What tames the Celtic Tiger? Portfolio implications from a Multivariate Markov Switching model

Abstract

We use multivariate regime switching vector autoregressive models to characterize the time-varying linkages among the Irish stock market, one of the top world performers of the 1990s, and the US and UK stock markets. We find that two regimes, characterized as bear and bull states, are required to characterize the dynamics of excess equity returns both at the univariate and multivariate level. This implies that the regimes driving the small open economy stock market are largely synchronous with those typical of the major markets. However, despite the existence of a persistent bull state in which the correlations among Irish and UK and US excess returns are low, we find that state comovements involving the three markets are so relevant to reduce the optimal mean–variance weight carried by ISEQ stocks to at most one-quarter of the overall equity portfolio. We compute time-varying Sharpe ratios and recursive mean–variance portfolio weights and document that a regime switching framework produces out-of-sample portfolio performance that outperforms simpler models that ignore regimes. These results appear robust to endogenizing the effects of dynamics in spot exchange rates on excess stock returns.

Acknowledgements

We thank Lieven Baele, Brian Lucey, Simone Varotto, participants at the European Finance Association conferenze in Zurich (August 2006), the European Financial Management conference in Madrid (July 2006) and seminar participants at Dublin City University and the University of Dundee. All errors remain our own.

Notes

¹ Gottheil (2003) discusses the causes for the ‘tiger-like’ economic growth observed in Ireland between 1995 and 2000; see also The Economist, ‘Green is Good’, 17 May 1997, issue 8017.

² This is less than surprising in the light of the existing literature, even with reference to ISEQ returns. Among others, Lucey (2001) tests whether there is evidence of long memory–and hence of nonlinear dependence–in daily ISEQ returns using the Fractional Differencing Model of Geweke and Porter-Hudak. Hamill et al. (2000) use a variety of statistical tools to test whether ISEQ returns are independently and identically distributed over time and reject the hypothesis in favour of fractionally integrated ARMA models.

³ Butler and Joaquin (2002) simply define their three regimes (bear, normal and bull) according to the level of domestic returns. Each regime is exogeneously constrained to collect exactly one-third of the sample. In our article, the regimes are endogeneously identified.

⁴ The only exception is Ang and Bekaert (2002) who model bi- and tri-variate vectors of national stock index returns (US and UK, US, UK and Germany) although their focus is mainly on optimal asset allocation issues.

⁵ Mean (as opposed to median) excess equity returns are surprisingly low (<1%) for the UK. This is caused by two extreme observations (of −19 and −16%) that lie more than 3 SDs away from the mean.

⁶ This result is partially explained by the presence of a few influential observations in the 1980s, in particular the large, negative returns of 17 October 1987. In fact, when we test for clustering in squares in a 1988:01–2004:12 sample, we find p-values of 0.01, 0.54 and 0.01, i.e. some evidence of ARCH reappears, with the UK exception.

⁷ The associated p-values for a eighth order Ljung–Box test on levels are 0.001, 0.41 and 0.51.

⁸ Unconditional, state-specific means are calculated as exploiting the simple AR(1) within-state structure implied by a MSIAH(2,1) model.

⁹ Unconditional, state-specific variances are calculated as .

¹⁰ e _j is defined as a k × 1 vector with zeros everywhere but in its j-th position, where a 1 appears.

¹¹ Less surprisingly, the FTSE and S&P 500 smoothed probabilities are also positively correlated (0.50) although we fail to detect any systematic difference versus the association characterizing ISEQ probabilities with other markets.

¹² Detailed specification test results are not reported to save space and are available from the authors on request.

¹³ In Tables 3 and 6, the VAR matrices have to be read by row, i.e. in each row we report the impact on the row variable of the lagged variables in the columns.

¹⁴ These are calculated as E[x _t |S _t ] = (I ₃ − A _{s t} )^− 1μ _{s t} .

¹⁵ There is evidence of this phenomenon concerning emerging markets, see e.g. Yang et al. (2003).

¹⁶ For instance, a 1 SD positive shock to the FTSE100 causes an excess return of +3.1% on the ISEQ, in the following month. The corresponding estimate for a 1 SD shock to the S&P 500 is −2.5%.

¹⁷ There are short periods of upward trending markets which are not captured as a bull regime: a feature of our econometric framework is that only protracted periods of positive and high excess stock returns lasting at least 5–7 months may be captured by the corresponding regime.

¹⁸ We also examine the ability of lagged excess returns of market i to predict forecast errors of market j, . There is some linear (cross-) structure only in FTSE 100 errors; in particular, t − 1 excess S&P returns predict time t FTSE 100 errors.

¹⁹ We formally test a regime switching ARCH(1) specification in which

This specification implies specifying 18 additional parameters, the elements of the matrix . A LR test resoundingly rejects this specification, consistently with our conclusion of no ARCH at the univariate level in Section ‘The data’.

²⁰ This implies that a unit, standardized shock to the excess return of national stock market i will be accompanied by contemporaneous shocks to the other markets, in accordance with the structure of the covariance matrix. The interpretation is that we must take into account that random influences on asset returns rarely appear in isolation, but tend instead to take the form of spreading bull or bear waves.

²¹ A large number (5000) of IRFs are generated in correspondence of a given type of shock (and initial state): each IRF is computed by randomly drawing (for h ≥ 1) both regimes and state-specific shocks from the estimated two-state models in Table 3. The 95% bands are obtained by reporting the 2.5 and 97.5 percentiles of the distribution of the responses in correspondence for each h.

²² Since the ergodic probability of the bear state exceeds the one for the bull state, the ergodic IRFs are similar to those obtained for the bear state.

²³ While predicted risk-premia are simply calculated as a predicted-probability weighted average of state-specific risk premia, predicted volatilities adjust for possible switches in means between t and t + 1 as shown by Timmermann (2000). The same applies to the correlations presented later on.

²⁴ An equivalent plot concerning the pairwise correlation between FTSE and S&P excess returns is omitted to save space and is available upon request. It shows a pairwise correlation that oscillates in the narrow range 0.4–0.6.

²⁵ Notice that is in fact the ratio of two predicted moments (or functions thereof) and not a direct implication of the two-state model.

²⁶ For instance, is based on estimated parameters obtained using data for the interval April 1978–January 1995, etc.

²⁷ The four columns concerning pure equity portfolios performance are identical across values for λ. The algebra of mean–variance optimization implies that when a riskless asset is available a two-fund separation result applies, such that heterogeneous risk preferences only produce different demands for the riskless asset and a homogeneous risky portfolio.

²⁸ Notice there is already one sense in which the extended model has confirmed our previous conclusions:we keep finding two regimes with a roughly equivalent interpretation, while the dynamic linkages between the three stock markets are hardly influenced by the expansion of y _t to include changes in spot rates.

²⁹ This is consistent with recent findings in Goetzmann et al. (2005) by which international equity correlation have moved dramatically over the last century and half so that diversification benefits to global investing are simply not constant, but not necessarily declining. Adjaouté and Danthine (2005) report that low frequency movements in the time series of return dispersions for European stocks are suggestive of cycles and long swings in return correlations that fail to imply a declining importance of international diversification.