Investigating International Asset Pricing Anomalies: Nonlinear SDFs and Time-Varying Risk Premiums

1. April 2007 • based on joint work with … • Daniel Hung • Durham Business School Global Price of Market Risk And Country Inflation Devraj Basu Devraj Basu Cass Business School

2. Introduction overview literature theory results extensions investigating international asset pricing anomalies … International Anomalies • International asset pricing anomalies have been observed-the value effect (Fama-French 1998), the momentum effect (Rouwenhorst 1998) • The international CAPM is unable to price these anomalies • The Fama-French factors, global or local arose to explain these anomalies • However Bansal, Hsieh and Vishwnathan (1993) suggested that nonlinear SDFs work better than linear models Devraj Basu Cass Business School

3. Introduction overview literature theory results extensions investigating international asset pricing anomalies … Nonlinear SDFs … • Higher moments of the market return had been used in the US context starting with Kraus and Litzenberger (1978) • More recently Harvey and Siddique (2000) and Dittmar (2002) used them to investigate asset pricing anomalies in the US • Errunza and Sy (2005) used country inflation and its higher powers to explain the international anomalies • Our goal is to use both global and local factors to try to price size, value and momentum effects in the US, UK and Japan Devraj Basu Cass Business School

4. Introduction overview literature theory results extensions investigating international asset pricing anomalies … Time-Varying Risk Premiums … • We first consider a global model with the World factor, its square and cube… • … and add to it country inflation and its square • A crucial aspect of our analysis is that the factor risk premiums are all time varying and are functions of lagged global variables (World index and term structure variables) • We compare performance of our model with the country-specific Fama-French factors Devraj Basu Cass Business School

5. predicted component set of (lagged) instruments for example … macro-economic indicators changes in the term-structure market sentiment indicators Introduction overview literature theory results extensions what is “conditioning information”? generic model: • asset returns given by … • with … • … no loss of generality! vector of traded asset returns unpredictable shock Devraj Basu Cass Business School

6. Introduction overview literature theory results extensions what can we do with “conditioning information”? using conditioning info … • we can model … • asset return predictability • serial correlation • seasonalities • time-varying moments • stochastic volatility • time-varying correlations • non-normality of returns • kurtosis (‘fat tails’) • skewness • time-varying risk premia • this allows us to study … • economic value of predictability • market timing • active asset management • conditional asset pricing • tests of factor models • time-varying ‘betas’ Devraj Basu Cass Business School

7. Introduction overview literature theory results extensions asset pricing in the presence of conditioning information pricing equation: • an SDF must satisfy … stochastic discount factor vector of ‘ones’ vector of traded asset returns Devraj Basu Cass Business School

8. Introduction overview literature theory results extensions asset pricing in the presence of conditioning information pricing equation: • an SDF must satisfy … stochastic discount factor vector of ‘ones’ vector of ‘weights’ given as … functions of instruments t-1 = f(zt-1) vector of traded asset returns Devraj Basu Cass Business School

9. Introduction overview literature theory results extensions asset pricing in the presence of conditioning information pricing equation: • an SDF must satisfy … taking unconditional expectations … Devraj Basu Cass Business School

10. price of portfolio Introduction overview literature theory results extensions asset pricing in the presence of conditioning information pricing equation: an SDF must satisfy … suppose we choose weights … so that E(1’t-1) = 1 this can be interpreted as the return on a managed portfolio! Devraj Basu Cass Business School

11. implication: • for any candidate SDF mt… • … the following are equivalent: • mt prices all traded assets • … conditionally correctly • mt prices managed portfolios • … unconditionally correctly Introduction overview literature theory results extensions asset pricing in the presence of conditioning information pricing equation: an SDF must satisfy … hence … … for all managed returnsrt = 1 Devraj Basu Cass Business School

12. Introduction overview literature theory results extensions asset pricing with conditioning information literature: • Chamberlain, Rothchild • E 51 (1983) • Hansen, Richard • E 55 (1987) • Ferson, Siegel • JF 56 (2001) • see also … • Cochrane “Asset Pricing” construct orthogonal representation of unconditionally efficient frontier extend CR’s framework to incorporate conditioning information derive weights of efficient portfolios as function of conditioning instruments Devraj Basu Cass Business School

13. Introduction overview literature theory results extensions tests of conditional asset pricing models literature: • Bansal, Hsieh, Vishwanathan (1993) • Ferson, Harvey • (1993) • Harvey, Siddique • (2000) • Errunza, Sy • (2005) Nonlinear SDFs for international pricing examine conditional international asset pricing models test augmented CAPM on US portfolios Country specific inflation factors Devraj Basu Cass Business School

14. Introduction overview literature theory results extensions conditional factor models generic factor model: asset returns are given by … vector of traded asset returns vector of factors residual (idiosyncratic risk) vector of factor loadings conditional expected return Devraj Basu Cass Business School

15. typically non-linear! Introduction overview literature theory results extensions conditional factor models generic factor model: factors loadings … asset returns are given by … • can be time-varying function … • … of conditioning info • capture asset’s exposure … • … to systematic risk factors • traditional approach: • linear function of instruments • in our framework: • solve for optimal loadings Devraj Basu Cass Business School

16. Introduction overview literature theory results extensions conditional factor models generic factor model: the residuals … asset returns are given by … • capture idiosyncratic risk … • … should not be priced! • properties: • zero mean • orthogonal to factor risk: • can be used to estimate model • … e.g. GMM Devraj Basu Cass Business School

17. Introduction overview literature theory results extensions conditional factor models generic factor model: SDF representation: asset returns are given by … • the following is equivalent: • there exist at-1 and Bt-1 so that • … is an admissible SDF • that is • … for all managed returns rt 1 Devraj Basu Cass Business School

18. Introduction overview literature theory results extensions tests of conditional factor models step 1: factor-mimicking portfolios with … the managed portfolio that has … maximal correlation with factor second-moment matrix of returns: mixed asset-factor moments: Devraj Basu Cass Business School

19. Introduction overview literature theory results extensions tests of conditional factor models step 2: • managed portfolio of factors • consider the set of returns … • … that can be written as • with • denote by RF … • … the set of all such returns rt managed portfolios made up of … factor-mimicking portfolios portfolio constraint Devraj Basu Cass Business School

20. managed portfolios of … traded base assets managed portfolios of … factor-mimicking portf’s Introduction overview literature theory results extensions tests of conditional factor models step 2: • now define … • frontier spanned by factors • consider the set of returns … • … that can be written as • with • denote by RF … • … the set of all such returns rt • maximum Sharpe ratio … • … spanned by base assets: • … and by the factors: Devraj Basu Cass Business School

21. Introduction overview literature theory results extensions tests of conditional factor models step 2: theorem: • managed portfolios of factors • consider the set of returns … • … that can be written as • with • denote by RF … • … the set of all such returns rt • we show … • for given set of factors … • … the following are equivalent: • the model admits an SDF • … of the form • there is a factor-portfolio that is • … unconditionally efficient • in other words, if 1 Devraj Basu Cass Business School

22. Introduction overview literature theory results extensions tests of conditional factor models just for the record … • the maximum Sharpe ratios are given by … • the latter is attained by the portfolio • with Devraj Basu Cass Business School

23. Introduction overview literature theory results extensions tests of conditional factor models An intermediate step • We also examine unconditional pricing • … that is if E(mR)=1where R are the base assets • This is via taking unconditional expectations of the original pricing equation • We test this by comparing • This is similar to the Gibbons-Ross-Shanken test, except that it is possible for the optimal factor Sharpe ratio to be higher than the fixed-weight asset Sharpe ratio Devraj Basu Cass Business School

24. Introduction overview literature theory results extensions tests of conditional factor models An intermediate step • We derive a heuristic test for • is asymptotically distributed as a chi-squared variable with (N-K)(1+J) degrees of freedom. The extra J degrees of freedom are to allow it to price the managed strategies Devraj Basu Cass Business School

25. Introduction overview literature theory results extensions synopsis: objectives: • in this paper … • … we develop the theory: • explicitly construct … • … factor-mimicking portfolio • develop definition of… • … ‘spanning distance’ • show distance proportional … • … to Sharpe ratio difference • explicitly characterize … • … optimal factor loadings • develop methodology … • … and investigate … • does optimal ‘scaling’ … • … improve performance? • do World skewness and kurtosis and country inflation • … really matter? Devraj Basu Cass Business School

26. Introduction overview literature theory results extensions results: Global versus Fama-French test results: US size portfolios Devraj Basu Cass Business School

27. Introduction overview literature theory results extensions results: Adding Country Inflation Factors test results Devraj Basu Cass Business School

28. Introduction overview literature theory results extensions results: US momentum portfolios test results: US Momentum Decile Portfolio Devraj Basu Cass Business School

29. Introduction overview literature theory results extensions results: Japanese Value Portfolios test results: Japan Book-to-Market Portfolios Devraj Basu Cass Business School

30. Introduction overview literature theory results extensions frontiers: US portfolios Devraj Basu Cass Business School

31. Introduction overview literature theory results extensions frontiers: UK portfolios Devraj Basu Cass Business School

32. Introduction overview literature theory results extensions frontiers: Japanese portfolios Devraj Basu Cass Business School

33. Introduction overview literature theory results extensions Premiums Model Implied Size, Value and Momentum Premiums • The US size, value and momentum premiums are 10.45%, 10.57% and 9.98% and the scaled five factor model captures over 90% of these premiums • The UK premiums are 8.27%, 12.59% and 7.84% and performance is similar although not quite as good • The Japanese premiums are lower and our model captures over 90% of these. • Scaled five factor augmented Fama-French under-performs except for US momentum and UK value premium. Unscaled model works best for US and UK value premiums Devraj Basu Cass Business School

34. Introduction overview literature theory results extensions Time Variation in Factor Risk Premiums Factor Risk Premiums • The predictive variables are market (World) and business cycle (term structure--How are the factor risk premiums correlated with these ? • The skewness and kurtosis factor risk premiums appear to be correlated with the market variable • The inflation risk factors appear to be functions of the term structure variables • Surprisingly, the Fama-French factor risk premiums appear to be functions of the market variables rather than term structure Devraj Basu Cass Business School