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Abstract
Changes in investors' risk appetite have been used to explain various phenomena in asset markets. And yet, the basis for their use is generally weak: popular indicators of changes in risk appetite typically have scant foundation in theory and give contradictory signals in practice. This has led to the views that it is a convenient ex post rationalization rather than a well-founded explanation of asset price movements. This paper starts from the premise that changing risk appetite might be a legitimate explanation, but that there is an identification problem, both theoretically and empirically. The solution offered here is based on the approach introduced by Kumar and Persaud (Kumar, M., and A. Persaud. 2002. Pure contagion and investors' shifting risk appetite: analytical issues and empirical evidence. International Finance 5: 401–36.), and on the work of Misina (Misina, M. 2003. What Does the Risk-Appetite Index Measure? Bank of Canada, Working Paper 2003–23.) who established the theoretical conditions under which that approach will correctly identify changes in risk appetite. We propose a method to implement these conditions and thus ensure that the resulting index is empirically sound. This index is then used to examine the presence of changes in risk appetite in the data, and, more generally, whether this explanation is appropriate in particular circumstances. The empirical illustration is based on a portfolio of foreign currencies, but the techniques are general and can be applied to any portfolio.
Acknowledgements
I would like to thank Mark Illing for valuable contributions to Section 3, Avinash Persaud for thought-provoking discussions, two anonymous referees for insightful comments and suggestions, and the participants and discussants at the Bank of Canada, Manchester Business School, Midwest Finance Association Conference (Chicago), and Forecasting Financial Markets Conference (Aix-en-Provence) for the feedback.
Notes
1. Endogenously changing risk attitudes can be accommodated within the standard framework. Habit-persistence utility functions deliver risk attitude that depends on surplus consumption and changes over time as surplus consumption changes. This mechanism, however, is typically found unsatisfactory, given that practitioners use changing risk attitudes to explain sudden movements in asset prices, or a shorter-term phenomena.
2. Illing and Aaron Citation(2005) offer a survey of the indicator properties of several risk appetite indices currently used.
3. Misina Citation(2005) shows how one can distinguish between risk aversion, which is assumed to be constant, and risk appetite, which is allowed to vary over time, within a standard framework. The reader is referred to that work for a discussion of the links to the literature of behavioural psychology and pertinent references.
4. An alternative to the approach in this paper is described in Pericoli and Sbracia Citation(2006). The authors build on the conditions established in Misina Citation(2003), but, rather than seeking to validate these conditions in the data, attempt to assess the sensitivity of the results to violations of these conditions. This is done by comparing Kumar and Persaud's GRAI to the estimates of risk aversion based on the standard CAPM model.
5. For the relationship between these two coefficients, see Zimmerman, Zumbo, and Williams Citation(2003). Intuitively, one can think of Pearson's correlation as answering the question. ‘How well can the relationhsip in the data be represented by a linear function?’ Spearman's correlation answers the question, ‘How well can the relationship in the data be represented by a monotonic but otherwise arbitrary function?’ When the underlying relationship is linear, the two measures will coincide. In capturing the rank effect, Pearson's correlation is overly restrictive, and Spearman's correlation is preferred.
6. See, for example, Cochrane (Citation2001, p. 154) for details.
7. Note that the criterion for establishing whether a shock is common is the direction of the impact on assets’ riskiness, rather than whether it can be traced to a single cause, as is usual in the macroeconomic literature.
8. The technical background of this procedure is described in the appendix.
9. In empirical implementation, the issue of the horizon over which returns and Σ R are computed arises. One can either use the full sample, or a subsample based on a rolling window. Our implementation in the empirical part is based on the full sample. In using a rolling window, one has to address the issue of the optimal window width since the results will be sensitive to the choice.
10. One could interpret these vectors as Arrow securities as well, but one need not. Arrow securities do form the ‘usual’ basis of the returns space. It is not necessary to use this usual basis, but the orthogonality property of vectors in the new basis is preserved.
11. Looking at this market, however, is not without its difficulties. Exchange rates are peculiar market prices, subject to limits in their movements, and interventions. For example, the European Exchange Rate Mechanism (ERM), introduced in 1979, placed restrictions on the cross-values of European currencies. The question arises whether in this context realized returns are an appropriate measure of expected returns. Whereas one could argue that the UK experience in 1992 indicates that it is not; it is equally conceivable that the restrictions acted as constraints on expected returns which were taken into account by speculators, and that these constraints were generally binding. I thank the referee for raising the issue.
12. In applying the above procedure to identify common shocks, one has to bear in mind that it is valid only when cross-correlations of asset returns are zero, since only in that case does asset volatility coincide with a measure of the riskiness of this asset as part of a portfolio. Furthermore, although the number of factors in the portfolio corresponds to the number of original assets, factors should not be interpreted as representing individual assets. As stated earlier, each factor is a derivative asset, a linear combination of original assets comprising a portfolio.
13. The P-values associated with these values of RAI-MI are 0.3 and 0.21, respectively, which would not lead to rejection of the null hypothesis of zero rank correlation.
14. The associated P-value is 0.018, which leads to rejection of the null hypothesis of zero correlation.
15. Shiller Citation(2000) offers a good analysis of the factors that underlie more presistent changes in risk appetites. Shleifer (2000), Chapter 5, is an example of a formal model that incorporates investor sentiment. Misina Citation(2005) discusses the relationship between future outlook and risk attitudes.
16. Another issue is data availability. One can construct portfolios of up to 25 currencies, for samples starting in 1998.
