Timing and diversification: A state-dependent asset allocation approach

Abstract

The influence of changing economic environment leads the distribution of stock market returns to be time-varying. A conditionally optimal investment hence requires a dynamic adjustment of asset allocation. In this context, this paper examines the improvement in portfolio performance by simulating portfolio strategies that are conditioned on the Markov regime switching behaviour of stock market returns. Including a memory effect eliminates the empirical shortcoming of discrete state models, namely that they produce a standard and an extreme state in stock returns. So far, this has prevented the regimes from being used as a valuable conditioning variable. Based on a discrete state indicator variable, is presented evidence of considerable performance improvement relative to the static model due to optimal shifting between aggressive and well diversified portfolio structures.

Keywords:

• Asymmetric stock return distribution
• conditional asset pricing
• dynamic diversification
• Markov regime switching
• timing

Notes

1. Part of this paper was written when the author was affiliated with Instituto Tecnológico Autónomo de México.

2. Our evidence of high comovement in turbulent times at a sector level of stock return is in line with similar observation at an individual stock level (Lamont et al., 2001; Perez-Quiros and Timmermann, 2001). On an international stock market level (Chesnay and Jondeau, 2001; Ang and Bekaert, 2002) the findings are similar and frequently cited in the context of financial market contagion (Forbes and Rigobon, 2002).

3. Note, that in this study S _t is of more interest than s _t as we adopt the standard CAPM assumption of well informed market participants. Hence, past period regimes are irrelevant for optimizing the asset allocation.

4. In an analysis by Hess (2003) the second-order Markov chain employed setup emerges as the most appropriate from a large number of specifications for the Swiss stock market.

5. See Lo and MacKinlay (1999) for an overview of the causes of non-random stock market behaviour.

6. The nature of this problem is well illustrated in van Norden and Schaller (1997) who report a single state during most of the time interrupted by some isolated bursts of high volatility. Similar to the memory effect of higher order switching processes, switching ARCH models as in Hamilton and Susmel (1994) and Ang and Bekaert (2002) also produce persistent regimes.

7. We perform the estimation with the EM-algorithm.

8. The closeness of the solid and the dashed line in Figure 1 shows that the introduction of discrete state probabilities does not represent a restrictive assumption.

9. Billio and Pelizzon (2000) reduce the number of parameter estimates by restricting specific risk not to switch. Applied to our dataset their model requires a minimum of a 7-year historic period while our procedure theoretically needs less than 1 year for estimation, allowing for robust estimates and a longer simulation period.

10. Any other portfolio is ad hoc and therefore omitted.

11. See Huang and Litzenberger (1988) for the mathematics of the efficient frontier that lead to the asset weights.

12. There is a tradeoff between estimation accuracy and the length of the simulation period, which is severely limited if the historic period is chosen too long.

13. The first asset allocation after a switch to regime j is set equal to the portfolio structure when state j prevailed for the last time.

14. The model is estimated under the restriction of no short sales.

15. Nevertheless, despite of the larger readjustment volume of the time-varying strategies they generally exhibit outperformance even net of transaction costs (not reported) and may be further improved by lowering the rebalancing frequency.

16. Detailed results available from the author upon request.

17. On an individual firm level, Ang and Chen (2002) report asymmetric patterns that are similar to our observations on the sector level.

18. The bh and the fw strategy reveal that the optimal strategy is to not diversify sector specific risk by allocating 100% to the insurance sector. This extreme allocation is a mere product of the optimizing process at the 30th observation which then, due to the definition of the bh and the fw strategy remains, unlike rbi, unchanged. Note, that as the investment opportunities are industry indices, firm-specific risk of the individual shares is diversified away and, hence, the variance of riskier strategies does not explode.

19. This observation also holds net of transaction costs of a conservative 1%. Results are available from the author upon request.

20. We use the mean absolute deviation of the investment return relative to the market index as a measure of tracking error. See Rudolf et al. (1999) for a discussion of further measures and a method for minimizing the tracking error.

21. A similar observation in a time-series dimension is made by Dacco and Satchell (1999) who show that only a small out-of-sample regime misclassification is sufficient to lose any advantage of a superior model.

Additional information

Notes on contributors

Martin K. Hess

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