Bayesian Inference for the Tangent Portfolio

Bauder, David; Bodnar, Taras; Mazur, Stepan; Okhrin, Yarema

doi:10.1142/s0219024918500541

Cited by 17 publications

(12 citation statements)

References 29 publications

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“…In the case of k = 1, a = 0, and A = 1, we use the simplified notation t d instead. The following proposition is taken from Bauder et al ().…”

Section: Bayesian Inference For the Efficient Frontiermentioning

confidence: 99%

“…In Bayesian statistics, stochastic representations showed to be advantageous as well because they allow to access the posterior distribution of a parameter directly without the need for more complex and resource‐consuming methods such as Markov Chain Monte Carlo and circumventing the evaluation of complicated integral expressions. The application of stochastic representations in Bayesian portfolio selection was recently demonstrated by Bauder, Bodnar, Mazur, and Okhrin () and Bauder, Bodnar, Parolya, and Schmid (). In addition to this, we use the stochastic representations to calculate Bayesian estimates for the parameters, as well as their asymptotic distributions.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian estimation of the efficient frontier

Bauder

Bodnar

et al. 2018

Scandinavian J Statistics

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In this paper, we consider the estimation of the three determining parameters of the efficient frontier, the expected return, and the variance of the global minimum variance portfolio and the slope parameter, from a Bayesian perspective. Their posterior distribution is derived by assigning the diffuse and the conjugate priors to the mean vector and the covariance matrix of the asset returns and is presented in terms of a stochastic representation. Furthermore, Bayesian estimates together with the standard uncertainties for all three parameters are provided, and their asymptotic distributions are established. All obtained findings are applied to real data, consisting of the returns on assets included into the S&P 500. The empirical properties of the efficient frontier are then examined in detail.

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“…In the case of k = 1, a = 0, and A = 1, we use the simplified notation t d instead. The following proposition is taken from Bauder et al ().…”

Section: Bayesian Inference For the Efficient Frontiermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bayesian estimation of the efficient frontier

Bauder

Bodnar

et al. 2018

Scandinavian J Statistics

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“…An alternative approach to deal with the parameter uncertainty in portfolio analysis is to employ the methods of Bayesian statistics (cf. Barry 1974, Brown 1976, Klein and Bawa 1976, Frost and Savarino 1986, Aguilar and West 2000, Rachev et al 2008, Avramov and Zhou 2010, Sekerke 2015, Bodnar et al 2017, Bauder et al 2018. It is remarkable that the Bayesian approach is potentially more attractive since: (i) it uses prior information about quantities of interest; (ii) it facilitates the use of fast, intuitive, and easily implementable numerical algorithms in order to simulate complex economic quantities; (iii) it accounts for estimation risk and model uncertainty in the portfolio choice problem.…”

Section: Introductionmentioning

confidence: 99%

Bayesian mean–variance analysis: optimal portfolio selection under parameter uncertainty

Bauder

Bodnar

Parolya

et al. 2020

Quantitative Finance

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The paper solves the problem of optimal portfolio choice when the parameters of the asset returns distribution, for example the mean vector and the covariance matrix, are unknown and have to be estimated by using historical data on asset returns. Our new approach employs the Bayesian posterior predictive distribution which is the distribution of future realizations of asset returns given the observable sample. The parameters of posterior predictive distributions are functions of the observed data values and, consequently, the solution of the optimization problem is expressed in terms of data only and does not depend on unknown quantities. By contrast, the optimization problem of the traditional approach is based on unknown quantities which are estimated in the second step, and lead to a suboptimal solution. We also derive a very useful stochastic representation of the posterior predictive distribution whose application not only gives the solution of the considered optimization problem, but also provides the posterior predictive distribution of the optimal portfolio return which can be used to construct a prediction interval. A Bayesian efficient frontier, the set of optimal portfolios obtained by employing the posterior predictive distribution, is constructed as well. Theoretically and using real data we show that the Bayesian efficient frontier outperforms the sample efficient frontier, a common estimator of the set of optimal portfolios which is known to be overoptimistic.

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“…Shrinkage estimators for the optimal portfolio weights that allow us to shrink the estimated classical Markowitz weights to the deterministic target portfolio weights are proposed by, for example, Wang [47]. More recently, Bauder et al [5] studied the distributional properties of the weights of the TP from the Bayesian point of view.…”

Section: Introductionmentioning

confidence: 99%

Higher order moments of the estimated tangency portfolio weights

Javed

Mazur

Ngailo

2020

Journal of Applied Statistics

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In this paper, we consider the estimated weights of the tangency portfolio. We derive analytical expressions for the higher order noncentral and central moments of these weights when the returns are assumed to be independently and multivariate normally distributed. Moreover, the expressions for mean, variance, skewness and kurtosis of the estimated weights are obtained in closed forms. Later, we complement our results with a simulation study where data from the multivariate normal and t-distributions are simulated, and the first four moments of estimated weights are computed by using the Monte Carlo experiment. It is noteworthy to mention that the distributional assumption of returns is found to be important, especially for the first two moments. Finally, through an empirical illustration utilizing returns of four financial indices listed in NASDAQ stock exchange, we observe the presence of time dynamics in higher moments.

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Bayesian Inference for the Tangent Portfolio

Cited by 17 publications

References 29 publications

Bayesian estimation of the efficient frontier

Bayesian estimation of the efficient frontier

Bayesian mean–variance analysis: optimal portfolio selection under parameter uncertainty

Higher order moments of the estimated tangency portfolio weights

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