Detecting log-periodicity in a regime-switching model of stock returns

Log-periodic precursors have been identified before most and perhaps all financial crashes of the Twentieth Century, but efforts to statistically validate the leading model of log-periodicity, the Johansen–Ledoit–Sornette (JLS) model, have generally failed. The main feature of this model is that log-harmonic fluctuations in financial prices are driven by similar fluctuations in expected daily returns. Here we search more broadly for evidence of any log-periodic variation in expected daily returns by estimating a regime-switching model of stock returns in which the mean return fluctuates between a high and a low value. We find such evidence prior to the two largest drawdowns in the S&P 500 since 1950. However, if we estimate a log-harmonic specification for the stock index for the same time periods, fixing the frequency and critical time according to the results of the regime-switching model, the parameters do not satisfy restrictions imposed by the JLS model.     

A Bayesian analysis of log-periodic precursors to financial crashes

A large number of papers have been written by physicists documenting an alleged signature of imminent financial crashes involving so-called log-periodic oscillations–oscillations which are periodic with respect to the logarithm of the time to the crash. In addition to the obvious practical implications of such a signature, log-periodicity has been taken as evidence that financial markets can be modelled as complex statistical-mechanics systems. However, while many log-periodic precursors have been identified, the statistical significance of these precursors and their predictive power remain controversial in part because log-periodicity is ill-suited for study with classical methods. This paper is the first effort to apply Bayesian methods in the testing of log-periodicity. Specifically, we focus on the Johansen–Ledoit–Sornette (JLS) model of log periodicity. Using data from the S&P 500 prior to the October 1987 stock market crash, we find that, if we do not consider crash probabilities, a null hypothesis model without log-periodicity outperforms the JLS model in terms of marginal likelihood. If we do account for crash probabilities, which has not been done in the previous literature, the JLS model outperforms the null hypothesis, but only if we ignore the information obtained by standard classical methods. If the JLS model is true, then parameter estimates obtained by curve fitting have small posterior probability. Furthermore, the data set contains negligible information about the oscillation parameters, such as the frequency parameter that has received the most attention in the previous literature.     

Information Aggregation Bias and Samuelson's Dictum

Under the assumption of incomplete information, idiosyncratic shocks may not dissipate in the aggregate. An econometrician who incorrectly imposes complete information and applies the law of large numbers may be susceptible to information aggregation bias. Tests of aggregate economic theory will be misspecified even though tests of the same theory at the microlevel deliver the correct inference. A testable implication of information aggregation bias is “Samuelson's Dictum” or the idea that stock prices can simultaneously display “microefficiency” and “macroinefficiency;” an idea accredited to Paul Samuelson. Using firm-level data from the Center for Research in Security Prices, we present empirical evidence consistent with Samuelson's dictum. Specifically, we conduct two standard tests of the linear present value model of stock prices: a regression of future dividend changes on the dividend-price ratio and a test for excess volatility. We show that the dividend price ratio forecasts the future growth in dividends much more accurately at the firm level as predicted by the present value model, and that excess volatility can be rejected for most firms. When the same firms are aggregated into equal-weighted or cap-weighted portfolios, the estimated coefficients typically deviate from the present value model and “excess” volatility is observed; this is especially true for aggregates (e.g., S&P 500) that are used in most asset pricing studies. To investigate the source of our empirical findings, we propose a theory of aggregation bias based on incomplete information and segmented markets. Traders specializing in individual stocks conflate idiosyncratic and aggregate shocks to dividends. To an econometrician using aggregate data, these assumptions generate a rejection of the present value model even though individual traders are efficiently using their available information.     

Identifying Monetary Policy Shocks via Changes in Volatility

A central issue of monetary policy analysis is the specification of monetary policy shocks. In a structural vector autoregressive setting there has been some controversy about which restrictions to use for identifying the shocks because standard theories do not provide enough information to fully identify monetary policy shocks. In fact, to compare different theories it would even be desirable to have over-identifying restrictions that would make statistical tests of different theories possible. It is pointed out that some progress toward over-identifying monetary policy shocks can be made by using specific data properties. In particular, it is shown that changes in the volatility of the shocks can be used for identification. Based on monthly U.S. data from 1965 to 1996 different theories are tested and it is found that associating monetary policy shocks with shocks to nonborrowed reserves leads to a particularly strong rejection of the model whereas assuming that the Fed accommodates demand shocks to total reserves cannot be rejected.     

Modelling stock returns in Africa's emerging equity markets

We investigate the behaviour of stock returns in Africa's largest markets namely, Egypt, Kenya, Morocco, Nigeria, South Africa, Tunisia and Zimbabwe. The validity of the random walk hypothesis is examined and rejected by employing a battery of tests. Secondly we employ smooth transition and conditional volatility models to uncover the dynamics of the first two moments and examine weak form efficiency. The empirical stylized facts of volatility clustering, leptokurtosis and leverage effect are present in the African data.     

Temporal Aggregation and the Continuous-Time Capital Asset Pricing Model

We examine how the empirical implications of the Capital Asset Pricing Model (CAPM) are affected by the length of the period over which returns are measured. We show that the continuous-time CAPM becomes a multifactor model when the asset pricing relation is aggregated temporally. We use Hansen's Generalized Method of Moments (GMM) approach to test the continuous-time CAPM at an unconditional level using size portfolio returns. The results indicate that the continuous-time CAPM cannot be rejected. In contrast, the discrete-time CAPM is easily rejected by the tests. These results have a number of important implications for the interpretation of tests of the CAPM which have appeared in the literature.     

Feeling the blues Moral hazard and debt dilution in Eurobonds before 1914

Debt mutualisation through Eurobonds has been proposed as a solution to the Euro crisis. Although this proposal found some support, it also attracted strong criticisms as it risks raising the spreads for strong countries, diluting legacy debt and promoting moral hazard by weak countries. Because Eurobonds are a new addition to the policy toolkit, there are many untested hypotheses in the literature about the counterfactual behaviour of markets and sovereigns. This paper offers some tests of the issues by drawing from the closest historical parallel – five guaranteed bonds issued in Europe between 1833 and 1913. The empirical evidence suggests that contemporary concerns about fiscal transfers and debt dilution may be overblown, and creditors' moral hazard may be as much of a problem as debtors'.     

Conducting Event Studies on a Small Stock Exchange

Abstract

This paper analyses whether it is possible to perform an event study on a small stock exchange with thinly trade stocks. The main conclusion is that event studies can be performed provided that certain adjustments are made. First, a minimum of 25 events appears necessary to obtain acceptable size and power in statistical tests. Second, trade to trade returns should be used. Third, one should not expect to consistently detect abnormal performance of less than about 1% (or perhaps even 2%), unless the sample contains primarily thickly traded stocks. Fourth, nonparametric tests are generally preferable to parametric tests of abnormal performance. Fifth, researchers should present separate results for thickly and thinly traded stock groups. Finally, when nonnormality, event induced variance, unknown event day, and problems of very thin trading are all considered simultaneously, no one test statistic or type of test statistic dominates the others.     

A MULTIVARIATE TEST OF THE GENERALISED MEAN-LOWER PARTIAL MOMENT ASSET PRICING MODEL: AUSTRALIAN EVIDENCE

This paper tests the Mean-Lower Partial Moment (MLPM) model of asset pricing, using the Gibbons (1982) multivariate methodology, as developed by Hariow and Rao (1989). The MLPM model specifies risk to be a measure of the downside deviations of return relative to a prespecified and exogenous target rate of return. The MLPM model of Hariow and Rao is a new model which has only been tested once, using US data. Therefore, further tests using independent data will help to assess whether the model deserves more serious consideration as a possible alternative to the Capital Asset Pricing Model (CAPM). In general, tests in this paper using Australian data confirm the results of Hariow and Rao (1989). The MLPM model cannot be rejected against an unspecified alternative, nor can it be rejected against the zero-beta CAPM. Conditional on the MLPM model's validity, the optimal target rate appears to be more closely related to mean market returns than either to a risk-free return or to a zero return. In addition, there is some evidence to support an intertemporally constant target rate of around 3 percent per month, over the 30 year period examined.     

A description of farmland investor expectations

We consider how best to characterize agricultural real estate market participants' expectation formation mechanism. The expectation formation mechanism links current agricultural policies to asset prices and tells us how current policies change expectations for future transfers. We examine behavior of real estate prices and returns using the present value model. We derive estimable equations incorporating two rival expectation formation mechanisms: rational and adaptive expectations. Assuming rational expectations, the present value model yields parameter estimates that imply the model should be rejected. Instead of rejecting the present value model while maintaining the rational expectations hypothesis, we let the data reveal which expectations hypothesis best fits the data. When we assume the rival hypothesis, the model yields parameter estimates that conform to adaptive expectations.     

Can the evolution of implied volatility be forecasted? Evidence from European and US implied volatility indices

We address the question whether the evolution of implied volatility can be forecasted by studying a number of European and US implied volatility indices. Both point and interval forecasts are formed by alternative model specifications. The statistical and economic significance of these forecasts is examined. The latter is assessed by trading strategies in the recently inaugurated CBOE volatility futures markets. Predictable patterns are detected from a statistical point of view. However, these are not economically significant since no abnormal profits can be attained. Hence, the hypothesis that the volatility futures markets are efficient cannot be rejected.     

Do Interest Rates Follow Unit-Root Processes? Evidence from Cross-Maturity Treasury Bill Yields

Abstract. It is widely reported in the literature that interest rates follow integrated processes. Many empirical studies have, in fact, taken this result as a maintained hypothesis. This article demonstrates that the failure to reject the hypothesis that interest rates contain a unit root may be due to the severe power problem of standard test procedures in small samples. We analyze a panel of cross-maturity Treasury-bill yield series by employing a panel-based test. This test exploits cross-maturity variations of the data to improve estimation efficiency and is more powerful than standard tests for unit roots. The critical values of the test statistics are computed by Monte Carlo simulations tailored to our samples. It is found that the null hypothesis that each yield series contains a unit root can be decisively rejected. Our findings cast some doubt on previous studies that rely on the nonstationarity assumption of interest rates.     

Large investors’ portfolio composition and firms value

We analyze new Swedish data on the portfolio holdings of large blockholders and find that firm value increases with the weight of a stock in a large blockholder's portfolio. In our sample, this weight may be greater than 50%. We are the first to show that this value premium is correlated with portfolio weights for any large blockholders, not just institutions. We find some evidence that indicates that “stock importance” (high portfolio weight) can mitigate the negative effects of a dual-class structure on firm value. Further, it does not seem that a large blockholder's tenure as a CEO or as a board chairman affects this value premium. We conduct a variety of tests to rule out endogeneity and reverse causality.     

Structural change in the forward discount: Implications for the forward rate unbiasedness hypothesis

It is a well-accepted empirical result that forward exchange rate unbiasedness is rejected in tests using the “differences regression” of the change in the logarithm of the spot exchange rate on the forward discount. We model the forward discount as an AR(1) process and argue that its persistence is exaggerated due to the presence of structural breaks. We show using a stochastic multiple break model that the forward discount persistence is substantially less if one allows for multiple structural breaks in the mean of the process. We argue that these breaks could be identified as monetary shocks to the central bank's reaction function. Using Monte Carlo simulations, we show that if we do not account for structural breaks that are present in the forward discount process, the forward discount coefficient in the “differences regression” is severely biased downward, away from its true value of 1.     

TESTING THE PRESENT VALUE MODEL OF EQUITY PRICES FOR THE UK STOCK MARKET

This paper applies present value tests to the UK stock market. Using monthly data from 1965 to 1990 on real equity price and dividend indices, it is found that the restrictions imposed by the present value model on a vector autoregression comprised of the 'spread' between prices and dividends and the change in real dividends can be rejected both for the complete sample period and for a shorter sample which omits the early years of dividend control and the run up to and aftermath of the stock market 'Crash' of October 1987. These tests are supplemented by informal methods for evaluating the 'fit' of the present value model: the observed spread is found to move 'too much', so that deviations from the model are persistent and long-lasting.     

Non-Segmented Equilibria Under Differential Taxation: Evidence from the Canadian Government Bond Market

This paper investigates tax effects in the Canadian government bond market during the period 1964–1986. Unlike previous studies, we apply both statistical and nonstatistical tests to analyze clientele effects and market equilibria. The results divide the sample into two distinct periods of time, with the end of 1976 marking the division. We find that taxeffects are almost non-existent in the Canadian government bond market before the end of 1976, but are predominant in the post-1976 period. Non-segmented market equilibria cannot be rejected before 1977, but are strongly rejected after 1976. In fact, segmented equilibria with clientele effects in both quantities and prices characterize the entire five year period from 1982 to 1986. These findings are consistent with tax reforms, government deficit financing and interest rate fluctuations in Canada during our sample period.     

Further remarks on Laplace' and Gauss' summation formulas

1. The practical form of the remainder terms of Laplace' and Gauss' summation formulas which I have employed in earlier papers and in my book on Interpolation suffers from the inconvenience that it is inapplicable in the case of infinite limits of summation and integration. The purpose of the present paper is to show, how this inconvenience may be avoided.     

Budget deficits,money growth and causality: Further OECD evidence

This paper investigates the causal linkage between budget deficits and money growth in seven major OECD countries using multivariate Granger-causality tests combined with Akaike's AIC criterion and Zellner's iterative seemingly unrelated regressions. The accommodation hypothesis that deficits Granger-cause positive long-run changes in money growth is systematically rejected across all countries. The reverse hypothesis that money growth Granger-causes long-run changes in deficits is also rejected across countries. These results suggest that monetary and fiscal policies are set independently in each of the OECD countries.     

Drawdowns preceding rallies in the Brownian motion model

We study drawdowns and rallies of Brownian motion. A rally is defined as the difference of the present value of the Brownian motion and its historical minimum, while the drawdown is defined as the difference of the historical maximum and its present value. This paper determines the probability that a drawdown of a units precedes a rally of b units. We apply this result to examine stock market crashes and rallies in the geometric Brownian motion model.     

The expectation hypothesis of the term structure of very short-term rates: Statistical tests and economic value

This paper reexamines the validity of the expectation hypothesis (EH) of the term structure of US repo rates ranging in maturity from overnight to 3 months. We extend the work of Longstaff [2000b. The term structure of very short term rates: new evidence for the expectations hypothesis. Journal of Financial Economics 58, 397–415] in two directions: (1) we implement statistical tests designed to increase test power in this context; (2) more important, we assess the economic value of departures from the EH based on criteria of profitability and economic significance in the context of a simple trading strategy. The EH is rejected throughout the term structure examined on the basis of the statistical tests. However, the results of our economic analysis are favorable to the EH, suggesting that the statistical rejections of the EH in the repo market are economically insignificant.