EQUITY FACTORS Guillaume SIMON 2 Contents 1 Introduction 1 1.1 From passive to active management . .1 1.1.1 A bit of history... .1 1.1.2 Deviating from the benchmark? . .2 1.2 Active management and the financial industry . .4 1.2.1 Generating alpha is a hard task . .4 1.2.2 A first (intuitive) definition of factors . .5 1.2.3 Active management? Not everywhere! . .6 1.2.4 From Factors to Smart Beta . .7 1.2.5 Finally, is Alpha Dead? . .9 1.2.6 Structure of this course . 10 2 A Statistical Toolkit 11 2.1 Modelling equity returns . 11 2.1.1 Discrete-time modelling . 11 2.1.2 Continuous-time modelling . 12 2.2 A first glance at equity returns’ moments . 13 2.3 Usual statistical assumptions on returns’ distribution . 13 2.4 Aggregating returns . 15 2.4.1 Aggregation in the asset-dimension on one period . 15 2.4.2 Aggregation in the time-dimension on a single asset . 15 2.4.3 General case . 15 2.5 Moment Estimation . 16 2.5.1 Sample counterparts . 16 2.5.2 Estimation under the Gaussian assumption . 16 2.5.3 Volatility estimators . 17 2.5.4 Skewness and kurtosis . 18 3 Equity Factors: General Presentation 23 3.1 The Capital Asset Pricing Model . 23 3.1.1 Lessons from the CAPM . 23 3.1.2 Some elementary CAPM theory . 25 3.1.3 Empirical illustration . 26 3.2 Factor Theory . 28 3.2.1 Extending the CAPM equation: the three types of factor models . 28 3.2.2 Macroeconomic Factors . 31 3.2.3 Statistical Factors . 32 3.2.4 Fundamental Factors with observable betas . 34 3.2.5 Fundamental Factors with estimated factors: Fama and French . 35 i 3.3 Open questions . 39 3.3.1 Factors, the minimal requirements . 39 3.3.2 So, what is the message? . 41 3.4 Factors and the financial industry . 41 3.4.1 ARP or Smart Beta? Long Only or Long-Short ? . 42 3.4.2 How does the financial industry use those ideas? . 44 3.4.3 The importance of portfolio construction . 44 3.4.4 The performance puzzle . 45 3.4.5 Factors or anomalies? . 45 4 Intermezzo : Backtesting 47 4.1 Backtesting . 48 4.1.1 Providing accurate backtests . 48 4.1.2 In/Out-Of-Sample . 48 4.1.3 Biases . 49 4.2 Performance statistics . 51 4.2.1 Sharpe ratio . 51 4.3 Statistical significance of performance . 56 4.3.1 Sharpe ratio annualization . 56 4.3.2 Testing significance with the Sharpe ratio . 57 5 Main Equity Factors 61 5.1 Presentation of main factors . 64 5.1.1 Value . 64 5.1.2 Momentum . 67 5.1.3 Size . 69 5.1.4 Low Vol . 73 5.1.5 Quality . 76 5.2 Correlation and statistical properties . 78 5.2.1 Foreword . 78 6 The Dark Side of Equity Factors 85 6.1 So many factors... 85 6.1.1 Number of factors and p-hacking . 85 6.1.2 Alpha decay . 87 6.2 Disappointing performance . 88 6.3 Implementation Costs . 89 6.3.1 Estimating costs . 90 6.3.2 The optimistic figures . 91 6.3.3 The pessimistic figures . 92 6.4 Crowding . 93 6.4.1 General intuition . 93 6.4.2 Some crowding measures . 94 6.4.3 The particular case of the value spread . 96 7 Stylized Facts on Equities 99 7.1 What are stylized facts? . 99 7.2 Stylized facts on stock returns . 100 7.2.1 Returns . 100 7.2.2 Volatility . 101 ii 7.2.3 Skewness . 104 8 Markets’ Heuristics 107 8.1 Objectives of this chapter . 107 8.1.1 Motivations . 107 8.1.2 Computations and numerical examples . 108 8.2 Risk . 109 8.2.1 Volatility . 109 8.2.2 Betas . 110 8.3 Correlations . 111 8.4 Stock size . 114 8.4.1 Market capitalization . 114 8.4.2 Turnover . 115 8.5 Biases and links between variables . 116 8.6 Heuristics for stock characteristics . 117 8.6.1 Dividends . 117 8.6.2 Earnings and multiples . 119 9 A Focus on Covariance Matrix 123 9.1 One Word On The Stock Covariance Matrix . ..