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Multifactor Risk Models and Heterotic CAPM

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  • Zura Kakushadze
  • Willie Yu

Abstract

We give a complete algorithm and source code for constructing general multifactor risk models (for equities) via any combination of style factors, principal components (betas) and/or industry factors. For short horizons we employ the Russian-doll risk model construction to obtain a nonsingular factor covariance matrix. This generalizes the heterotic risk model construction to include arbitrary non-industry risk factors as well as industry risk factors with generic "weights". The aim of sharing our proprietary know-how with the investment community is to encourage organic risk model building. The presentation is intended to be essentially self-contained and pedagogical. So, stop wasting money and complaining, start building risk models and enjoy!

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  • Zura Kakushadze & Willie Yu, 2016. "Multifactor Risk Models and Heterotic CAPM," Papers 1602.04902, arXiv.org, revised Mar 2016.
    • Handle: RePEc:arx:papers:1602.04902
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    1. Wayne E. Ferson & Campbell R. Harvey, 1999. "Conditioning Variables and the Cross Section of Stock Returns," Journal of Finance, American Finance Association, vol. 54(4), pages 1325-1360, August.
    2. Scholes, Myron & Williams, Joseph, 1977. "Estimating betas from nonsynchronous data," Journal of Financial Economics, Elsevier, vol. 5(3), pages 309-327, December.
    3. John Y. Campbell & Martin Lettau & Burton G. Malkiel & Yexiao Xu, 2001. "Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk," Journal of Finance, American Finance Association, vol. 56(1), pages 1-43, February.
    4. Jagannathan, Ravi & Wang, Zhenyu, 1996. "The Conditional CAPM and the Cross-Section of Expected Returns," Journal of Finance, American Finance Association, vol. 51(1), pages 3-53, March.
    5. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    6. Motta, Giovanni & Hafner, Christian M. & von Sachs, Rainer, 2011. "Locally Stationary Factor Models: Identification And Nonparametric Estimation," Econometric Theory, Cambridge University Press, vol. 27(6), pages 1279-1319, December.
    7. Acharya, Viral V. & Pedersen, Lasse Heje, 2005. "Asset pricing with liquidity risk," Journal of Financial Economics, Elsevier, vol. 77(2), pages 375-410, August.
    8. Stephen A. Ross, 2005. "Mutual Fund Separation in Financial Theory—The Separating Distributions," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 10, pages 309-356, World Scientific Publishing Co. Pte. Ltd..
    9. Chen, Nai-Fu & Grundy, Bruce & Stambaugh, Robert F, 1990. "Changing Risk, Changing Risk Premiums, and Dividend Yield Effects," The Journal of Business, University of Chicago Press, vol. 63(1), pages 51-70, January.
    10. Ng, Victor & Engle, Robert F. & Rothschild, Michael, 1992. "A multi-dynamic-factor model for stock returns," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 245-266.
    11. Kothari, S. P. & Shanken, Jay, 1997. "Book-to-market, dividend yield, and expected market returns: A time-series analysis," Journal of Financial Economics, Elsevier, vol. 44(2), pages 169-203, May.
    12. Roll, Richard & Ross, Stephen A, 1980. "An Empirical Investigation of the Arbitrage Pricing Theory," Journal of Finance, American Finance Association, vol. 35(5), pages 1073-1103, December.
    13. Campbell, John Y., 1987. "Stock returns and the term structure," Journal of Financial Economics, Elsevier, vol. 18(2), pages 373-399, June.
    14. Blume, Marshall E & Friend, Irwin, 1973. "A New Look at the Capital Asset Pricing Model," Journal of Finance, American Finance Association, vol. 28(1), pages 19-33, March.
    15. John Y. Campbell, Robert J. Shiller, 1988. "The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors," The Review of Financial Studies, Society for Financial Studies, vol. 1(3), pages 195-228.
    16. Pastor, Lubos & Stambaugh, Robert F., 2003. "Liquidity Risk and Expected Stock Returns," Journal of Political Economy, University of Chicago Press, vol. 111(3), pages 642-685, June.
    17. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    18. Banz, Rolf W., 1981. "The relationship between return and market value of common stocks," Journal of Financial Economics, Elsevier, vol. 9(1), pages 3-18, March.
    19. repec:bla:jfinan:v:58:y:2003:i:3:p:975-1008 is not listed on IDEAS
    20. Rosenberg, Barr, 1974. "Extra-Market Components of Covariance in Security Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 9(2), pages 263-274, March.
    21. Schwert, G William, 1990. "Stock Returns and Real Activity: A Century of Evidence," Journal of Finance, American Finance Association, vol. 45(4), pages 1237-1257, September.
    22. Shanken, Jay & Weinstein, Mark I., 2006. "Economic forces and the stock market revisited," Journal of Empirical Finance, Elsevier, vol. 13(2), pages 129-144, March.
    23. Bansal, Ravi & Viswanathan, S, 1993. "No Arbitrage and Arbitrage Pricing: A New Approach," Journal of Finance, American Finance Association, vol. 48(4), pages 1231-1262, September.
    24. Ross, Stephen A, 1978. "A Simple Approach to the Valuation of Risky Streams," The Journal of Business, University of Chicago Press, vol. 51(3), pages 453-475, July.
    25. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    26. Goyal, Amit & Pérignon, Christophe & Villa, Christophe, 2008. "How common are common return factors across the NYSE and Nasdaq?," Journal of Financial Economics, Elsevier, vol. 90(3), pages 252-271, December.
    27. Fama, Eugene F. & French, Kenneth R., 2015. "A five-factor asset pricing model," Journal of Financial Economics, Elsevier, vol. 116(1), pages 1-22.
    28. De Bondt, Werner F M & Thaler, Richard, 1985. "Does the Stock Market Overreact?," Journal of Finance, American Finance Association, vol. 40(3), pages 793-805, July.
    29. Andrew Ang & Robert J. Hodrick & Yuhang Xing & Xiaoyan Zhang, 2006. "The Cross‐Section of Volatility and Expected Returns," Journal of Finance, American Finance Association, vol. 61(1), pages 259-299, February.
    30. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-1304, September.
    31. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1113-1141, December.
    32. Connor, Gregory, 1984. "A unified beta pricing theory," Journal of Economic Theory, Elsevier, vol. 34(1), pages 13-31, October.
    33. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2005. "The Generalized Dynamic Factor Model: One-Sided Estimation and Forecasting," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 830-840, September.
    34. Hall, Anthony D. & Hwang, Soosung & Satchell, Stephen E., 2002. "Using Bayesian variable selection methods to choose style factors in global stock return models," Journal of Banking & Finance, Elsevier, vol. 26(12), pages 2301-2325.
    35. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
    36. Connor, Gregory & Korajczyk, Robert A., 1988. "Risk and return in an equilibrium APT : Application of a new test methodology," Journal of Financial Economics, Elsevier, vol. 21(2), pages 255-289, September.
    37. Basu, S, 1977. "Investment Performance of Common Stocks in Relation to Their Price-Earnings Ratios: A Test of the Efficient Market Hypothesis," Journal of Finance, American Finance Association, vol. 32(3), pages 663-682, June.
    38. Fama, Eugene F & MacBeth, James D, 1973. "Risk, Return, and Equilibrium: Empirical Tests," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 607-636, May-June.
    39. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
    40. Fama, Eugene F & French, Kenneth R, 1996. "Multifactor Explanations of Asset Pricing Anomalies," Journal of Finance, American Finance Association, vol. 51(1), pages 55-84, March.
    41. Narasimhan Jegadeesh & Sheridan Titman, 2001. "Profitability of Momentum Strategies: An Evaluation of Alternative Explanations," Journal of Finance, American Finance Association, vol. 56(2), pages 699-720, April.
    42. Lakonishok, Josef & Shleifer, Andrei & Vishny, Robert W, 1994. "Contrarian Investment, Extrapolation, and Risk," Journal of Finance, American Finance Association, vol. 49(5), pages 1541-1578, December.
    43. Daniel, Kent & Titman, Sheridan, 1997. "Evidence on the Characteristics of Cross Sectional Variation in Stock Returns," Journal of Finance, American Finance Association, vol. 52(1), pages 1-33, March.
    44. Jegadeesh, Narasimhan & Titman, Sheridan, 1993. "Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency," Journal of Finance, American Finance Association, vol. 48(1), pages 65-91, March.
    45. Heston, Steven L. & Rouwenhorst, K. Geert, 1994. "Does industrial structure explain the benefits of international diversification?," Journal of Financial Economics, Elsevier, vol. 36(1), pages 3-27, August.
    46. Fama, Eugene F & French, Kenneth R, 1992. "The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-465, June.
    47. William F. Sharpe, 1963. "A Simplified Model for Portfolio Analysis," Management Science, INFORMS, vol. 9(2), pages 277-293, January.
    48. Zura Kakushadze, 2014. "Russian-Doll Risk Models," Papers 1412.4342, arXiv.org, revised Nov 2017.
    49. Korajczyk, Robert A. & Sadka, Ronnie, 2008. "Pricing the commonality across alternative measures of liquidity," Journal of Financial Economics, Elsevier, vol. 87(1), pages 45-72, January.
    50. Ferson, Wayne E & Harvey, Campbell R, 1991. "The Variation of Economic Risk Premiums," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 385-415, April.
    51. Lo, Andrew W & MacKinlay, A Craig, 1990. "Data-Snooping Biases in Tests of Financial Asset Pricing Models," The Review of Financial Studies, Society for Financial Studies, vol. 3(3), pages 431-467.
    52. Carhart, Mark M, 1997. "On Persistence in Mutual Fund Performance," Journal of Finance, American Finance Association, vol. 52(1), pages 57-82, March.
    53. Lehmann, Bruce N. & Modest, David M., 1988. "The empirical foundations of the arbitrage pricing theory," Journal of Financial Economics, Elsevier, vol. 21(2), pages 213-254, September.
    54. Jason MacQueen, 2003. "The structure of multifactor equity risk models," Journal of Asset Management, Palgrave Macmillan, vol. 3(4), pages 313-322, March.
    55. Chen, Nai-Fu & Roll, Richard & Ross, Stephen A, 1986. "Economic Forces and the Stock Market," The Journal of Business, University of Chicago Press, vol. 59(3), pages 383-403, July.
    56. Shanken, Jay, 1987. "Nonsynchronous Data and the Covariance-Factor Structure of Returns," Journal of Finance, American Finance Association, vol. 42(2), pages 221-231, June.
    57. Liew, Jimmy & Vassalou, Maria, 2000. "Can book-to-market, size and momentum be risk factors that predict economic growth?," Journal of Financial Economics, Elsevier, vol. 57(2), pages 221-245, August.
    58. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    59. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    60. Shanken, Jay, 1990. "Intertemporal asset pricing : An Empirical Investigation," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 99-120.
    61. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    62. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    63. Dhrymes, Phoebus J & Friend, Irwin & Gultekin, N Bulent, 1984. "A Critical Reexamination of the Empirical Evidence on the Arbitrage Pricing Theory," Journal of Finance, American Finance Association, vol. 39(2), pages 323-346, June.
    64. Michael W. Brandt & Alon Brav & John R. Graham & Alok Kumar, 2010. "The Idiosyncratic Volatility Puzzle: Time Trend or Speculative Episodes?," The Review of Financial Studies, Society for Financial Studies, vol. 23(2), pages 863-899, February.
    65. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-162, April.
    66. Zhang, Chu, 2010. "A Reexamination of the Causes of Time-Varying Stock Return Volatilities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(3), pages 663-684, June.
    67. Zura Kakushadze, 2014. "4-Factor Model for Overnight Returns," Papers 1410.5513, arXiv.org, revised Jun 2015.
    68. Burmeister, Edwin & Wall, Kent D, 1986. "The Arbitrage Pricing Theo;ry and Macroeconomic Factor Measures," The Financial Review, Eastern Finance Association, vol. 21(1), pages 1-20, February.
    69. Chan, K. C. & Chen, Nai-fu & Hsieh, David A., 1985. "An exploratory investigation of the firm size effect," Journal of Financial Economics, Elsevier, vol. 14(3), pages 451-471, September.
    70. Black, Fischer, 1972. "Capital Market Equilibrium with Restricted Borrowing," The Journal of Business, University of Chicago Press, vol. 45(3), pages 444-455, July.
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    Cited by:

    1. Zura Kakushadze & Willie Yu, 2018. "Decoding stock market with quant alphas," Journal of Asset Management, Palgrave Macmillan, vol. 19(1), pages 38-48, January.
    2. Zura Kakushadze & Willie Yu, 2017. "How to combine a billion alphas," Journal of Asset Management, Palgrave Macmillan, vol. 18(1), pages 64-80, January.
    3. Zura Kakushadze & Willie Yu, 2017. "Dead Alphas as Risk Factors," Papers 1709.06641, arXiv.org.
    4. Zura Kakushadze & Willie Yu, 2016. "Statistical Industry Classification," Papers 1607.04883, arXiv.org, revised Dec 2018.
    5. Zura Kakushadze & Willie Yu, 2017. "*K-means and Cluster Models for Cancer Signatures," Papers 1703.00703, arXiv.org, revised Jul 2017.
    6. Zura Kakushadze & Willie Yu, 2019. "Machine Learning Risk Models," Papers 1903.06334, arXiv.org, revised Apr 2019.
    7. Zura Kakushadze, 2020. "Quant Bust 2020," Papers 2006.05632, arXiv.org.
    8. Zura Kakushadze & Willie Yu, 2017. "Notes on Fano Ratio and Portfolio Optimization," Papers 1711.10640, arXiv.org, revised Apr 2018.
    9. Zura Kakushadze & Willie Yu, 2016. "Statistical Risk Models," Papers 1602.08070, arXiv.org, revised Jan 2017.
    10. Kakushadze, Zura & Yu, Willie, 2016. "Factor models for cancer signatures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 527-559.
    11. Zura Kakushadze & Willie Yu, 2017. "Open Source Fundamental Industry Classification," Data, MDPI, vol. 2(2), pages 1-77, June.
    12. Zura Kakushadze & Willie Yu, 2017. "Decoding Stock Market with Quant Alphas," Papers 1708.02984, arXiv.org.
    13. Zura Kakushadze & Willie Yu, 2017. "Open Source Fundamental Industry Classification," Papers 1706.04210, arXiv.org, revised Dec 2017.
    14. Zura Kakushadze & Willie Yu, 2018. "Betas, Benchmarks and Beating the Market," Papers 1807.09919, arXiv.org.
    15. Zura Kakushadze & Willie Yu, 2018. "Dead alphas as risk factors," Journal of Asset Management, Palgrave Macmillan, vol. 19(2), pages 110-115, March.
    16. Zura Kakushadze & Willie Yu, 2021. "ETF Risk Models," Papers 2110.07138, arXiv.org.
    17. Zura Kakushadze & Willie Yu, 2016. "Factor Models for Cancer Signatures," Papers 1604.08743, arXiv.org, revised Jan 2017.

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