Large time and small noise asymptotic results for mean reverting diffusion processes with applications

Summary. We use the theory of large deviations to investigate the large time behavior and the small noise asymptotics of random economic processes whose evolutions are governed by mean-reverting stochastic differential equations with (i) constant and (ii) state dependent noise terms. We explicitly show that the probability is exponentially small that the time averages of these process will occupy regions distinct from their stable equilibrium position. We also demonstrate that as the noise parameter decreases, there is an exponential convergence to the stable position. Applications of large deviation techniques and public policy implications of our results for regulators are explored. Received: December 7, 1998; revised version: October 25, 1999     

Market Overreaction to Product Recall Revisited—The Case of Firestone Tires and the Ford Explorer

We revisit the issue of market reaction to product recall and evaluate the magnitude of market reaction to the news of recall. We also examine how the competitors' stock prices are affected by the product recall. Specifically, we evaluate the stock price effects of events relating to the recall of Firestone tires by the Bridgestone Corporation, which were linked to the rollover accidents of the Ford Explorer SUVs. Our results indicate that the initial loss in the market value both for the Bridgestone Corporation and Ford Motor Company was far in excess of direct costs associated with recall. The market losses are approximately equal to the near worst-case estimates of direct and indirect costs, litigation costs, regulation compliance costs and costs associated with future losses in sales. The firms recovered their market value as more information on actual costs became available. These results suggest that the market initially overreacts negatively to the recall news and this reaction is generally based on all potential losses associated with recall. This reaction is corrected as information on actual costs becomes available. With regard to the competitors, our results show that the major competitors in the tire and auto industries experienced a significant gain in the market value of their stocks probably because their products were substitutes for the products affected by recall.     

Management’s tone change, post earnings announcement drift and accruals

This study explores whether the management discussion and analysis (MD&A) section of Forms 10-Q and 10-K has incremental information content beyond financial measures such as earnings surprises and accruals. It uses a classification scheme of words into positive and negative categories to measure the tone change in the MD&A section relative to prior periodic SEC filings. Our results indicate that short window market reactions around the SEC filing are significantly associated with the tone change of the MD&A section, even after controlling for accruals and earnings surprises. We show that management’s tone change adds significantly to portfolio drift returns in the window of 2 days after the SEC filing date through 1 day after the subsequent quarter’s preliminary earnings announcement, beyond financial information conveyed by accruals and earnings surprises. The drift returns are affected by the ability of the tone change signals to help predict the subsequent quarter’s earnings surprise but cannot be completely attributed to this ability. We also find that the incremental information of management’s tone change depends on the strength of the firm’s information environment.     

The effect of option transaction costs on informed trading in the options market around earnings announcements

We investigate the effect of option market transaction costs (a form of market imperfection) on the ability of option implied volatility-based measures to predict future stock returns and volatility around quarterly earnings announcements. We find that the predictability is significantly stronger for firms with lower option relative bid-ask spreads. The effect is more pronounced around positive rather than negative earnings news. We find no significant effect of option transaction costs around randomly chosen dates when there is no clustering of major information events. Trading strategies based on option market predictors and transaction costs earn monthly abnormal returns of 1.39% to 1.91%.     

Accounting Earnings Processes,Inter-temporal Incentives and Their Implications for Valuation

Accounting measures such as levels and changes in residual earnings are widely used for performance evaluation and executive compensation (Healy, 1985). Quite often, these compensation contracts are of the linear form. In a multiperiod agency setting with hidden actions, where the agent's effort influences the random evolution of a general model of residual earnings, we show that linear compensation contracts based on weighted sum of the levels and changes of residual earnings are indeed optimal. We characterize the contract explicitly and show that the weights are determined by the earnings persistence parameter. Residual earnings are known to be important for valuation too (Ohlson, 1995; Easton and Harris, 1991). In our setting, we demonstrate that residual earnings are also sufficient for valuation. This implies that residual earnings can be used to align incentive goals with valuation objectives. In essence, our paper provides the theoretical underpinnings for linear contracts based on residual earnings and their implications for valuation.     

The value relevance of corporate restructuring charges

We document in this study that investors react positively to restructuring that is expected to be successful in improving firm performance. Investors’ reaction is significantly negative to unsuccessful firms when the magnitude of restructuring charges is high. Our results also show that investors’ reaction is significantly positive to restructuring that is intended to save costs through “workforce reduction” and “facility closings/consolidations”, but it is insignificant when restructuring is undertaken to recognize decline in asset values by asset write-offs and/or write-downs. Investor reaction is measured by 12-month buy-and-hold abnormal returns, whereas successful restructuring to improve the firm performance is based on the change in operating performance, measured by the industry-adjusted return on equity (ROE), over two subsequent years after restructuring.

Cities,slums, and child nutrition in Bangladesh

This study uses novel household survey data that are representative of Bangladesh's large cities, and of slum and nonslum areas within the cities, to investigate the effects of demographic and socioeconomic factors on child nutrition status in 2013. The study also decomposes the difference in mean child nutrition status between slum and nonslum areas in 2013, and the increase in mean child nutrition status in slum and nonslum areas from 2006 to 2013. Mother's education attainment and household wealth largely explain the cross‐sectional difference and intertemporal change in mean child nutrition status. Although positive in some cases, the effects of maternal and child health services, and potential health‐protective household amenities, on child nutrition status differ by the type of health facility, household amenity, and urban area (slum or nonslum). Focusing on nutrition‐sensitive programs for slum residents and the urban poor is consistent with the results.     

Hypothesis testing for diffusion processes with continuous observations: Direct computation of large deviation results for error probabilities

We propose statistical tests for deciding between two alternatives for diffusion processes observed continuously over a finite time interval. Our tests emphasize the large deviation aspects, or equivalently, the asymptotic behavior of probabilities of type I and type II errors and the rate at which these probabilities go to zero as the observation time increases. We obtain these rates using direct methods of calculation. We provide specific computational examples for diffusion processes commonly used in finance and show that the error probabilities for these cases go to zero exponentially fast. Applications in finance and economics are discussed.