homogeneous approach. We calculate the factor score of each stock within a starting universe and standardise it, before selecting a fixed number of stocks with the highest factor score, typically around 10% of the original set. We then weight stocks equally within each factor index, rebalancing the index monthly. By adding the five new risk factors to the market risk factor used in CAPM, we are able to explain a greater proportion of historical stock returns. For example, based on our analysis of past US equity portfolio returns, the six factors accounted for -% of past performance, compared with as little as % using a single factor model. LYXOR S EQUITY FACTOR FRAMEWORK Value Low o l Allocation Quality PORTFOLIO ALLOCATION: FROM ASSETS TO FACTORS Traditionally, asset allocators have constructed portfolios by diversifying across asset classes and, within individual asset classes, diversifying across geographical markets, sectors and industries. A factor-based allocation approach requires a rethink of this traditional method. But diversification across risk factor strategies makes a great deal of sense, particularly since the past correlation levels between individual factors have been quite weak. Low size % Value 52.7% % Low size Value Momentuml Low Quality Momentum 54.0% 19.7% % Low 61.4% 15.8% 61.3% % Quality 61.0% 37.1% 58.2% 54.9% % Source: Lyxor Asset Management, Richard and Roncalli (2015). Correlation levels are measured using returns relative to the MSCI Europe Index, January 2000 - January 2015. Past performance is not a guide to future returns. Whether allocation across factors should be strategic or tactical depends on investors time horizon and risk tolerance. Many large institutional investors are taking a longterm view of factors by embedding factor risk premia in the portfolio benchmark. For example, this was the recommendation of the authors of the study of the past performance of Norway s Government Pension Fund Global, the world s largest sovereign wealth fund. On the other hand, the performance of individual risk premia varies across market and economic cycles, generating opportunities for investors interested in tactical allocation approaches. Low Size Momentum Common risk (in %) 30 1F model 6F model 20 *1F: market beta factor model. 6F: 6 factor model (market beta, low size, value, quality, low beta, momentum). Source: Cazalet and Roncalli (2014) Source: Lyxor Asset Management, factor analysis of US equity portfolio returns. Past performance is not a guide to future returns.
BE LOCAL, NOT GLOBAL Factor investing is best conducted on a local or regional basis. If we implement the factor scoring process on a global basis we tend to arrive at portfolios that are heavily concentrated in particular geographical markets. Also, the performance of individual risk factor strategies has diverged across different markets. For example, the size factor has done well in the US, Europe and Japan over the period since 2000, but has underperformed in the Asia Pacific region. These performance differences often reflect differences in market structure. SIZE FACTOR RETURNS BY REGION Asia Pacific Europe Japan 130 North America 120 Source: Lyxor Asset Management and Kenneth French data library. The charts show the returns of the Fama-French SMB (Small Minus Big) factor in the respective geographical regions between 1995-2013 (1/1/95=).
A DYNAMIC FACTOR ALLOCATION APPROACH As can be seen from a heat map of factor performance since 2008, there has been a substantial variation in the returns of individual factors. Individual factors have also shown quite volatile performance: value, for example, was the bestperforming factor across European equities in 2009, 2012 and 2013, but the worst-performing in 2008, 2010 and 2011. This variation of course argues for a diversified approach to factor investing. But Thierry Roncalli and Jean-Charles Richard, quantitative researchers at Lyxor, have also identified an interesting fact: unlike asset class returns, risk factor returns exhibit some persistence over the short term. In other words, how individual factors performed over the previous month or months has a significant chance of predicting performance over the next month. A good starting point for a long-term, strategic allocation to factors is to use an equal risk contribution approach: individual factor weights are calculated on a monthly basis so as to contribute equally to the volatility of the overall factor portfolio. For investors wishing to add value, a dynamic tactical allocation approach exploits the tendency for the shortterm performance of risk factors to persist. By incorporating short-term expected returns into the asset allocation we can improve on the expected risk-adjusted return of the factor allocation 2. Based upon a recent analysis by Roncalli and Richard, using a back-test of Lyxor s factor framework and European equity market returns from 2000-2014, this so-called Active Risk Parity (ARP) approach to factor allocation contributed 7% a year in excess returns to the market portfolio and with lower historical volatility. The ARP approach had a modestly higher maximum historical drawdown than the market portfolio over that period. Equally-weighted Active RiskParity (ARP) Return 1.8 7.6 8.9 Volatility 20.2 18.2 16.9 Sharpe ratio 0.0 0.3 0.4 Excess return 5.8 7.0 Tracking error 8.4 8.9 Information ratio 0.7 0.8 Max. drawdown -58.5-65.7-63.2 Best month 14.2 17.6 15.8 Worst month -13.8-17.9-17 Correlation.9.2 0.8 0.8 Turnover (2x) 0.1 1.3 Source: Lyxor Asset Management, Richard and Roncalli (2015). MKT=market factor portfolio, EW=equally weighted factor portfolio, ARP=Active Risk Parity factor portfolio. Underlying market factor is the MSCI Europe index net total return. Returns are measured from January 2000-December 2014. Past performance is not a guide to future returns. Factor Performance Heat Map 2008 2009 2010 2011 2012 2013 2014 Low -41.0% Value76.1% Quality23.3% Low -2.2% Value32.8% Value30.5% Size10.7% Momentum-41.3% Size45.9% Momentum22.7% Quality-4.6% Quality24.2% Momentum29.8% Quality8.6% -43.6% Quality.1% Low 18.0% -8.1% Momentum24.0% Size25.0% Low 8.1% Size-47.1% 31.6% Size17.7% Momentum-9.1% 17.3% Quality20.2% Value7.0% Quality-55.4% Momentum22.3% 11.4% Size-23.3% Low 15.8% 19.8% 6.8% Value-68.6% Low 18.8% Value1.1% Value-31.0% Size4.8% Low 17.0% Momentum5.2% (2)See Thierry Roncalli (2014), Introducing expected returns into risk parity portfolios: a new framework for asset allocation, Lyxor research paper Lyxor Asset Management, Richard and Roncalli (2015), market factor is the MSCI Europe index net total return. Past performance is not a guide to future returns. This material and its content are confidential and may not be reproduced or provided to others without the express written permission of Lyxor Asset Management ( Lyxor AM ). This material has been prepared solely for informational purposes only and it is not intended to be and should not be considered as an offer, or a solicitation of an offer, or an invitation or a personal recommendation to buy or sell participating shares in any Lyxor Fund, or any security or financial instrument, or to participate in any investment strategy, directly or indirectly. It is intended for use only by those recipients to whom it is made directly available by Lyxor AM. Lyxor AM will not treat recipients of this material as its clients by virtue of their receiving this material. This material reflects the views and opinions of the individual authors at this date and in no way the official position or advices of any kind of these authors or of Lyxor AM and thus does not engage the responsibility of Lyxor AM nor of any of its officers or employees. Services and marks appearing herein are the exclusive property of SG and its affiliates, as the case may be. Services and marks appearing herein are the exclusive property of Lyxor AM and its affiliates, as the case may be. Ref. 631211 228220 Studio Société Générale +33 (0)1 42 14 27 05 06/2015