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Register a new userMeasuring economic inequality and risk: a unifying approach based on personal gambles, societal preferences and references
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Added by
Francesca Greselin
Publication date
2015
fields
Mathematical Statistics
and research's language is
English
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The underlying idea behind the construction of indices of economic inequality is based on measuring deviations of various portions of low incomes from certain references or benchmarks, that could be point measures like population mean or median, or curves like the hypotenuse of the right triangle where every Lorenz curve falls into. In this paper we argue that by appropriately choosing population-based references, called societal references, and distributions of personal positions, called gambles, which are random, we can meaningfully unify classical and contemporary indices of economic inequality, as well as various measures of risk. To illustrate the herein proposed approach, we put forward and explore a risk measure that takes into account the relativity of large risks with respect to small ones.
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Financial advisors use questionnaires and discussions with clients to determine a suitable portfolio of assets that will allow clients to reach their investment objectives. Financial institutions assign risk ratings to each security they offer, and those ratings are used to guide clients and advisors to choose an investment portfolio risk that suits their stated risk tolerance. This paper compares client Know Your Client (KYC) profile risk allocations to their investment portfolio risk selections using a value-at-risk discrepancy methodology. Value-at-risk is used to measure elicited and revealed risk to show whether clients are over-risked or under-risked, changes in KYC risk lead to changes in portfolio configuration, and cash flow affects a clients portfolio risk. We demonstrate the effectiveness of value-at-risk at measuring clients elicited and revealed risk on a dataset provided by a private Canadian financial dealership of over $50,000$ accounts for over $27,000$ clients and $300$ advisors. By measuring both elicited and revealed risk using the same measure, we can determine how well a clients portfolio aligns with their stated goals. We believe that using value-at-risk to measure client risk provides valuable insight to advisors to ensure that their practice is KYC compliant, to better tailor their client portfolios to stated goals, communicate advice to clients to either align their portfolios to stated goals or refresh their goals, and to monitor changes to the clients risk positions across their practice.
Multilevel or hierarchical data structures can occur in many areas of research, including economics, psychology, sociology, agriculture, medicine, and public health. Over the last 25 years, there has been increasing interest in developing suitable techniques for the statistical analysis of multilevel data, and this has resulted in a broad class of models known under the generic name of multilevel models. Generally, multilevel models are useful for exploring how relationships vary across higher-level units taking into account the within and between cluster variations. Research scientists often have substantive theories in mind when evaluating data with statistical models. Substantive theories often involve inequality constraints among the parameters to translate a theory into a model. This chapter shows how the inequality constrained multilevel linear model can be given a Bayesian formulation, how the model parameters can be estimated using a so-called augmented Gibbs sampler, and how posterior probabilities can be computed to assist the researcher in model selection.
A partial least squares regression is proposed for estimating the function-on-function regression model where a functional response and multiple functional predictors consist of random curves with quadratic and interaction effects. The direct estimation of a function-on-function regression model is usually an ill-posed problem. To overcome this difficulty, in practice, the functional data that belong to the infinite-dimensional space are generally projected into a finite-dimensional space of basis functions. The function-on-function regression model is converted to a multivariate regression model of the basis expansion coefficients. In the estimation phase of the proposed method, the functional variables are approximated by a finite-dimensional basis function expansion method. We show that the partial least squares regression constructed via a functional response, multiple functional predictors, and quadratic/interaction terms of the functional predictors is equivalent to the partial least squares regression constructed using basis expansions of functional variables. From the partial least squares regression of the basis expansions of functional variables, we provide an explicit formula for the partial least squares estimate of the coefficient function of the function-on-function regression model. Because the true forms of the models are generally unspecified, we propose a forward procedure for model selection. The finite sample performance of the proposed method is examined using several Monte Carlo experiments and two empirical data analyses, and the results were found to compare favorably with an existing method.
Nonparametric methodologies are proposed to assess college students performance. Emphasis is given to gender and sector of High School. The application concerns the University of Campinas, a research university in Southeast Brazil. In Brazil college is based on a somewhat rigid set of subjects for each major. Thence a students relative performance can not be accurately measured by the Grade Point Average or by any other single measure. We then define individual vectors of course grades. These vectors are used in pairwise comparisons of common subject grades for individuals that entered college in the same year. The relative college performances of any two students is compared to their relative performances on the Entrance Exam Score. A test based on generalized U-statistics is developed for homogeneity of some predefined groups. Asymptotic normality of the test statistic is true for both null and alternative hypotheses. Maximum power is attained by employing the union intersection principle.
We propose a novel approach to infer investors risk preferences from their portfolio choices, and then use the implied risk preferences to measure the efficiency of investment portfolios. We analyze a dataset spanning a period of six years, consisting of end of month stock trading records, along with investors demographic information and self-assessed financial knowledge. Unlike estimates of risk aversion based on the share of risky assets, our statistical analysis suggests that the implied risk aversion coefficient of an investor increases with her wealth and financial literacy. Portfolio diversification, Sharpe ratio, and expected portfolio returns correlate positively with the efficiency of the portfolio, whereas a higher standard deviation reduces the efficiency of the portfolio. We find that affluent and financially educated investors as well as those holding retirement related accounts hold more efficient portfolios.
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