Paramater estimation bias and volatility scaling in Black-Scholes option prices

When asset returns conform to a Gaussian distribution, the moments of the distribution over long return intervals may be estimated by scaling the moments of shorter return intervals. While it is well known that asset returns are not normally distributed, a key empirical question concerns the effect that scaling the volatility of dependent processes will have on the pricing of related financial assets. This study investigates the return properties of the most important currencies traded in spot markets against the U.S. dollar: the Japanese yen, the British pound, and the Swiss franc during the period November 1983 to April 2004. The novelty of this paper is that the volatility properties of the series are tested utilising statistical procedures developed from fractal geometry, with the economic impact determined within an option-pricing framework.     

The Effect of Serial Dependence on Multiperiod Holding Period Return Performance

The impact of the investment time horizon on risk‐return properties of asset returns depends on the presence of serial correlation and higher order serial dependencies. We present a methodology for decomposing multiperiod holding period return covariance into serial and cross‐sectional components using a recursive multiplicative model that captures the effects of serial and cross‐sectional dependencies and their joint effects without requiring a distributional form assumption. Applying this model to historical monthly return series for commonly held financial assets and portfolios of assets, we investigate the significance of the investment time horizon, the existence and relevance of time diversification, the inflation‐hedging effectiveness of different assets, and the appropriateness of applying traditional capital market theory in a multiperiod framework.     

Aggregational Gaussianity and barely infinite variance in financial returns

This paper aims at reconciling two apparently contradictory empirical regularities of financial returns, namely, the fact that the empirical distribution of returns tends to normality as the frequency of observation decreases (aggregational Gaussianity) combined with the fact that the conditional variance of high frequency returns seems to have a (fractional) unit root, in which case the unconditional variance is infinite. We provide evidence that aggregational Gaussianity and infinite variance can coexist, provided that all the moments of the unconditional distribution whose order is less than two exist. The latter characterizes the case of Integrated and Fractionally Integrated GARCH processes. Finally, we discuss testing for aggregational Gaussianity under barely infinite variance. Our empirical motivation derives from commodity prices and stock indices, while our results are relevant for financial returns in general.     

Turbulence in financial markets: the surprising explanatory power of simple cascade models

Price changes in financial markets have been found to share many of the features characterizing turbulent flows. In particular, a number of recent contributions have highlighted that time series from both stock and foreign exchange markets possess multifractal statistics, i.e. the scaling behaviour of absolute moments is described by a convex function. These findings have stimulated the application of certain cascade models from statistical physics to financial data. Extant work in this area has so far been confined to parameter estimation and visual comparison of empirical and theoretical scaling properties. The lack of rigorous statistical measures of goodness of fit in the literature on turbulence has, however, impeded a comparison of these new models with standard approaches in empirical finance. Here we try to fill this gap and provide a first assessment of two elementary cascade models based on elementary goodness-of-fit criteria. As it turns out, these relatively simple one-parameter models are not only capable of accommodating the multiscaling behaviour of price changes, but also provide a perplexingly good fit of the unconditional distribution of the data. In a double-blind test, we would, in fact, be unable to reject identity of the data-generating processes underlying empirical records and simulated data from stochastic cascades.     

The influence of systematic risk factors and econometric adjustments in catastrophic event studies

Event study methodology is a well-accepted technique in finance. Although its application is popular, there have not been many critical assessments of this practice. For instance, in the estimation process, the researcher has to make a choice in terms of which asset pricing model to adopt when calculating expected returns. Different expected return models and financial econometrics adjustments may give rise to different results. This study explores seven commonly employed approaches. Using terrorist attacks and the subprime crisis as events, we calculate abnormal returns with different expected return techniques and then assess if there is a change in the result. Our evidence shows that the results vary according to the choice of the technique in estimating an expected return.     

Commodity volatility breaks

Volatility is a key determinant of derivative prices and optimal hedge ratios. This paper examines whether there are structural breaks in commodity spot return volatility using an iterative cumulative sum of squares procedure and then uses GARCH (1,1) to model volatility during each regime.The main empirical finding is the very limited evidence of commodity volatility breaks during the recent financial crisis. This suggests commodity return volatility was not exceptionally high during the recent financial crisis compared to the 1985–2010 sample period as a whole. For many commodities there are multiple idiosyncratic breaks in volatility; this suggests commodity specific supply or demand factors are important determinants of volatility. The empirical results overall are consistent with the view that commodities are too diverse to be considered as an asset class. Finally, we find commodity volatility persistence remains very high for many commodity returns even after structural breaks are accounted for.     

Does Trading Volume Contain Information to Predict Stock Returns? Evidence from China's Stock Markets

This paper examines empirical contemporaneous and causal relationships between trading volume, stock returns and return volatility in China's four stock exchanges and across these markets. We find that trading volume does not Granger-cause stock market returns on each of the markets. As for the cross-market causal relationship in China's stock markets, there is evidence of a feedback relationship in returns between Shanghai A and Shenzhen B stocks, and between Shanghai B and Shenzhen B stocks. Shanghai B return helps predict the return of Shenzhen A stocks. Shanghai A volume Granger-causes return of Shenzhen B. Shenzhen B volume helps predict the return of Shanghai B stocks. This paper also investigates the causal relationship among these three variables between China's stock markets and the US stock market and between China and Hong Kong. We find that US return helps predict returns of Shanghai A and Shanghai B stocks. US and Hong Kong volumes do not Granger-cause either return or volatility in China's stock markets. In short, information contained in returns, volatility, and volume from financial markets in the US and Hong Kong has very weak predictive power for Chinese financial market variables.     

A fully parametric approach to return modelling and risk management of hedge funds

This paper examines the empirical properties of hedge fund returns and proposes a fully parametric model capable of adequately describing both univariate and multivariate return properties. The suggested model is based on the multivariate extension of the Normal Inverse Gaussian (NIG) distribution and will be shown to be capable of capturing the characteristic distributional features of hedge fund returns. Drawing on recent research in the area of Generalized Hyperbolic distributions and their calibration, we will elaborate on the application of the NIG-model for risk management purposes, and highlight the differences between the NIG and the Gaussian model.      

ESTIMATING RETURNS ON FINANCIAL INSTRUMENTS: TIME VERSUS MONEY-WEIGHTED RETURNS

The present paper addresses the problem of estimating returns on financial instruments when there is incomplete information about the instrument's cash flows. Two return metrics are analysed; namely, the money-weighted return and the time-weighted return. Returns are usually reported in the financial media on a money-weighted basis. However, there is increasing evidence that returns measured on a time-weighted basis are more appropriate for the evaluation of financial performance. The present note outlines the relationship between the two return metrics and examines some estimation procedures which may be used.     

Optimal portfolio positioning within generalized Johnson distributions

Many empirical studies have shown that financial asset returns do not always exhibit Gaussian distributions, for example hedge fund returns. The introduction of the family of Johnson distributions allows a better fit to empirical financial data. Additionally, this class can be extended to a quite general family of distributions by considering all possible regular transformations of the standard Gaussian distribution. In this framework, we consider the portfolio optimal positioning problem, which has been first addressed by Brennan and Solanki [J. Financial Quant. Anal., 1981, 16, 279–300], Leland [J. Finance, 1980, 35, 581–594] and further developed by Carr and Madan [Quant. Finance, 2001, 1, 9–37] and Prigent [Generalized option based portfolio insurance. Working Paper, THEMA, University of Cergy-Pontoise, 2006]. As a by-product, we introduce the notion of Johnson stochastic processes. We determine and analyse the optimal portfolio for log return having Johnson distributions. The solution is characterized for arbitrary utility functions and illustrated in particular for a CRRA utility. Our findings show how the profiles of financial structured products must be selected when taking account of non Gaussian log-returns.     

Usefulness of comprehensive income reporting in Canada

In January 2005 the Canadian Accounting Standards Board (AcSB) issued three new accounting standards that require Canadian firms to mark-to-market certain financial assets and liabilities and recognize the holding gains and losses related to these items as other comprehensive income or as part of net income. The Board’s objectives for issuing the new standards are (i) to harmonize Canadian GAAP with US and International GAAP, (ii) to enhance the transparency and usefulness of financial statements, and (iii) to keep pace with changes in accounting standards in other countries that are moving towards fair value accounting. This paper investigates empirically whether requiring Canadian companies to report comprehensive income and its components provides the securities market with incremental value-relevant information over the traditional historical-cost earnings approach.Previous empirical studies provide mixed evidence on the value relevance of other comprehensive income and its components. This mixed evidence may be attributed partially to the use of as if methodology to construct an ex-ante measure of other comprehensive income prior to the implementation of SFAS 130, which introduces measurement error. In contrast, this study uses actual data on other comprehensive income for a sample of Canadian firms cross-listed in the US in the period 1998–2003. We find evidence that available-for-sale and cash flow hedges components are significantly associated with price and market returns. We also find that aggregate comprehensive income is more strongly associated (in terms of explanatory power) with both stock price and returns compared to net income. However, we find that net income is a better predictor of future net income relative to comprehensive income. Our findings suggest that mandating all Canadian firms to adopt the new accounting standards is expected to enhance the usefulness of financial statements. Our findings, therefore, should be of interest to Canadian accounting policy makers as they provide ex-ante evidence on the potential usefulness of mandating firms to report comprehensive income and the components of other comprehensive income in their financial statements.     

Dissecting Earnings Recognition Timeliness

We dissect the portion of stock price change of the fiscal year that is recognized in reported accounting earnings of the year. We call this portion earnings recognition timeliness (ERT). The emphasis in our dissection is on empirical identification of two fundamental precepts of financial accounting: (1) the matching principle, which is manifested in the recognition of expenses in the same period as the related benefits (i.e., sales revenue) accrue; and (2) recognition of expenses in the current period due to changes in expectations regarding earnings of future periods (we refer to these expenses as the expectations element of expenses). Although the expectations element has implicitly been at the core of much of the recent empirical literature on asymmetry in the earnings/return relation, it has not been explicitly identified. This recent literature is based on the premise that bad news about the future leads to more recognition of expenses in the current period (such as write‐downs) whereas good news about the future tends to have a much lesser effect on expenses of the current period; asymmetry in the expenses/return relation is captured implicitly via the observation of asymmetry in the earnings/return relation (i.e., asymmetry in ERT). Since the ERT reflects the relation between sales revenue and returns, matched expenses and returns, as well as the relation between the expectations element of expenses and returns, a focus on the expectations element may lead to sharper inferences. Our straightforward empirical procedure permits a focus on this element.     

Constructing Asset Pricing Models With Specific Factor Loadings

We demonstrate how one can build pricing formulae in which factors other than beta may be viewed as determinants of asset returns. This is important conceptually as it demonstrates how the additional factors can compensate for a market portfolio proxy that is mis‐specified, and also shows how such a pricing model can be specified ex ante. The procedure is implemented by first selecting an ‘orthogonal’ portfolio which falls on the mean‐variance efficient frontier computed from the empirical average returns, variances and covariances on the equity securities of a large sample of firms. One then determines the inefficient index portfolio which leads to a vector of betas that when multiplied by the average return on the orthogonal portfolio, and which when subtracted from the vector of average returns for the firms comprising the sample, yields an error vector that is equal to the vector of numerical values for the variables that are to form the basis of the asset pricing formula. There will then be a perfect linear relationship between the vector of average returns for the firms comprising the sample, the vector of betas based on the inefficient index portfolio and such other factors that are deemed to be important in the asset pricing process. We illustrate computational procedures using a numerical example based on the quality of information contained in published corporate financial statements.     

Long-term asset tail risks in developed and emerging markets

A power law typically governs the tail decay of financial returns but the constancy of the so-called tail index which dictates the tail decay remains relatively unexplored. We study the finite sample properties of some recently proposed endogenous tests for structural change in the tail index. Given that the finite sample critical values strongly depend on the tail parameters of the return distribution we propose a bootstrap-based version of the structural change test. Our empirical application spans developed and emerging financial asset returns. Somewhat surprisingly, emerging stock market tails are not more inclined to structural change than their developed counterparts. Emerging currency tails, on the contrary, do exhibit structural shifts in contrast to developed currencies. Our results suggest that extreme value theory (EVT) applications in hedging tail risks can assume stationary tail behavior over long time spans provided one considers portfolios that solely consist of stocks or bonds.     

Estimation of the underlying structure of systematic risk with the use of principal component analysis and factor analysis

We present an improved methodology to estimate the underlying structure of systematic risk in the Mexican Stock Exchange with the use of Principal Component Analysis and Factor Analysis. We consider the estimation of risk factors in an Arbitrage Pricing Theory (APT) framework under a statistical approach, where the systematic risk factors are extracted directly from the observed returns on equities, and there are two differentiated stages, namely, the risk extraction and the risk attribution processes. Our empirical study focuses only on the former; it includes the testing of our models in two versions: returns and returns in excess of the riskless interest rate for weekly and daily databases, and a two-stage methodology for the econometric contrast. First, we extract the underlying systematic risk factors by way of both, the standard linear version of the Principal Component Analysis and the Maximum Likelihood Factor Analysis estimation. Then, we estimate simultaneously, for all the system of equations, the sensitivities to the systematic risk factors (betas) by weighted least squares. Finally, we test the pricing model with the use of an average cross-section methodology via ordinary least squares, corrected by heteroskedasticity and autocorrelation consistent covariances estimation. Our results show that although APT is very sensitive to the extraction technique utilized and to the number of components or factors retained, the evidence found partially supports the APT according to the methodology presented and the sample studied.     

Selecting Australian equity superannuation funds: A retail investor's perspective

In this performance persistence study, two questions are addressed. First, what is the relationship between past fund returns and future performance? Secondly, does a ’hot hand‘ fund selection system deliver economically significant returns to investors? Using a sample of Australian equity superannuation funds over the 1990s, the answers from this study are as follows: on a raw and risk-adjusted return basis the authors find evidence of mean reversion, with prior annual performance having little influence on future fund return. Selecting funds based on a persistence strategy resulted in underperformance of industry and passive returns for the retail superannuation investor over the sample period. The findings of the study have serious implications for financial planning advisers who market superannuation funds based on past performance. The results suggest that previous annual performance has little influence on future returns.     

Risk,Mispricing, and Value Investing

We evaluate the stock return performance of a modified version of the book-to-market strategy and its implications for market efficiency. If the previously documented superior stock return of the book-to-market strategy represents mispricing, its performance should be improved by excluding fairly valued firms with extreme book-to-market ratios. To attain this, we classify stocks as value or glamour on book-to-market ratios and accounting accruals jointly. This joint classification is likely to exclude stocks with extreme book-to-market ratios due to mismeasured accounting book values reflecting limitations underlying the accounting system. Using both 12-month buy-and-hold returns and earnings announcement returns, our results show that this joint classification generates substantially higher portfolio returns in the post-portfolio-formation year than the book-to-market classification alone with no evidence of increased risk. In addition, this superior stock return performance is more pronounced among firms held primarily by small (unsophisticated) investors and followed less closely by market participants (stock price <$10). Finally, and most importantly, financial analysts are overly optimistic (pessimistic) about earnings of glamour (value) stock, and for a subset of firms identified as overvalued by our strategy, the earnings announcement raw return, as well as abnormal return, is negative. These last results are particularly important because it is hard to envision a model consistent with rational investors holding risky stocks with predictable negative raw returns for a long period of time rather than holding fT-bills and with financial analysts systematically overestimating the earnings of these stocks while underestimating earnings of stocks that outperform the stock market.     

互联网货币基金的多重分形分析——以余额宝、理财通为例

本文以余额宝、理财通为互联网货币基金代表,选取两种货币基金2013-2020年的七日年化收益率数据为研究区间,运用多重分形分析方法研究了两种货币基金的对数日收益率序列的多标度行为及其之间的非线性动态关系。研究结果表明,余额宝与理财通两收益率序列均存在时变的多重分形特征。比较而言,理财通收益率序列的多重分形强度更大,而余额宝收益率序列的正持续性更强;在小波动下,两收益率序列均表现出强持续性;两种互联网货币基金之间的交互相关关系是正相关的,具有多重分形性。同时,讨论了新冠肺炎疫情对互联网货币基金收益率的影响,并针对当前新冠肺炎疫情形势,给出投资理财建议。