Block bootstrap methods and the choice of stocks for the long run

Financial advisors commonly recommend that the investment horizon should be rather long in order to benefit from the ‘time diversification’. In this case, in order to choose the optimal portfolio, it is necessary to estimate the risk and reward of several alternative portfolios over a long-run given a sample of observations over a short-run. Two interrelated obstacles in these estimations are lack of sufficient data and the uncertainty in the nature of the return generating process. To overcome these obstacles researchers rely heavily on block bootstrap methods. In this paper we demonstrate that the estimates provided by a block bootstrap method are generally biased and we propose two methods of bias reduction. We show that an improper use of a block bootstrap method usually causes underestimation of the risk of a portfolio whose returns are independent over time and overestimation of the risk of a portfolio whose returns are mean-reverting.     

Robust bootstrap procedures for the chain-ladder method

Insurers are faced with the challenge of estimating the future reserves needed to handle historic and outstanding claims that are not fully settled. A well-known and widely used technique is the chain-ladder method, which is a deterministic algorithm. To include a stochastic component one may apply generalized linear models to the run-off triangles based on past claims data. Analytical expressions for the standard deviation of the resulting reserve estimates are typically difficult to derive. A popular alternative approach to obtain inference is to use the bootstrap technique. However, the standard procedures are very sensitive to the possible presence of outliers. These atypical observations, deviating from the pattern of the majority of the data, may both inflate or deflate traditional reserve estimates and corresponding inference such as their standard errors. Even when paired with a robust chain-ladder method, classical bootstrap inference may break down. Therefore, we discuss and implement several robust bootstrap procedures in the claims reserving framework and we investigate and compare their performance on both simulated and real data. We also illustrate their use for obtaining the distribution of one year risk measures.     

Evaluating implied RNDs by some new confidence interval estimation techniques

This paper evaluates the precision of the parametric double lognormal and the non-parametric smoothing spline method for estimating risk-neutral distributions (RNDs) from observed option prices. By using a bootstrap technique, confidence bands are estimated for the risk-neutral distributions and the width of the confidence bands is used as a criterion when evaluating the precision of the two methods. Previous literature on estimating confidence bands has to a large extent been estimated using Monte Carlo methods. This paper argues that the bootstrap technique is to be preferred due to the non-normality feature of the error structure. Furthermore, it is shown that the inclusion of a heteroscedastic error structure improves the precision of the estimated RNDs. Our findings favour the smoothing spline method as it produces tighter confidence bands. In addition, an example of how to apply the estimated confidence bands in practice is also provided.     

Can Mutual Fund “Stars” Really Pick Stocks? New Evidence from a Bootstrap Analysis

We apply a new bootstrap statistical technique to examine the performance of the U.S. open‐end, domestic equity mutual fund industry over the 1975 to 2002 period. A bootstrap approach is necessary because the cross section of mutual fund alphas has a complex nonnormal distribution due to heterogeneous risk‐taking by funds as well as nonnormalities in individual fund alpha distributions. Our bootstrap approach uncovers findings that differ from many past studies. Specifically, we find that a sizable minority of managers pick stocks well enough to more than cover their costs. Moreover, the superior alphas of these managers persist.     

REGULARITIES IN THE VARIATION OF SKEWNESS IN ASSET RETURNS

This paper documents regularities in the comparative skewness characteristics across several classes of assets and over time. We find smaller capitalized stock indices are more negatively skewed than larger stock indices. Over time, the skewness of stock indices follows a business-cycle-related variation. Skewness is more negative during economic upturns and less negative, even positive, during downturns. Three alternative methods for testing the statistical significance of skewness and for making confidence interval estimates of skewness are presented. These include a bootstrap methodology and a test that allows for nonindependent observations.     

Non-parametric and parametric bootstrap techniques for age-to-age development factor methods in stochastic claims reserving

In the literature, one of the main objects of stochastic claims reserving is to find models underlying the chain-ladder method in order to analyze the variability of the outstanding claims, either analytically or by bootstrapping. In bootstrapping these models are used to find a full predictive distribution of the claims reserve, even though there is a long tradition of actuaries calculating the reserve estimate according to more complex algorithms than the chain-ladder, without explicit reference to an underlying model. In this paper we investigate existing bootstrap techniques and suggest two alternative bootstrap procedures, one non-parametric and one parametric, by which the predictive distribution of the claims reserve can be found for other age-to-age development factor methods than the chain-ladder, using some rather mild model assumptions. For illustration, the procedures are applied to three different development triangles.     

基于GLM的未决赔款准备金评估的随机性链梯法

为度量未决赔款准备金评估结果的波动性,需要研究随机性评估方法。基于GLM的随机性方法,得到准备金估计及预测均方误差。特别地,在过度分散泊松模型中,分别应用参数Bootstrap方法和非参数Bootstrap方法,得到两种方法下未决赔款准备金的预测分布,进而由该分布得到各个分位数以及其它分布度量,并通过精算实务中的数值实例应用R软件加以实证分析。实证结果表明,两种Bootstrap方法得到的参数误差、过程标准差、预测均方误差都与解析表示估计的结果很接近。     

A response surface analysis of critical values for the lead-lag ratio with application to high frequency and non-synchronous financial data

Granger causality tests are being supplanted by new methods such as the Lead-Lag Ratio, particularly in finance where data arrives at random times and systematic sampling often produces spurious results. Existing approaches are insufficient; outside of block-sampling using a bootstrap, the lead-lag ratio has generally been assessed against a benchmark of 1 without regard for statistical significance. We use simulations to generate a response surface for the Lead-Lag Ratio. Our modelled critical values are applied to reassess the findings of three previous studies of lead/lag relations between financial return series with high frequency data. Our response surface method proves to be a convenient and efficient alternative to using a bootstrap.     

Confidence intervals for probabilities of default

In this paper we conduct a systematic comparison of confidence intervals around estimated probabilities of default (PD) using several analytical approaches as well as parametric and nonparametric bootstrap methods. We do so for two different PD estimation methods, cohort and duration (intensity), with 22 years of credit ratings data. We find that the bootstrapped intervals for the duration-based estimates are relatively tight when compared to either analytic or bootstrapped intervals around the less efficient cohort estimator. We show how the large differences between the point estimates and confidence intervals of these two estimators are consistent with non-Markovian migration behavior. Surprisingly, even with these relatively tight confidence intervals, it is impossible to distinguish notch-level PDs for investment grade ratings, e.g. a PD_AA− from a PD_A+. However, once the speculative grade barrier is crossed, we are able to distinguish quite cleanly notch-level estimated PDs. Conditioning on the state of the business cycle helps: it is easier to distinguish adjacent PDs in recessions than in expansions.     

Bootstrap Tests for Multivariate Event Studies

Statistical tests for multivariate event studies—exact or asymptotic—are derived based on multivariate normality. As it has been previously documented that the performances of these tests are not satisfactory, because stock returns are far from normally distributed (especially for daily returns), this paper proposes the use of bootstrap methods, which are free from any specific distributional assumption, to provide better approximations to the sampling distributions of test statistics in multivariate event studies. The Monte Carlo experiments based on real daily returns data show that the bootstrap tests outperform the traditional tests by having close rejection rates to the nominal significance levels. The traditional tests, in contrast, tend to reject the null hypotheses too often.     

The Causal Relationship Between Economic Policy Uncertainty and Stock Returns in China and India: Evidence from a Bootstrap Rolling Window Approach

This article applies a bootstrap rolling-window causality test to assess the causal relationship between economic policy uncertainty (EPU) and stock returns in China and India. Empirical literature examining causality between two time series may suffer from inaccurate results when the underlying full-sample time series have structural changes. However, the bootstrap rolling-window approach enables us to identify possible time-varying causalities between time series based on sub-sample data. Using a twenty-four-months rolling window over the period 1995:02 to 2013:02 in China and 2003:02–2013:02 in India, we do find that there are bidirectional causal relationships between EPU and stock returns in several sub-periods rather than in the whole sample period. However, the association between EPU and stock returns is, in general, weak for these two emerging countries. Our findings have important implications for policy makers and investors.     

Capital Allocation Using the Bootstrap

Abstract

This paper investigates the use of the bootstrap in capital allocation. In particular, for the distortion risk measure (DRM) class, we show that the exact bootstrap estimate is available in analytic form for the allocated capital. We then theoretically justify the bootstrap bias correction for the allocated capital induced from the concave DRM when the conditional mean function is strictly monotone. A numerical example shows a tradeoff exists between the bias reduction and variance increase in bootstrapping the allocated capital. However, unlike the aggregate capital case, the variance increase of the bias-corrected allocated capital estimate substantially outweighs the benefit of bias correction, making the bootstrap bias correction at the allocated capital level not as useful. Overall, the exact bootstrap without bias correction offers an efficient method for determining allocation over the ordinary resampling bootstrap estimate and the empirical counterpart.     

Evaluating the properties of analysts’ forecasts: A bootstrap approach

Previous research has reported that analysts’ forecasts of company profits are both optimistically biased and inefficient. However, many prior studies have applied ordinary least-squares regression to data where heteroskedasticity and non-normality are common problems, potentially resulting in misleading inferences. Furthermore, most prior studies deflate earnings and forecasts in an attempt to correct for non-constant error variances, often changing the specification of the underlying regression equation. We describe and employ the wild bootstrap—a technique that is robust both to heteroskedasticity and non-normality—to assess the reliability of prior studies of analysts’ forecasts. Based on a large sample of 23,283 firm years covering the period 1981–2002, our main results confirm the findings of prior research. Our results also suggest that deflation may not be a successful method of correcting for heteroskedasticity, providing a strong rationale for using the wild bootstrap in future work in this, and other areas of accounting and finance research.     

Bootstrap refinements in tests of microstructure frictions

Bootstrapping is often used as a substitute for asymptotic distributions when the latter are not available. Recent developments in the theory of the bootstrap show that combining the bootstrap with a known asymptotic distribution yields inferences that improve on those drawn from asymptotic distribution theory or bootstrapping alone. We review the key to obtaining the improvement and compare asymptotic and bootstrap inferences of three variance ratio tests used in microstructure research. The more precise bootstrap inferences lead to conclusions that differ from those found in extant research on transitory volatility. Asymptotic tests are biased toward rejection, and bootstrap and asymptotic critical values are not generally close to each other. These findings suggest that the more precise bootstrap inferences should be used in future applications of these tests, as well as in various other empirical applications where intradaily or other high frequency data are modeled using vector autoregressions     

The Retail Price Index and the Cost‐of‐Living Index: testing for consistency in theory and practice

This paper tests the published section‐level price and weight data used in the compilation of the UK retail price index (RPI) for consistency with the theory of the cost‐of‐living index. We use a non‐parametric test of theoretical consistency and bootstrap statistical methods to estimate the probability of consistency.     

Examining the Effect of Globalization on Insurance Activities in Large Emerging Market Economies

This study applies the cross-sectionally augmented distributed lag long-run estimation technique alongside bootstrap panel Granger causality testing to examine the impact of globalization on insurance market activities in large emerging market economies. Economic, social and political globalization indices are considered separately. Two alternative measures of globalization (de facto and de jure) are also used in each case for our estimations. The empirical results confirm the following; first, empirical outcomes are slightly sensitive to the choice of globalization measure used. Second, cross-sectional dependence and cross-country heterogeneity exist among large emerging market economies. Third, causality varies across large emerging economies with different conditions. We make a case for de facto measures as the most appropriate since they reflect actual practices rather than policy claims. We thus reach the conclusion that all dimensions of globalization positively impact life and non-life insurance density.     

A skeptical appraisal of the bootstrap approach in fund performance evaluation

It has become standard practice in the fund performance evaluation literature to use the bootstrap approach to distinguish “skills” from “luck”, while its reliability has not been subject to rigorous statistical analysis. This paper reviews and critiques the bootstrap schemes used in the literature, and provides a simulation analysis of the validity and reliability of the bootstrap approach by applying it to evaluating the performance of hypothetical funds under various assumptions. We argue that this approach can be misleading, regardless of using alpha estimates or their t‐statistics. While alternative bootstrap schemes can result in improvements, they are not foolproof either. The case can be worse if the benchmark model is misspecified. It is therefore only with caution that we can use the bootstrap approach to evaluate the performance of funds and we offer some suggestions for improving it.     

Using a Bootstrap Approach to Rate the Raters

This paper compares the accuracy of credit ratings of Moody's and Standard and Poor's. Based on 11,428 issuer ratings and 350 defaults in several datasets from 1999 to 2003 a slight advantage for the rating system of Moody's is detected. Compared to former research, the robustness of the results is increased by using nonparametric bootstrap approaches. Furthermore, robustness checks are made to control for the impact of watchlist entries, staleness of ratings, and the effect of unsolicited ratings on the results.     

Machine learning loss given default for corporate debt

We apply multiple machine learning (ML) methods to model loss given default (LGD) for corporate debt using a common dataset that is cross-sectional but collected over different time periods and shows much variation over time. We investigate the efficacy of three cross-validation (CV) schemes for hyper-parameter tuning and bootstrap aggregation (Bagging) in preventing out-of-time model performance deterioration. The three CV methods are shuffled K-fold, unshuffled K-fold and sequential blocked, which completely destroys, keeps some and completely retains the chronological order in the data, respectively. We find that it is important to keep the chronological order in the data when creating the training and testing samples, and the more the chronological order that can be retained, the more stable the out-of-time ML LGD model performance. By contrast, although bagging improves out-of-time fit in some cases, its effectiveness is rather marginal relative to that from the unshuffled K-fold and sequential blocked CV methods. Substantial uncertainty in relative out-of-time performance remains, however, thus ongoing model performance monitoring and benchmarking are still essential for sound model risk management for corporate LGD and other ML models.