Learning about beta: Time-varying factor loadings, expected returns, and the conditional CAPM

We amend the conditional CAPM to allow for unobservable long-run changes in risk factor loadings. In this environment, investors rationally “learn” the long-run level of factor loadings from the observation of realized returns. As a consequence of this assumption, we model conditional betas using the Kalman filter. Because of its focus on low-frequency variation in betas, our approach circumvents recent criticisms of the conditional CAPM. When tested on portfolios sorted by size and book-to-market, our learning-augmented conditional CAPM passes the specification tests.     

A re-examination of the asymmetric power ARCH model

The purpose of this paper is to provide a comprehensive methodology for the analysis of the Asymmetric Power ARCH model. First, it gives the ARMA representations of a power transformation of the conditional variance and the absolute returns. Second, it derives a certain fractional moment of the absolute observations. Third, it obtains the autocorrelation function of the power-transformed absolute returns. Finally, the practical implications of the results are illustrated empirically using daily data on five East Asia stock indices.     

The intertemporal relationship between market return and variance: an Australian perspective

In this paper we investigate the intertemporal relationship between the market risk premium and its conditional variance in an Australian setting. Using a bivariate EGARCH‐M model combined with the dynamic conditional correlation (DCC) framework as proposed by Engle (2000), we find evidence of a positive relationship between the market risk premium and its variance and evidence of two distinct interest rate effects. Furthermore, while the bond market's own variance is not priced by investors, we find that the covariance between equity and bond markets is a significant risk factor that is priced in the market.     

The Determinants of Conditional Autocorrelation in Stock Returns

We investigate whether return volatility, trading volume, return asymmetry, business cycles, and day‐of‐the‐week are potential determinants of conditional autocorrelation in stock returns. Our primary focus is on the role of feedback trading and the interplay of return volatility. We present empirical evidence using conditional autocorrelation estimates generated from multivariate generalized autoregressive conditional heteroskedasticity (M‐GARCH) models for individual U.S. stock and index data. In addition to return volatility, we find that trading volume and market returns are important in explaining the time‐varying patterns of return autocorrelation.     

A Bayesian analysis of a variance decomposition for stock returns

We apply Bayesian methods to study a common vector autoregression (VAR)-based approach for decomposing the variance of excess stock returns into components reflecting news about future excess stock returns, future real interest rates, and future dividends. We develop a new prior elicitation strategy, which involves expressing beliefs about the components of the variance decomposition. Previous Bayesian work elicited priors from the difficult-to-interpret parameters of the VAR. With a commonly used data set, we find that the posterior standard deviations for the variance decomposition based on these previously used priors, including “non-informative” limiting cases, are much larger than classical standard errors based on asymptotic approximations. Therefore, the non-informative researcher remains relatively uninformed about the variance decomposition after observing the data. We show the large posterior standard deviations arise because the “non-informative” prior is implicitly very informative in a highly undesirable way. However, reasonably informative priors using our elicitation method allow for much more precise inference about components of the variance decomposition.     

Hourly index return autocorrelation and conditional volatility in an EAR–GJR-GARCH model with generalized error distribution

We study the autocorrelation and conditional volatility of the hourly Dow Jones Industrial Index return data from October 1974 to September 2002 using an exponential asymmetric AR–GARCH specification with a generalized error distribution. Our findings document a positive autocorrelation in hourly return data in the early years of the sampling period, but the autocorrelation turns negative after 1986 and the negative shock causes more impact on the conditional volatility. This latter period evidence stands in contrast to prior findings employing lower frequency and/or earlier year data. In addition, our results present some evidence of a negative relation between autocorrelation and conditional volatility before 1986 (albeit weaker than prior findings), but this negative relationship disappears after 1986.     

Conditional and Unconditional Conservatism:Concepts and Modeling

We develop a model that captures the distinct natures of and interactions between conditional and unconditional conservatism. Under unconditional conservatism, the book value of net assets is understated due to predetermined aspects of the accounting process. Under conditional conservatism, book value is written down under sufficiently adverse circumstances, but not up under favorable circumstances. The specification of earnings provided by the model yields hypotheses about how unconditional conservatism and other factors preempt conditional conservatism and so affect the asymmetric response of earnings to positive and negative share returns, both current and lagged, documented by Basu (1995, “Conservatism and the Asymmetric Timeliness of Earnings.” Ph.D. dissertation, University of Rochester’ 1997, “The Conservatism Principle and the Asymmetric Timeliness of Earnings.” Journal of Accounting and Economics 24, 3–37).This revised version was published online in August 2005 with a corrected cover date.     

Volatility and cross correlation across major stock markets

Several papers have documented the fact that correlations across major stock markets are higher when markets are more volatile—this is done by comparing unconditional correlations over sub-periods or by using conditional correlations that are time varying. In this paper we examine the relation between correlation and variance in a conditional time and state varying framework. We use a switching ARCH (SWARCH) technique that does two things. One, it enables us to model variance as state varying. Two, a bivariate SWARCH model allows us to go from conditional variance to state varying covariances and correlations and hence test for differences in correlations across variance regimes. We find that the correlations between the U.S. and other world markets are on average 2 to 3.5 times higher when the U.S. market is in a high variance state as compared to a low variance regime. We also find that, compared to a GARCH framework, the portfolio choices resulting from our SWARCH model lead to higher Sharpe ratios.     

Distribution of parallel exchange rates in African countries

This paper investigates the distribution of parallel exchange rates in African countries using exploratory data analysis techniques and model fitting. Stable laws are fitted to empirical distributions using the maximum likelihood estimation method. Empirical evidence supports the stable hypothesis these distributions are positively skewed and have tails that are much heavier than Gaussian counterparts. The stable hypothesis is further supported by the “converging variance test,” which suggests that these distributions have infinite variance.     

Measuring performance in a dynamic world: Conditional mean–variance fundamentals

We develop conditional alpha performance measures that are consistent with conditional mean–variance analysis and the magnitude and sign of the implied true conditional time-varying alphas. The sequence of conditional alphas and betas is estimable from surprisingly simple unconditional regressions. Other common performance measures are derivable from the conditional investment opportunity set based on its conditional asset return moments. Our bootstrap analysis of Morningstar mutual fund returns data demonstrates that the differences between existing conditional alpha measures and our proposed alpha are substantive for typical parameterizations.     

Empirical study on relationship between persistence-free trading volume and stock return volatility

A large body of literature finds that the unexpected trading volume, which is obtained by filtering out time trend, autocorrelation, can be used as a proxy of the information flow and can explain the heteroskedasticity of stock return in some degrees. In this paper, we find that the heteroskedasticity exists in the unexpected trading volume, and we further generate a new information proxy by filtering out the heteroskedasticity from the unexpected trading volume, termed “persistence-free trading volume”. Our empirical results indicate that the persistence-free trading volume can explain the heteroskedasticity of the return better than the unexpected trading volume; moreover, the explanatory power of the persistence-free trading volume is positively related to market maturity.     

Evidence of an asymmetry in the relationship between volatility and autocorrelation

This paper focuses on the general determinants of autocorrelation and the relationship between autocorrelation and volatility in particular. Using UK stock market index and individual stock price data, a multivariate generalized autoregressive conditional heteroskedasticity (M-GARCH) model is used to generate estimates of conditional autocorrelation. The covariance equation of this model is modified to include the potential determinants of autocorrelation including volatility, which is proxied using the time series of filtered probabilities of a Markov regime switching model. Consistent with the previous literature, this paper documents a negative relationship between volatility and autocorrelation. The results suggest that an asymmetry exists in this relationship which is attributed to the constraints placed on short selling.     

Modeling conditional return autocorrelation

Empirical estimates of conditional return autocorrelation are generated over the period 1973 to 2000 for S&P500 index data, as well as for a small selection of individual U.S. stocks. We find that conditional autocorrelation is highly variable, and these dynamics are consistent with changes in point autocorrelation estimates generated in various subperiods. The conditional autocorrelation estimates for some stocks exhibited a pattern of mean reversion, while for others, evidence of long-term trends and structural breaks was found. While we were unable to uncover what characteristics drive the nature of these autocorrelation patterns, our analysis ruled out industry, investor type or degree of internationalisation as explanations.     

Psychology, meaning and the challenges of longevity

Humankind has begun to reap one of the most valued harvests of its scientific and technological pursuits: a significant increase in human longevity. We now live longer than ever before, due in large part to advances in medicine and health care that provide those who have the opportunity to afford them a lifespan that for many approaches or exceeds the 100-year mark. It is now within the realm of possibility that people will live lives of 125 years or more within the next century. However, our ability to increase physical longevity may have outstripped our ability to deal individually and socially with these new lives, these new existences that go well beyond what has traditionally been considered a “working life”. How well-prepared are we psychologically to cope with the meaning of a life that extends to as much as 150 years or more? In this new “age of longevity”, what are the challenges for psychology as a resource for humanity in its quest to give definition to the experience of being alive, as well as for managing the affairs of everyday life? Traditional developmental theories in psychology tend to articulate early stages of life in detail, but are generally mute on the matter of later life. Cognitive psychology has been inclined to view longevity as leading to a deterioration of mental faculties due to “aging”. This paper examines the psychological implications of increased lifespans from an optimistic perspective by reviewing current developments in research on cognition, emotion and aging. The review identifies trends in psychology that, if emphasized and strengthened, may lead to improved theoretical frameworks that cast longevity in a positive light, and that identify how people can find meaning and fulfillment throughout their whole lifespan.

“Grow old along with me! The best is yet to be, The last of life for which the first was made.” Robert Browning “Rabbi Ben Ezra”

I first encountered Browning’s works as an undergraduate, and being a pre-engineering student at the time my tendencies toward poetry were stunted to say the best. Few of the great works of literature my teachers compelled me to read at that stage of my life and development made enough of an impact to last beyond the length of the course requiring their reading. Much has changed since then and my interests in literature and what literature has to say that is of value for our lives has deepened. But Browning’s enthusiastic call to join him in aging has always been a fascination. Indeed, what could be more of a contradiction to modern attitudes about becoming elderly than to claim “the best is yet to be”? What can be more of a challenge to how we approach the relationship between being young and being old than to claim that the last of life is “for which the first was meant”? What can the possible rewards of the golden years be that transcend the glorious enthusiasms, unfettered optimisms, and just pure physical conveniences of being young? Or, was Browning simply trying to sucker us all into a fait accompli, the hopeful outcome of which is the envy of the very youth that the aged often envy so much?There is little enough envy of the aged today. I approach these years with great caution, recognizing that how I look upon those who are two decades older than myself will, in turn, condition me to see myself in those years much in the way that I see them now. “Aging” is not something anyone really wants to do. We want to, at best, “grow older”, a perspective that carries with it a more positive spin: growing wiser, growing up, or simply “growing” with all of its new-age connotations of personal enlightenment and becoming. I am not “aging”, I am “becoming at one”.The language we have adopted to talk about the time-course of life, and particularly about the years in the latter third of that course, does much to frame both how we live those years and how we anticipate them in our youth. Our expectations are ones of decline, physical debilitation and mental infirmity. We “retire”, as in withdrawal into seclusion, away from the mainstream of life and into the backwater eddy of inaction. On the shelf.Much of this view has been reinforced by how humanity has approached examining this aspect of its own time course through science. We study aging with an eye to how its effects influence the abilities of those so afflicted to perform or operate compared to those who still have a grasp on their full faculties. And, of course, we find that as people grow older, they do not approach life in the same way as do younger people.Part of our view on life comes from the very way in which science is funded: those interested in the last of life often receive their support from the National Institute on Aging, not the National Institute on The Last of Life for Which the First Was Made. Research agendas often focus on identifying sources of infirmity and potential prostheses, either physical or social, that can ease the lives of the elderly on their way toward achieving the goal of successful aging. All too often, success in aging means imposing relatively few demands on social resources or on the lives of younger people, such as family members. In our “ageist” society, elderliness is not generally equated with status and stature. Less and less, the young “listen” to the old out of deep interest in their lives and their experiences. Wisdom is the providence of the freshly matured and recently educated.The shortcomings of life in the advancing years are many and well-documented in the research literature. Memory spans decrease, information retrieval becomes less reliable, and new information is less readily assimilated. As people become older, they appear to rely more and more on automatic processing of information, quick associations and the like, rather than deliberative and conscious reasoning [1]. For the older mind, intuition is at least moderately preferred over analysis. For example, younger people tend to interpret stories analytically, focusing on details, while older people tend to focus less on a story’s details and more on its “gist” and its underlying significance to things that are important to them [2], and tend to do better at grasping and dealing with information in terms of its holistic meaning [3 and 4].The effects of these differences in information processing between young and old can be seen in practical matters of everyday life, such as decision making and judgment. Johnson [5], for example, found that older adults use simplifying decision strategies more often than younger adults. These strategies, such as noncompensatory rules that consider only the positive or the negative aspects of a decision option but not both, relieve one of the psychological burden of making complex and effortful tradeoffs, at the possible expense of efficiency and accuracy. Chasseigne et al. [6] found that as people age, they become less consistent in their use of information in making judgments and predictions; even reducing the overall information load and demands on memory does little to improve the reliability of their judgments. ¹     

On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks

We find support for a negative relation between conditional expected monthly return and conditional variance of monthly return, using a GARCH-M model modified by allowing (1) seasonal patterns in volatility, (2) positive and negative innovations to returns having different impacts on conditional volatility, and (3) nominal interest rates to predict conditional variance. Using the modified GARCH-M model, we also show that monthly conditional volatility may not be as persistent as was thought. Positive unanticipated returns appear to result in a downward revision of the conditional volatility whereas negative unanticipated returns result in an upward revision of conditional volatility.     

The effect of cognitive style and sponsorship bias on the treatment of opportunity costs in resource allocation decisions

The incorporation of opportunity cost is stressed in normative approaches to resource allocation decisions. Empirical evidence has revealed a variety of behaviours. A consequence of inappropriate treatment of opportunity costs is an incorrect assessment of the economic consequences of resource allocation decisions. Improved understanding of why some managers treat opportunity costs inappropriately permits identifying situations where the incorrect economic evaluations will lead to sub-optimal resource allocation and therefore provides a basis for remedial action. This study identifies two conditional factors which potentially influence the way managers respond to opportunity cost information.These factors are managers' cognitive style and whether or not managers sponsor a project (project sponsorship), and it is argued that they influence managers' decisions on opportunity costs in situations in which opportunity cost implications are implicit. In particular, the paper proposes, first, that in the absence of project sponsorship, managers with an “intuitive” style of “taking in data” will tend to incorporate opportunity costs in their economic decisions whereas those wiht a “sensation” style will not. Second, it is suggested that because sponsorship encourages managers to ignore negative economic signals (sponsorship bias) any effects of cognitive style will be moderated in conditions where sponsorship is evident.A laboratory experiment with managers as subjects was used to examine these propositions. The results indicated that intuitive managers tended to incorporate opportunity costs in their decisions whereas sensation individuals appeared to focus more on the directness of the relationship between expenditure and a project to determine the relevance of the cost. Opportunity cost implications tended not to be identified by the sensation group. Evidence was found that sponsorship moderated the influence of cognitive style on decisions to include opportunity costs.     

Dispersion trading: Empirical evidence from U.S. options markets

This paper develops empirical evidence on the viability of a form of volatility trading known as “dispersion trading.” The results shed light on the efficiency with which U.S. options markets price volatility.Using end-of-day implied volatilities extracted from equity option prices for the stocks that comprise the S&P 500, the implied volatility of the S&P 500 is computed using a modification of the Markowitz variance equation. This Markowitz-implied volatility is then compared to the implied volatility of the S&P 500 extracted directly from index options on the S&P 500. These contemporaneous measures of implied volatility are then examined for exploitable discrepancies both with and without transaction costs. The study covers the period October 31, 2005 through November 1, 2007.It is shown that, from a trader's perspective, index option implied volatility tended to be more often “rich” and component volatilities tended to be more often “cheap.” Nevertheless, there were times when the opposite was true; suggesting that potential dispersion trades can run in either direction.     

Testing for strict stationarity in financial variables

This paper considers the stationarity properties of a variety of financial variables using statistical tests for strict stationarity. We find that there has been a gradual shift in unconditional variances for the variables examined during the 90’s and 2000’s and that this is the main cause of the widespread rejection of the strict stationarity null hypothesis. This is a powerful result which suggests that the consideration of conditional mean and, especially, conditional variance models which assume stationarity is problematic for the period under examination. This casts serious doubts on the usefulness of models that assume strict stationarity and model conditional second moments, such as GARCH and stochastic volatility models.     

Automatic variance ratio test under conditional heteroskedasticity

An extensive Monte Carlo experiment is conducted to evaluate small sample properties of the automatic variance ratio test under conditional heteroskedasticity. It is found that the test shows serious size distortion in small samples. For improved small sample performance, this paper proposes the use of wild bootstrap. When wild bootstrapped, the automatic variance ratio test shows no size distortion, and it has power substantially higher than its competitors such as the Chen–Deo test and wild bootstrap Chow–Denning test.