Historical simulation approach to the estimation of stochastic discount factor models

We propose an approach to the estimation of the parameters of stochastic discount factor (SDF) models which is based on the idea that the next period joint distribution of the variables in a SDF and asset returns can be well approximated by their joint historical distribution. The estimates of the SDF parameters may therefore be found as the values of the parameters at which the mean of the historical distribution of the product of the SDF with an asset return equals one. Each time period, the estimates are updated using the most recent periods of data and hence can change over time. This method can be viewed as an alternative to the approaches that specify a particular functional form relating the SDF parameters to proxies for the state of the world.     

The puzzling peso

In the past decade, some observers have noted an unusual aspect of the Mexican peso’s behavior: During periods when the U.S. dollar has risen (fallen) against other major currencies such as the euro, the peso has risen (fallen) against the dollar. Very few other currencies display this behavior. In this paper, we attempt to explain the unusual pattern of the peso’s correlation with the dollar by developing some general empirical models of exchange rate correlations. Based on a study of 29 currencies, we find that most of the cross-country variation in exchange rate correlations with the dollar and the euro can be explained by just a few variables. First, a country’s currency is more likely to rise against the dollar as the dollar rises against the euro, the closer it is to the United States and the farther it is from the euro area. In this result, distance likely proxies for the role of economic integration in affecting exchange rate correlations. Second, a country’s currency is more likely to exhibit this unusual pattern when its sovereign credit rating is more risky. This may reflect that currencies of riskier countries are less substitutable in investor portfolios than those of better-rated countries. All told, these factors well explain the peso’s unusual behavior, as Mexico both is very close to the United States and has a lower credit rating than most industrial economies.     

Takeover premiums and the perception of auditor independence and reputation

This study investigates if there is a positive association between takeover premiums and the bidder’s perception of target firm auditor reputation and independence. Using auditor size as a proxy for auditor reputation, the results indicate that in hostile takeovers target shareholders receive a higher takeover premium when a Big 4 auditor audits the target firm prior to the takeover. This result is only significant, however, in the period prior to the highly publicised audit failures. The impact of perceived auditor independence on takeover premiums is studied using the levels and size of non-audit service (NAS) fees provided by the target firm auditor. Using three proxies for auditor independence, the results show no association between perceived auditor independence and takeover premiums. This finding is robust to partitioning the sample by auditor size, takeover hostility and splitting the sample into takeovers pre- and post- the corporate scandals that occurred in 2002.     

In- and out-of-sample specification analysis of spot rate models: Further evidence for the period 1982–2008

We review and construct consistent in-sample specification and out-of-sample model selection tests on conditional distributions and predictive densities associated with continuous multifactor (possibly with jumps) and (non)linear discrete models of the short term interest rate. The results of our empirical analysis are used to carry out a “horse-race” comparing discrete and continuous models across multiple sample periods, forecast horizons, and evaluation intervals. Our evaluation involves comparing models during two distinct historical periods, as well as across our entire weekly sample of Eurodollar deposit rates from 1982 to 2008. Interestingly, when our entire sample of data is used to estimate competing models, the “best” performer in terms of distributional “fit” as well as predictive density accuracy, both in-sample and out-of-sample, is the three factor Chen (Chen, 1996) model examined by Andersen, Benzoni and Lund (2004). Just as interestingly, a logistic type discrete smooth transition autoregression (STAR) model is preferred to the “best” continuous model (i.e. the one factor Cox, Ingersoll, and Ross (CIR: 1985) model) when comparing predictive accuracy for the “Stable 1990s” period that we examine. Moreover, an analogous result holds for the “Post 1990s” period that we examine, where the STAR model is preferred to a two factor stochastic mean model. Thus, when the STAR model is parameterized using only data corresponding to a particular sub-sample, it outperforms the “best” continuous alternative during that period. However, when models are estimated using the entire dataset, the continuous CHEN model is preferred, regardless of the variety of model specification (selection) test that is carried out. Given that it is very difficult to ascertain the particular future regime that will ensue when constructing ex ante predictions, thus, the CHEN model is our overall “winning” model, regardless of sample period.     

Macroeconomic control, political costs and earnings management: Evidence from Chinese listed real estate companies

Firms in China have faced high political costs during China’s economic transition, because they are affected by macroeconomic policies. However, research to date has offered no consistent conclusions on the relationship between political costs and earnings management in China. This study tests whether real estate firms attempt to decrease earnings during periods of macroeconomic control, using variables related to the national real estate market as proxies for political costs. We find that political costs are negatively related to earnings management in listed real estate firms. In addition, we find that non-state-owned enterprises utilized more income-decreasing accruals during this period. Our results are consistent with the political costs hypothesis.     

Real exchange rate behavior

Using random simulations with artificial data with identical sample characteristics to the long-sample exchange rate data employed by Lothian and Taylor (Lothian, J.R. and Taylor, M.P. (1996). The recent float from the perspective of the past two centuries. Journal of Political Economy 104, 488–509.), we show that standard unit-root tests have extremely low power over sample sizes corresponding to the recent float. The probability of rejecting the null hypothesis when it is false is extremely low with 20 years or even 50 years of data and only reaches an acceptable level over much longer spans.     

Predicting dividends in log-linear present value models

In a present value model, high dividend yields imply that either future dividend growth must be low, or future discount rates must be high, or both. While previous studies have largely focused on the predictability of future returns from dividend yields, dividend yields also strongly predict future dividends, and the predictability of dividend growth is much stronger than the predictability of returns at a one-year horizon. Inference from annual regressions over the 1927–2000 sample imputes over 85% of the variation of log dividend yields to variations in dividend growth. Point estimates of the predictability of both dividend growth and discount rates are stronger when the 1990–2000 decade is omitted.     

Long term dependence in stock returns

We show, using the modified rescaled range statistic, that none of the return series of indices of five European countries, the United States and Japan exhibits long term dependence. This statistic — introduced by Lo (1991) — correct Hurst's (1951) ‘classical’ rescaled range statistic for short term dependence. We also report the classical rescaled range statistic after adjusting the series for short term dependence. This procedure shows, for cases where the results of the modified rescaled range statistic are mixed, that no long term dependence can be found. Simulations indicate reasonable power of this adjustment procedure. Furthermore, we find that estimates of the Hurst exponent, a related measure of long term dependence, are also biased by short term dependence. Simulations show that this measure — that has recently attracted growing interest — cannot distinguish between models with or without long term dependence.     

BE/ME and E/P work better than ME/BE or P/E in regressions

Researchers often form ratios of variables to measure firm characteristics, but which ratios create the most powerful tests? For example, if we use ratios of book value of equity (BE) and market value of equity (ME), or earnings (E) and price (P), does it matter which variable appears in the denominator? Any variable in the denominator, when close to zero, creates outliers and is less likely to produce effective tests. Our tests, using data from 1972 to 2008, indicate the choice between reciprocals often produces significantly different outcomes. While ME/BE is a more commonly used control variable than BE/ME or LN(BE/ME), we find the latter two produce better results, even if the data are trimmed to mitigate the outlier problem. Similarly, using E/P generally produces better results than P/E, and while ratios with book value of assets (BA) in the numerator work better than those with it in the denominator, the difference is less pronounced than when BE or E is part of the ratio. While the focus of our empirical findings is on growth measures, the principal applies anytime a ratio has a denominator that is frequently near zero.     

A Critique of the Stochastic Discount Factor Methodology

In this paper, we point out that the widely used stochastic discount factor (SDF) methodology ignores a fully specified model for asset returns. As a result, it suffers from two potential problems when asset returns follow a linear factor model. The first problem is that the risk premium estimate from the SDF methodology is unreliable. The second problem is that the specification test under the SDF methodology has very low power in detecting misspecified models. Traditional methodologies typically incorporate a fully specified model for asset returns, and they can perform substantially better than the SDF methodology.     

The economic value of range-based covariance between stock and bond returns with dynamic copulas

The covariance between stock and bond returns plays important roles in the setting up of asset allocation strategies and portfolio diversification. In the present study, we propose a multivariate range-based volatility model incorporating dynamic copulas into a range-based volatility model to describe the volatility and dependence structures of stock and bond returns. We then go on to assess the economic value of the covariance forecasts based on our proposed model under a mean-variance framework. The out-of-sample forecasting performance reveals that investors would be willing to pay between 39 and 2081 basis points per year to switch from a dynamic trading strategy under the return-based volatility model to a dynamic trading strategy under the range-based volatility model, with more risk-averse investors being willing to pay even higher switching fees. Furthermore, additional economic gains of between 33 and 1471 annualized basis points are achieved when taking the leverage effect into consideration.     

Possible solutions to the forward bias paradox

This note outlines the economic theory behind the theory of uncovered interest parity and some of the econometric issues involved in testing and interpretation. I illustrate some of the issues involved by estimating a rolling regression of the forward premium regression from 22 years of eight major currencies. I also conclude that Pippenger's model is not consistent with the theory of UIP and that furthermore there are severe econometric problems in estimating his model. The forward premium anomaly remains a paradox in international finance that is important and worthwhile to understand more fully.     

CAPM option pricing

This paper extends the option pricing equations of [Black and Scholes, 1973] , [Jarrow and Madan, 1997] and [Husmann and Stephan, 2007] . In particular, we show that the length of the individual planning horizon is a determinant of an option’s value. The derived pricing equations can be presented in terms of the Black and Scholes [1973. Journal of Political Economy 81, 637–654] option values which ensures an easy application in practice.     

Investor sentiment and feedback trading: Evidence from the exchange-traded fund markets

This paper extends the standard feedback trading model of Sentana and Wadhwani (1992) by allowing the demand for shares by feedback traders to depend on sentiment. Our empirical analysis of three largest Exchange-Traded Fund (ETF) contracts in the U.S. suggests that there is a significant positive feedback trading in these markets and the intensity of which is generally linked to investor sentiment. Specifically, the level of feedback trading tends to increase when investors are optimistic. In addition, we find that the influence of sentiment on feedback trading varies across market regimes. These results are consistent with the view that feedback trading activity is largely caused by the presence of sentiment-driven noise trading. Overall, the findings are important in understanding the role of sentiment in investment behaviour and market dynamics and are of direct relevance to the regulators and investors in ETF markets.     

Comparison of modeling methods for Loss Given Default

We compare six modeling methods for Loss Given Default (LGD). We find that non-parametric methods (regression tree and neural network) perform better than parametric methods both in and out of sample when over-fitting is properly controlled. Among the parametric methods, fractional response regression has a slight edge over OLS regression. Performance of the transformation methods (inverse Gaussian and beta transformation) is very sensitive to ε, a small adjustment made to LGDs of 0 or 1 prior to transformation. Model fit is poor when ε is too small or too large, although the fitted LGDs have strong bi-modal distribution with very small ε. Therefore, models that produce strong bi-model pattern do not necessarily have good model fit and accurate LGD predictions. Even with an optimal ε, the performance of the transformation methods can only match that of the OLS.     

Measuring price discovery: The variance ratio, the R, and the weighted price contribution

We analyze the statistical properties of three price discovery measures: The variance ratio, the weighted price contribution (WPC), and the R² of unbiasedness regressions. We find that, if the price process is a driftless martingale, only the WPC is an unbiased estimator for the return variance explained during a time interval. For autocorrelated processes with a drift, only the R² of the unbiasedness regression is consistent, but it is biased for small samples.     

Conditional beta pricing models: A nonparametric approach

We propose a two-stage procedure to estimate conditional beta pricing models that allows for flexibility in the dynamics of asset betas and market prices of risk (MPR). First, conditional betas are estimated nonparametrically for each asset and period using the time-series of previous data. Then, time-varying MPR are estimated from the cross-section of returns and betas. We prove the consistency and asymptotic normality of the estimators. We also perform Monte Carlo simulations for the conditional version of the three-factor model of Fama and French (1993) and show that nonparametrically estimated betas outperform rolling betas under different specifications of beta dynamics. Using return data on the 25 size and book-to-market sorted portfolios, we find that the nonparametric procedure produces a better fit of the three-factor model to the data, less biased estimates of MPR and lower pricing errors than the Fama–MacBeth procedure with betas estimated under several alternative parametric specifications.     

Optimizing international portfolios with options and forwards

We develop a stochastic programming model to address in a unified manner a number of interrelated decisions in international portfolio management: optimal portfolio diversification and mitigation of market and currency risks. The goal is to control the portfolio’s total risk exposure and attain an effective balance between risk and expected return. By incorporating options and forward contracts in the portfolio optimization model we are able to numerically assess the performance of alternative tactics for mitigating exposure to the primary risks. We find that control of market risk with options has more significant impact on portfolio performance than currency hedging. We demonstrate through extensive empirical tests that incremental benefits, in terms of reducing risk and generating profits, are gained when both the market and currency risks are jointly controlled through appropriate means.     

Extreme dependence with asymmetric thresholds: Evidence for the European Monetary Union

Existing papers on extreme dependence use symmetrical thresholds to define simultaneous stock market booms or crashes such as the joint occurrence of the upper or lower one percent return quantile in both stock markets. We show that the probability of the joint occurrence of extreme stock returns may be higher for asymmetric thresholds than for symmetric thresholds. We propose a non-parametric measure of extreme dependence which allows capturing extreme events for different thresholds and can be used to compute different types of extreme dependence. We find that extreme dependence among the stock markets of ten initial EMU member countries, the United Kingdom, and the United States is largely asymmetrical in the pre-EMU period (1989–1998) and largely symmetrical in the EMU period (1999–2010). Our findings suggest that ignoring the possibility of asymmetric extreme dependence may lead to an underestimation of the probability of co-booms and co-crashes.