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Think on the Downside Multifactor Asset Pricing Models Based on Downside Risk and Their Performance Relative to the CAPM, FF3F and Momentum

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Think on the Downside Multifactor Asset Pricing Models Based on Downside Risk and Their Performance Relative to the CAPM, FF3F and Momentum MSc Thesis, Fall 2012 Stockholm School of Economics Department of Finance Think on the Downside Multifactor asset pricing models based on downside risk and their performance relative to the CAPM, FF3F and Momentum Author: Daniil Bargman1 Supervisor: Roméo Tédongap Abstract This paper introduces two new measures of asset performance in a downside risk-reward framework. The first measure, Omega-H, is an extension of the Omega ratio from Keating and Shadwick (2002a) that captures an asset’s idiosyncratic downside risk and upside potential. The second measure, the Vega, captures the asset’s systematic downside risk and upside potential. The two measures are used to construct two factor portfolios which act as an extension of the CAPM, thus forming a three-factor model incorporating downside risk. As a control, an alternative three- factor model is introduced that extends the CAPM to include factors formed on asset co-skewness and co-kurtosis with the market. The two models, called MOV (Market-Omega-Vega) and MCC (Market-Co-skewness-Co-kurtosis), are tested in a time series and in the cross-section together with the CAPM, the Fama-French three-factor model, and the Fama-French three-factor model extended by Momentum (Carhart, 1997). The Co-skewness and Co-kurtosis portfolios are priced by the other factor models, and the MCC model performs poorly in the cross-section. At the same time, the MOV model outperforms the FF3F model in the cross-section and prices the Momentum factor. Further tests show that the performance of all factor models in the cross-section is conditional on the market return for the period, consistent with conditionally varying risk premia. All factor models perform well in bull markets and poorly in bear markets. Unlike the other models, the MOV model outperforms the CAPM in extreme bear markets. A simple portfolio allocation test shows that including the Co-skewness, Co-kurtosis, Omega and Vega factors into an international index portfolio mitigates the home bias of US investors in portfolio allocation, consistent with Guidolin and Timmermann (2008). __________________________________________________________________________________________________________________________ Keywords: downside risk, MLPM, Omega, co-skewness, co-kurtosis, multifactor model, home bias 1 [email protected], [email protected] Table of Contents Introduction ................................................................................................................................................ 5 Asymmetric risk preferences in prior asset pricing literature ................................................. 7 Higher moments .................................................................................................................................................... 8 Downside risk ........................................................................................................................................................ 9 Partial Moments ................................................................................................................................................................... 10 The MLPM framework vs. the MV framework: a closer look at the MLPM-CAPM .................................. 11 The Omega ratio .................................................................................................................................................................. 13 Portfolio optimization with Omega ............................................................................................................................. 15 Some alternative asymmetric risk measures .......................................................................................................... 16 Kappa as an extension of Omega .................................................................................................................................. 18 Factor pricing through asymmetric betas .................................................................................................. 19 International portfolio diversification with asymmetric risk preferences .................................... 20 Omega-H and Vega as Measures of Downside Risk-Return Trade-off .................................. 22 Market assumptions .......................................................................................................................................... 22 The Hybrid Omega measure ........................................................................................................................... 23 The Vega Measure ............................................................................................................................................... 24 A note on portfolio optimization with the Vega measure ................................................................................. 27 The significance of Omega-H and Vega in the downside risk framework ....................................... 28 Factor Portfolios ..................................................................................................................................... 29 Formation Rules .................................................................................................................................................. 29 The Omega and Vega portfolios .................................................................................................................................... 30 The Coskewness and Cokurtosis portfolios ............................................................................................................. 31 Size, Value and Momentum ............................................................................................................................................. 32 Data ......................................................................................................................................................................... 33 Book value data .................................................................................................................................................................... 34 Portfolio properties and some preliminary results ................................................................................ 35 Persistence in portfolio composition .......................................................................................................................... 35 Correlation with the Kenneth French database factors ..................................................................................... 37 The properties of the finalized factor set .................................................................................................................. 38 Time series regression tests ............................................................................................................... 40 The CAPM ............................................................................................................................................................... 41 The FF3F model ................................................................................................................................................... 42 FF3F and Momentum ......................................................................................................................................... 43 The MOV model ................................................................................................................................................... 44 1 The MCC model .................................................................................................................................................... 45 Beta-Lambda representation tests and a time variation in cross-sectional risk premia, ...................................................................................................................................................................... 47 Cross-sectional tests with varying risk premia ........................................................................................ 49 Graphical results .................................................................................................................................................................. 51 An examination of the selected regression outputs ............................................................................................. 51 A closer look at the conditional performance of the factor models .................................................. 57 Implications of the asymmetric risk factors for international portfolio diversification 63 Summary and Conclusion .................................................................................................................... 67 References ................................................................................................................................................ 69 Appendix 1: A theoretical Vega-efficient portfolio ..................................................................... 72 Appendix 2: List of Data Variables .................................................................................................... 74 Appendix 3: All Time Series Test Results ....................................................................................... 76 Appendix 4a: Main Cross-Sectional Test Results, five-year periods ..................................... 77 Appendix 4b: Fama-MacBeth Procedure Results, five-year periods ....................................
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