Steve Satchell

Why do regime-switching models forecast so badly?

Most non-linear techniques give good in-sample fits to exchange rate data but are usually outperformed by random walks or random walks with drift when used for out-of-sample forecasting. In the case of regime-switching models it is possible to understand why forecasts based on the true model can have higher mean squared error than those of a random walk or random walk with drift. In this paper we provide some analytical results for the case of a simple switching model, the segmented trend model. It requires only a small misclassification, when forecasting which regime the world will be in, to lose any advantage from knowing the correct model specification. To illustrate this we discuss some results for the DM/dollar exchange rate. We conjecture that the forecasting result is more general and describes limitations to the use of switching models for forecasting. This result has two implications. First, it questions the leading role of the random walk hypothesis for the spot exchange rate. Second, it suggests that the mean square error is not an appropriate way to evaluate forecast performance for non-linear models. Copyright

Statistical modelling of asymmetric risk in asset returns

The purpose of this article is to provide a straightforward model for asset returns which captures the fundamental asymmetry in upward versus downward returns. We model this feature by using scale gamma distributions for the conditional distributions of positive and negative returns. By allowing the parameters for positive returns to differ from parameters for negative returns we can test the hypothesis of symmetry. Some applications of this process to expected utility and semi-variance calculations are considered. Finally we estimate the model using daily UK FT100 index and Futures data.

GARCH model with cross-sectional volatility: GARCHX models

This study introduces GARCH models with cross-sectional market volatility, which are called GARCHX models. The cross-sectional market volatility is a special case of common heteroscedasticity in asset specific returns, which is suggested by Connor and Linton (2001) as an important component in individual asset volatility. Using UK and US data, we find that daily return volatility can be better specified with GARCHX models, but GARCHX models do not necessarily perform better than conventional GARCH models in forecasting.

On the optimality of adaptive expectations: Muth revisited

Abstract Muth (1960, J. American Statistical Association 55, 299–306) showed that adaptive expectations are optimal, in the sense that they minimise the mean squared forecast error of an infinite-history random walk series observed with noise. This paper derives an explicit formula for the optimal forecasting weights for the IMA(1,1) series analysed by Muth when the series has a finite history. We find that the optimality of adaptive expectations is a very robust result for the IMA(1,1) process; this will hold even in very small samples, unless the ratio of the innovation variance of the random walk component to the variance of the noise component is very small. The exact relationship between our explicit forecasting weights and the weights derived from a recursive updating scheme is also explained in the paper.

Changing Correlation and Equity Portfolio Diversification Failure for Linear Factor Models during Market Declines

The paper considers a linear factor model (LFM) to study the behaviour of the correlation coefficient between various stock returns during a downturn. Changing correlation is related to the tail distribution of the driving factors, which is the market for Sharpes one‐factor model. General classes of distribution functions are considered and asymptotic conditions found on the tails of the distribution, which determine whether diversification will succeed or fail during a market decline.

Valuing information using utility functions: how much should we pay for linear factor models?

Thus paper reports on an investigation into what is an appropriate level of investment management fees. Existing results are extended and several formulae are provided for the case of power utility and normal returns. Using the CRRA utility function with the range of the coefficient of the CRRA suggested by Mehra and Prescott, it is found that the value of information added by the linear factor models of Fama and French exceeds observed management fees and only equals them for hitherto unmeasured magnitudes of risk aversion.

Calculating hedge fund risk: the draw down and the maximum draw down

Hedge funds, defined in this context as geared financial entities, frequently use some measure of point loss as a risk measure. This paper considers the statistical properties of an uninterrupted fall in a security price; called a draw down. The distribution of the draw downs in an N‐trading period is derived together with an approximation to the distribution of the maximum. Complementary results are provided which are useful for risk calculations. A brief empirical study of the S&P futures is included in order to highlight some of the limitations in the presence of extreme events.

Theoretical decompositions of the cross-sectional dispersion of stock returns

We present theoretical decompositions of cross-sectional return dispersion, assuming either a one-factor model, or a constant parameter model. This allows us to calculate expected return dispersion, based on dispersions in alpha and beta, and their cross-sectional correlation. We find that expected dispersion matches up reasonably well with actual realised dispersion - periods of high expected dispersion correspond to periods of high realised dispersion. Using U.S. equity portfolio data, we find that approximately 80% of expected dispersion is determined by extreme returns in the market.

The Low Beta Anomaly and Interest Rates

The reasons for outperformance in smart beta portfolios remains a mystery. We extend previous literature on the link between portfolio performance and macroeconomic factors by exploring the response of a low beta portfolio to interest rate movements. The implications for fund managers heavily invested in low-risk strategies where the immediate risk lies in the future rise in interest rates are worth considering. In particular, low beta funds appear to go up when interest rates fall more than when interest rates rise. We focus on the case of US equity investment based on the capital asset pricing model (CAPM). We find that the anomaly is partially explained by interest sign changes due to macroeconomic events, and observe heterogeneous impacts for low and high beta portfolios.