QUESTIONS

1. 1. Why is the portfolio sorts methodology used?
   2. What is an application of the portfolio sort methodology?
2. How is the interpretation of a factor model using stock returns influenced by the specification of time lag of the (or no time lag) dependent variable?
3. Explain some of the common inference problems that arise in cross-sectional regressions where the dependent variable is a stock's return.
4. 1. What are factor portfolios?
   2. What methodologies can be used to build these portfolios?
5. What is the difference between in-sample and out-of-sample testing?

¹ For a good overview of the most common issues, see Jonathan B. Berk, “Sorting out Sorts,” Journal of Finance 55, no. 1 (2000): 407–427 and references therein.

² See Richard C. Grinold and Ronald N. Kahn, Active Portfolio Management: A Quantitative Approach for Providing Superior Returns and Controlling Risk (New York: McGraw-Hill, 1999), the authors discuss the differences between the t-statistic and the information ratio. Both measures are closely related in their calculation. The t-statistic is the ratio of mean return of a strategy to its standard error. Grinold and Kahn state the related calculations should not obscure the distinction between the two ratios. The t-statistic measures the statistical significance of returns while the IR measures the risk-reward trade-off and the value added by an investment strategy.

³ Andrew J. Patton and Allan Timmermann, “Monotonicity in Asset Returns: New Tests with Applications to the Term Structure, the CAPM and Portfolio Sorts,” working paper, University of California–San Diego, 2009.

⁴ See, for example, Eugene F. Fama and Kenneth R. French, “The Capital Asset Pricing Model: Theory and Evidence,” Journal of Economic Perspectives 18, no. 3 (2004): 25–46.

⁵ One approach is to use the Bayesian or model averaging techniques. For more details on the Bayesian approach, see, for example, Svetlozar T. Rachev, John S. J. Hsu, Biliana S. Bagasheva, and Frank J. Fabozzi, Baysian Methods in Finance (Hoboken, NJ: John Wiley & Sons, 2008).

⁶ For a discussion of dealing with these econometric problems, see Chapter 2 in Frank J. Fabozzi, Sergio Focardi, and Petter N. Kolm, Quantitative Equity Investing (Hoboken, NJ: John Wiley & Sons, 2010).

⁷ John H. Cochrane, Asset Pricing (Princeton, NJ: Princeton University Press, 2005).

⁸ Whitney K. Newey and Kenneth D. West, “A Simple, Positive Semidefinite Heteroskedasticity and Autocorrelation Consistent Covariance Matrix,” Econometrica 56, no. 3 (1987): 703–708.

⁹ Donald W. K. Andrews, “Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation,” Econometrica 59, no. 3 (1991): 817–858.

¹⁰ Mitchell A. Petersen, “Estimating Standard Errors in Finance Panel Sets: Comparing Approached,” Review of Financial Studies 22, no. 1 (2009): 435–480.

¹¹ We cover Fama-MacBeth regression in this section.

¹² Ian D. Gow, Gaizka Ormazabal, and Daniel J. Taylor, “Correcting for Cross-Sectional and Time-Series Dependence in Accounting Research,” working paper, Kellogg School of Business and Stanford Graduate School, 2009.

¹³ Eugene F. Fama and James D. MacBeth, “Risk, Return, and Equilibrium: Empirical Tests,” Journal of Political Economy 81, no. 3 (1973): 607–636.

¹⁴ Fama and French, “The Capital Asset Pricing Model: Theory and Evidence.”

¹⁵ Cochrane, Asset Pricing.

¹⁶ See, for example, Grinold and Kahn, Active Portfolio Management A Quantitative Approach for Providing Superior Returns and Controlling Risk; and Edward E. Qian, Ronald H. Hua, and Eric H. Sorensen, Quantitative Portfolio Management: Modern Techniques and Applications (New York: Chapman & Hall/CRC, 2007).

¹⁷ Eric H. Sorensen, Ronald Hua, and Edward Qian, “Contextual Fundamentals, Models, and Active Management,” Journal of Portfolio Management 32, no. 1 (2005): 23–36.

¹⁸ A factor normalized z-score is given by the formula z-score = where f is the factor, is the mean and std(f) is the standard deviation of the factor.

¹⁹ Ronald Hua and Edward Qian, “Active Risk and Information Ratio,” Journal of Investment Management 2, no. 3 (2004): 1–15.

²⁰ We are conforming to the notation used in Qian and Hua, “Active Risk and Information Ratio.” To avoid confusion, Qian and Hua use dis() to describe the cross-sectional standard deviation and std() to describe the time series standard deviation.

²¹ The earnings estimates come from the IBES database. See Appendix A for a more detailed description of the data.

²² Leigh Sneddon, “The Tortoise and the Hare: Portfolio Dynamics for Active Managers,” Journal of Investing 17, no. 4 (2008): 106–111.

²³ Petter N. Kolm, “Multi-Period Portfolio Optimization with Transaction Costs, Alpha Decay, and Constraints,” working paper, Courant Institute of Mathematical Sciences, New York University, 2010.

²⁴ This derivation of factor portfolios is presented in Grinold and Kahn, Active Portfolio Management A Quantitative Approach for Providing Superior Returns and Controlling Risk.

²⁵ Dimitris Melas, Raghu Suryanarayanan, and Stefano Cavaglia, “Efficient Replication of Factor Returns,” MSCI Barra Research Insight, June 2009.

²⁶ An exception is the constraint on the number of assets that results in integer constraints.

²⁷ For a more detailed discussion on portfolio optimization problems and optimization software see, for example, Frank J. Fabozzi, Petter N. Kolm, Dessislava Pachamanova, and Sergio M. Focardi, Robust Portfolio Optimization and Management (Hoboken, NJ: John Wiley & Sons, 2007).

²⁸ Manfred Deistler and Eva Hamann, “Identification of Factor Models for Forecasting Returns,” Journal of Financial Econometrics 3, no. 2 (2005): 256–281.

²⁹ The hit rate is calculated as

where is one-step ahead realized value and is the one-step ahead predicted value.

³⁰ For calculation of this measure, see Francis X. Diebold and Roberto S. Mariano, “Comparing Predictive Accuracy,” Journal of Business and Economic Statistics 13, no. 3 (2005): 253–263.

³¹ Kenneth D. West, Forecast Evaluation”, in Handbook of Economic Forecasting, vol. 1, edited by Graham Elliot, Clive W. J. Granger, and Allan G. Timmermann (Amsterdam: Elsevier, 2006).

³² Joseph D. Piotroski, “Value Investing: The Use of Historical Financial Statement Information to Separate Winners from Losers,” Journal of Accounting Research 38, no. 3 supplement (2000): 1–41.

³³ The nine factors are return on assets, change in return on assets, cash flow from operations scaled by total assets, cash compared to net income scaled by total assets, change in long-term debt/assets, change in current ratio, change in shares outstanding, change in gross margin, and change in asset turnover.

³⁴ Eric H. Sorensen, Ronald Hua, Edward Qian, and Robert Schoen, “Multiple Alpha Sources and Active Management,” Journal of Portfolio Management 30, no. 2 (2004): 39–45.

³⁵ Eric H. Sorensen, Ronald Hua, and Edward Qian, “Contextual Fundamentals, Models, and Active Management,” Journal of Portfolio Management 32, no. 1 (2005): 23–36.

³⁶ Vadim Zlotnikov, Ann Marie Larson, Wally Cheung, Serdar Kalaycioglu, Ronna D. Lao, and Zachary A. Apoian, “Quantitative Research—January 2007: Survey of Quantitative Models—Vastly Different Rankings and Performance, Despite Similarity in Factor Exposures,” Bernstein Research, January 16, 2007.

³⁷ Vadim Zlotnikov, Ann Marie Larson, Serdar Kalaycioglu, Ronna D. Lao, and Zachary A. Apoian, “Quantitative Research: Survey of Quantitative Models—Continued Emphasis on EV/EBIT, Momentum, Increased Focus on Capital Use; Some Evidence on Non-linear Factor Implementation; Low Return Consistency,” Bernstein Research, November 21, 2007.

³⁸ We use a combination of growth, value, quality, and momentum factors. The appendix to this chapter contains definitions of all of them.

³⁹ See Joseph A. Cerniglia and Petter N. Kolm, “Factor-Based Trading Strategies and Market Impact Costs,” working paper, Courant Institute of Mathematical Sciences, New York University, 2010.

⁴⁰ Matthew S. Rothman, “Turbulent Times in Quant Land,” Lehman Brothers Equity Research, August 9, 2007; and Kent Daniel, “The Liquidity Crunch in Quant Equities Analysis and Implications,” Goldman Sachs Asset Management, December 13, 2007 presentation from The Second New York Fed-Princeton Liquidity Conference.

⁴¹ We ran additional analysis on the model by extending the holding period of the model from 1 to 3 months. The results were much stronger as returns increased to 1.6% per month for a two-month holding period and 1.9% per month for a three-month holding period. The risk as measured by drawdown was higher at −17.4% for a two-month holding period and −29.5% for the three-month holding period.

⁴² Atsushi Inoune and Lutz Kilian, “In-Sample or Out-of-Sample Tests of Predictability: Which One Should We Use?” working paper, North Carolina State University and University of Michigan, 2002.

⁴³ Jyh-Huei Lee and Dan Stefek, “Do Risk Factors Eat Alphas?” Journal of Portfolio Management 34, no. 4 (2008): 12–24.

⁴⁴ Here we calculate the Sharpe ratio as portfolio excess return (over the risk-free rate) divided by the standard deviation of the portfolio excess return.

⁴⁵ Capital IQ, Compustat, http://www.compustat.com.

⁴⁶ Thomson Reuters, http://www.thomsonreuters.com.

⁴⁷ LTM refers to the last four reported quarters.