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In this paper, we analyze the relative performances of pairs trading and cross-sectional momentum (CSM) strategies by comparing their expected returns. It is shown that the Sharpe ratio and the autocorrelation in the spread between the asset returns are the key factors in determining the relative performances of the two strategies, and an analytic expression for the condition under which one strategy outperforms the other is obtained in terms of these factors. It is also shown that the pairs trading strategy outperforms the CSM strategy in the majority of practically relevant situations.

In this article, the authors revisit a neglected paper written by Rubinstein in which he advocated a generalized logarithmic utility function. The profession has rather ignored his model in favor of the mean–variance approach, for reasons that are well known. The authors note that generalized logarithmic utility allows us to identify absolute risk aversion more directly and intuitively than the approaches adopted in mean–variance portfolio construction. They demonstrate that, for top-level asset allocation in which the conditions required by mean–variance are satisfied and mean–variance gives a good approximation to expected utility, generalized logarithmic utility gives essentially the same answer. In situations not suited to mean–variance, such as the inclusion of derivatives in portfolios or, more generally, when higher moments in return and utility probability distributions are unavoidable, Rubinstein’s model appears superior and seems particularly well suited to multi-asset investment. The authors’ simplified Bayesian model shows out-of-sample advantages for broad US asset allocation for the 2000 through mid-2020 period. TOPICS:Quantitative methods, statistical methods, portfolio theory, portfolio construction Key Findings ▪ Maximizing the expected Rubinstein utility increases expected surplus growth for conservative investors and for those who do not rebalance frequently. Markowitz’s risk aversion parameter is replaced without requiring subjective judgement of aversion to return variance. ▪ Bayesian prediction can incorporate both scenario priors and observed return data in a simple grid form. This increases model flexibility and decreases sensitivity to errors in estimates of return probability distribution parameters. ▪ We demonstrate out-of-sample advantages for Rubinstein utility with simplified Bayesian prediction in broad US stock, bond, and cash allocation for the most recent decades. This is based on a prior inferred from earlier history, including the 1929 crash.

We propose a multivariate model of returns that accounts for four of the stylised facts of financial data: heavy tails, skew, volatility clustering, and asymmetric dependence with the aim of improving the accuracy of risk estimates and increasing out-of-sample utility of investors’ portfolios. We accommodate volatility clustering, the generalised Pareto distribution to capture heavy tails and skew, and the skewed-t copula to provide for asymmetric dependence. The proposed approach produces more accurate VaR estimates than seven competing approaches across eight data sets encompassing five asset classes. We show that this produces portfolios with higher utility, and lower downside risk than alternative approaches including mean–variance. We confirm that investors can substantially increase utility by accounting for departures from normality.

We examine the 21-minute flash crash in the spot rate for Pound Sterling (GBP/USD) in October 2016. During this period, the sterling price fell 9%. Proprietary data reported to the Financial Conduc...

Existing approaches have considered characteristics of Environmental, Social and Corporate Governance (ESG) focused investments from a return-oriented perspective without paying due consideration to investors’ utility and how ESG features impact utility. We contribute to this literature by providing a model that captures the implications for investment if ESG is valued by the investor as well as wealth. We first present the necessary theory and discuss the rather challenging problem of calibration of the various risk and preference parameters. Using Thomson Reuters ESG data from 2002 to 2018, we provide further empirical evidence that investors who value ESG factors have improved utility which does not come at the cost of return performance.

Errors in variables in linear regression continue to be a major empirical issue in financial econometrics. We propose a method using the characteristic function (CF) to obtain estimates for linear models with errors in the variables. By assuming that the explanatory variable follows a flexible double-gamma distribution, we obtain closed-form expressions for the analytic CF of the data generating process. Through simulations, we show that our method performs well relative to existing techniques that address EIVs, including the most sophisticated CF-based techniques, the continuum generalized method of moments and nonparametric methods based on empirical cumulants. We further extend our CF technique to a multivariate setting where it continues to produce accurate estimates. We also provide guidance on implementing CF methods and apply the technique to estimating betas based on the capital asset pricing model.

We look at a technique of classification, based on convergent and divergent patterns of returns that has been applied to hedge funds and alternative investments, and apply it to US equity investment styles with a particular interest in ESG. We extend the technique by looking at the impact of price changes on factor-mimicking portfolio weights. This analysis leads to powerful insights into style return dynamics. In particular, an ESG-ranked long-short portfolio looks more like momentum than value.

Momentum-based investment strategies are widely used by practitioners, and their empirical properties have attracted considerable research interest from academics. This paper discusses some theoretical results on cross-sectional momentum, time-series momentum, and relative strength portfolio returns. We use simple examples to explain their relevance to both academics and practitioners alike despite the differences in their motivation and focus. We examine in detail the special case where there are only two underlying assets, and show analytically that many of the phenomena noted by empirical researchers have mathematical explanations.

The movement of international art prices in conjunction with other asset prices is preliminary to our understanding whether art is a luxury good. It is well known that there are linkages between art market prices and equity prices. However, less is known about the structure of dependence between these variables and the influence of gold prices and sentiment. We analyse art prices, at the outset using Granger causality and error correction models (ECM) to capture the long term dynamics between art prices, equity markets, gold prices and investor sentiment. The dataset we use is unique and covers British art prices from 1895 to the present. Initial results do not give a complete picture of price movements or a fitting description of wealth effects; to rectify this we look at short term dynamics in the art market. We assume a regime switching model to describe the movement of prices using a threshold variable that drives prices into possibly locally explosive regimes. These results indicate a dynamic wealth effect in that high (low) stock prices lead to subsequent increases (decreases) in art prices. However, this approach means that elasticities are now stochastic, and we redefine what a luxury good is. This is further explored by directly calculating elasticities from our model and its variants to analyse properties of art as a luxury good. Our threshold approach gives deeper insight into the impact of different market conditions than conventional ECM and cointegration modelling.

© 2019, © 2019, CFA Institute. We challenge the academic consensus that estimation error makes mean–variance portfolio strategies inferior to passive equal-weighted approaches. We demonstrate analytically, via simulation, and empirically that investors endowed with modest forecasting ability benefit substantially from a mean–variance approach. An investor with some forecasting ability improves expected utility by increasing the number of assets considered. We frame our study realistically using budget constraints, transaction costs, and out-of-sample testing for a wide range of investments. We derive practical decision rules to choose between passive and mean–variance optimization and generate results consistent with much financial market practice and the original Markowitz formulation.

Recent literature implies that despite being more diversified, fund of hedge funds (FOFs) are exposed to tail risk. We propose an explanation for this phenomenon; tail risk is a systematic ...

Endowments have been accused of hoarding their wealth. However, the theoretically ideal spending plan remains unclear and, in practice, endowments follow a range of rules. Here we derive and estima...

Although there is a vast empirical literature on cross sectional momentum (CSM) returns, there are no known analytical results on their distributional properties due, in part, to the mathematical complexity associated with their determination. In this paper, we derive the density of CSM returns in analytic form, along with moments of all orders, under the assumption that underlying asset returns are multivariate normal. The resulting expressions are highly non-trivial in general and involve truncated normal distributions. The distribution of CSM returns can be formally described as a mixture of the unified skew-normal family of distributions. However, if the asset returns are independent, then the density of the CSM returns is shown to be a mixture of univariate normals. In order to shed light on the general case, we present a detailed analysis of the case of two underlying assets, which is shown to explain many of the key features of CSM returns reported in the empirical literature.

Risk discriminating portfolio optimization provides a risk-related path to performance optimization

Given the key role of momentum-based trading strategies in active investing, assessing the merits of various trading strategies based on momentum should be of value to investors and managers alike. We summarise five momentum-based trading strategies which are well analysed in the academic literature, and introduce our new strategy named partial moment momentum (PMM) which distinguishes between upside and downside risks in the calculation of positions. Some empirical analyses suggest PMM outperforms the existing strategies.

In Kwon and Satchell (2018), a theoretical framework was introduced to investigate thedistributional properties of the cross-sectional momentum returns under the assumption that thevector of asset returns over the ranking and holding periods were multivariate normal. In thispaper, the framework is extended to derive the corresponding results when the asset returns aremultivariate Student&rsquo, s t. In particular, we derive the probability density function and the moments ofthe cross-sectional momentum returns and examine in detail the special case of two underlying assetsto demonstrate that many of the salient features reported in the empirical literature are consistentwith the theoretical implications.

A longstanding objective of managers is to reduce risk to their businesses. The conventional strategy for risk reduction is diversification, however, evidence for the effectiveness of diversification remains inconclusive. According to Organizational Portfolio Analysis, firms are viewed as portfolios of business units, and the key to risk reduction is both diversification and synchronization compensation. This study introduces &ldquo, desynchronicity&rdquo, a process that operationalizes synchronization compensation by assessing the degree of correlation between income streams of business units. Two samples of 737 and 332 firms (from COMPUSTAT) were used to empirically test the relationships between diversification and risk, and desynchronicity and risk. The results show that diversification alone will not always lead to a lower corporate risk. To reduce risk, firms also need to consider the desynchronicity of their business portfolios. Other practical implications include improved decisions on portfolio composition.

© 2016 The Journal of Risk and Insurance We investigate the role of individual capability and effort in the management of retirement ruin. In an experimental setting, we analyze how 854 defined contribution (DC) plan members reallocated wealth between a lifetime annuity and a phased withdrawal account when we increased the risk of exhausting the phased withdrawal account before the end of life. We find that more numerate individuals who put effort into understanding product features chose more longevity insurance at higher ruin risks. Financially literate members were more likely to show understanding of the product features, but general financial literacy did not directly improve ruin risk management. Initiatives aiming to help DC members understand income stream products at the time of the decision are warranted.

We identify two sources of bias arising from time-series regression used to compute beta. This bias arises due to the classical error in variables problem and a ‘mechanical interaction’ which exists when the index comprises the asset of interest. Assuming that the market is proxied by a fixed-weight index, we demonstrate that the relative weighting of an asset within the index, and/or the magnitude of its idiosyncratic risk, directly biases the beta estimate for the individual stock and also for all stocks within the index. Via simulations, we show that the problem is most pronounced for markets with a small number of highly concentrated assets. Finally, we propose a procedure to reduce this bias and apply the methods to equity data.

This paper introduces a generalization of quantiles, order statistics, and concomitants that we term co-quantiles, and investigates their statistical properties. The probability density functions for the co-quantiles are obtained along with their moments under the assumption that the distribution of the underlying data are multivariate normal. In contrast to the conventional order statistics that rank and record the same attribute of a population, or concomitants that consider different attributes observed over the same time period, co-quantiles allow the ranking and recording of different attributes across different time periods. The co-quantile results naturally reduce to those for order statistics and concomitants, and generalize those on the distributions of linear combinations and the maxima of vector valued random variables obtained in Arellano-Valle and Genton (2007, 2008) and those on cross sectional momentum returns obtained in Kwon and Satchell (2018). By applying the results to momentum spillover returns, we establish theoretically that these returns are susceptible to sudden changes in the skewness and the kurtosis during periods of market uncertainty. Since momentum spillover and cross sectional momentum are structurally very similar, this provides a theoretical explanation for the momentum crashes reported in the empirical literature over such periods.

We challenge academic consensus that estimation error makes mean-variance portfolio strategies inferior to passive equal-weighted approaches. We demonstrate analytically, via simulation and empirically that investors endowed with modest forecasting ability benefit substantially from an MV approach. An investor with some forecasting ability improves expected utility by increasing the number of assets considered. We frame our study realistically using budget constraints, transaction costs and out-of-sample testing for a wide range of investments. We derive practical decision rules to choose between passive and mean variance optimisation results and generate results consistent with much financial market practice and the original Markowitz formulation.

The transmission of risk among financial institutions is not limited to systematic risk and interest rate factors, but is also affected by the interconnectedness of institutions through balance sheet exposures. It is recognized that univariate specifications have severe limitations in explaining banks observed performance and measurement of risk, and may obscure possible unintended effects of bank capital regulation. Consequently, we link systematic risk to balance sheet factors and allow for dependencies in the covariance structure. We find that funding structure and balance sheet factors asymmetrically affect observed systematic risk in the largest Australian banks.

We assume that equity returns follow multi-state threshold autoregressions and generalize existing results for threshold autoregressive models presented in Knight and Satchell 2011. “Some new results for threshold AR(1) models,” Journal of Time Series Econometrics 3(2011):1–42 and Knight, Satchell, and Srivastava (2014) for the existence of a stationary process and the conditions necessary for the existence of a mean and a variance; we also present formulae for these moments. Using a simulation study, we explore what these results entail with respect to the impact they can have on tests for detecting bubbles or market efficiency. We find that bubbles are easier to detect in processes where a stationary distribution does not exist. Furthermore, we explore how threshold autoregressive models with i.i.d trigger variables may enable us to identify how often asset markets are inefficient. We find, unsurprisingly, that the fraction of time spent in an efficient state depends upon the full specification of the model; the notion of how efficient a market is, in this context at least, a model-dependent concept. However, our methodology allows us to compare efficiency across different asset markets.

© 2015 Taylor & Francis. We present new analytical results for the impact of portfolio weight constraints on an investor’s optimal portfolio when parameter uncertainty is taken into account. While it is well known that parameter uncertainty and imposing weight constraints results in reduced certainty equivalent returns, in the general case, there are no analytical results. In a special case, commonly used in the funds management literature, we derive analytical expression for the certainty equivalent loss that does not depend on the risk aversion parameter. We illustrate our theoretical results using hedge fund data, from the perspective of a fund-of-fund manager. Our contribution is to formalize the framework to investigate this problem, as well as providing tractable analytical solutions that can be implemented using either simulated or asset manager returns.

We propose a new approach to recover relative entropy measures of dependence from limited information by constructing the most entropic copulas (MEC) and their canonical forms, namely, the most entropic canonical copulas (MECC). We show that our approach is in duality with the existing approaches such as the approach of minimum Kullback-Leibler cross entropy. Our empirical analysis focuses on an application of the MEC theory to a 'style investing' problem for an investor with constant relative risk aversion allocating wealth between the Russell 1000 'growth' and 'value' indices. We found that the gains from using the MECC in forming investment strategies are economically and statistically significant for the case with/without short-sales constraints.

The well-documented negative association between idiosyncratic volatility (IV) and stock returns is puzzling if investors are risk-averse. We show that this anomaly is also prominent in the Chinese stock market. We attempt to explain the IV anomaly by using the key theories suggested by the literature, such as the lottery effect, arbitrage asymmetry, prospect theory, return reversals and more. None of these competing theories is able to justify the IV anomaly in China. Given that the Chinese stock market possesses both short selling constraints and heterogeneous beliefs, we employ resale option theory as a way to explain the IV puzzle. We find that the resale option value is consistently related to the IV effect in China, and that the explanatory power of the resale option value for the IV anomaly survives a range of robustness tests.

This paper investigates why general Moving Average (MA) trading rules are widely used by technical analysts and others. We assume general stationary processes for prices and we derive the autocorrelation function for an MA trading rule. Based on our results, we conjecture that autocorrelation amplification is one of the reasons why such trading rules are popular. Using simulated results, we show that the MA rule may be popular because it can identify price momentum and is a simple way of assessing and exploiting the price autocorrelation structure without necessarily knowing its precise structure. This paper then, provides empirical evidence of autocorrelation amplification using 15-year daily price data for 11 major international stock indices.

The use of correlation between forecasts and actual returns is commonplace in the literature, often used as a measurement of investors’ skill. A prominent application of this is the concept of the Information Coe!cient ( IC). Not only can IC be used as a tool to rate analysts and fund managers but it also represents an important parameter in the asset allocation and portfolio construction process. Nevertheless, theoretical understanding of it has typically been limited to the partial equilibrium context where the investing activities of each agent have no e"ect on other market participants. In this paper we show that this can be an undesirable oversimplification and we demonstrate plausible circumstances in which conventional empirical measurements of IC can be highly misleading. We suggest that improved understanding of IC in a general equilibrium setting can lead to refined portfolio decision making ex ante and more informative analysis of performance ex post.

In this paper, we present a unified theory of linear smoothing, which looks at the problem from a time-series perspective. We use the term ‘conversion’ to refer to generic operations that create a difference between true returns and reported returns. ‘Smoothing’ occurs when that conversion process leads to a reduction in the variance of the reported returns and we establish the conditions which guarantee smoothing. Most importantly, we discuss situations where ‘anti-smoothing’ can occur, i.e. reported returns become more volatile than their true counterparts. Finally, we present empirical evidence of the presence of both smoothing and anti-smoothing in returns data for a number of different classes of asset.

The purpose of this paper is to examine the properties of locally explosive regimes in the light of steady state results for threshold auto-regressive (TAR) models recently derived by Knight and Satchell (2011) [Journal of Time Series Econometrics, 3]. We study the conditions under which a steady state distribution of deviations of asset prices from fair value can be obtained using our simple model based on our particular definition of a bubble, noting that it is applicable to locally explosive regimes. After deriving general results, the analysis is further extended by considering the steady state distribution in three cases of a normally distributed error process, a non normally (exponentially) distributed steady-state process and a switching random walk with a fairly general iid error process. Then, the issues related to unit root testing for the presence of bubbles using standard econometric procedures are examined. Our results shed light on the ubiquitous finding of no bubbles in the econometric literature.

The purpose of this paper is to investigate the dynamics and statistics of style rotation based on the Barberis-Shleifer model of style switching. Investors in stocks regard the forecasting of style-relative performance, especially style rotation, as highly desirable but difficult to achieve in practice. Whilst we do not claim to be able to do this in an empirical sense, we do provide a framework for addressing these issues. We develop some new results from the Barberis-Shleifer model which allows us to understand some of the time series properties of style relative price performance and determine the statistical properties of the time until a switch between styles. We apply our results to a set of empirical data to get estimates of some of the model parameters including the level of risk aversion of market participants.

The purpose of this paper is to investigate the dynamics and steady-state properties of threshold autoregressive models with exogenous states that follow Markovian processes. Markovian processes are widely used in applied economics although their statistical properties have not been explored in detail. We use characteristic functions to carry out the analysis, and this allows us to describe limiting distributions for processes not considered in the literature previously. We also calculate analytical expressions for some moments. Furthermore, we see that we can have locally explosive processes that are explosive in one regime whilst being strongly stationary overall. This is explored through simulation analysis, where we also show how the distribution changes when the explosive state becomes more frequent although the overall process remains stationary. In doing so, we are able to relate our analysis to asset prices which exhibit similar distributional properties.