| 1. |
- Bauder, David, et al.
(författare)
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Bayesian estimation of the efficient frontier
- 2019
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Ingår i: Scandinavian Journal of Statistics. - : Wiley. - 0303-6898 .- 1467-9469. ; 46:3, s. 802-830
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Tidskriftsartikel (refereegranskat)abstract
- 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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| 2. |
- Bodnar, Rostyslav, et al.
(författare)
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Multivariate autoregressive extreme value process and its application for modeling the time series properties of the extreme daily asset prices
- 2016
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Ingår i: Communications in Statistics - Theory and Methods. - : Informa UK Limited. - 0361-0926 .- 1532-415X. ; 45:12, s. 3421-3440
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Tidskriftsartikel (refereegranskat)abstract
- In this article we suggest a new multivariate autoregressive process for modeling time-dependent extreme value distributed observations. The idea behind the approach is to transform the original observations to latent variables that are univariate normally distributed. Then the vector autoregressive DCC model is fitted to the multivariate latent process. The distributional properties of the suggested model are extensively studied. The process parameters are estimated by applying a two-stage estimation procedure. We derive a prediction interval for future values of the suggested process. The results are applied in an empirically study by modeling the behavior of extreme daily stock prices.
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| 3. |
- Bodnar, Taras, et al.
(författare)
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Determination and estimation of risk aversion coefficients
- 2018
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Ingår i: Computational Management Science. - : Springer Science and Business Media LLC. - 1619-697X .- 1619-6988. ; 15:2, s. 297-317
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Tidskriftsartikel (refereegranskat)abstract
- In the paper we consider two types of utility functions often used in portfolio allocation problems, i.e. the exponential utility and the quadratic utility. We link the resulting optimal portfolios obtained by maximizing these utility functions to the corresponding optimal portfolios based on the minimum value-at-risk (VaR) approach. This allows us to provide analytic expressions for the risk aversion coefficients as functions of the VaR level. The results are initially derived under the assumption that the vector of asset returns is multivariate normally distributed and they are generalized to the class of elliptically contoured distributions thereafter. We find that the choice of the coefficients of risk aversion depends on the stochastic model used for the data generating process. Finally, we take the parameter uncertainty into account and present confidence intervals for the risk aversion coefficients of the considered utility functions. The theoretical results are validated in an empirical study.
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| 4. |
- Bodnar, Taras, et al.
(författare)
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How risky is the optimal portfolio which maximizes the Sharpe ratio?
- 2017
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Ingår i: AStA Advances in Statistical Analysis. - : Springer Science and Business Media LLC. - 1863-8171 .- 1863-818X. ; 101:1, s. 1-28
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we investigate the properties of the optimal portfolio in the sense of maximizing the Sharpe ratio (SR) and develop a procedure for the calculation of the risk of this portfolio. This is achieved by constructing an optimal portfolio which minimizes the Value-at-Risk (VaR) and at the same time coincides with the tangent (market) portfolio on the efficient frontier which is related to the SR portfolio. The resulting significance level of the minimum VaR portfolio is then used to determine the risk of both the market portfolio and the corresponding SR portfolio. However, the expression of this significance level depends on the unknown parameters which have to be estimated in practice. It leads to an estimator of the significance level whose distributional properties are investigated in detail. Based on these results, a confidence interval for the suggested risk measure of the SR portfolio is constructed and applied to real data. Both theoretical and empirical findings document that the SR portfolio is very risky since the corresponding significance level is smaller than 90 % in most of the considered cases.
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| 5. |
- Bodnar, Taras, et al.
(författare)
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Statistical Inference for the Beta Coefficient
- 2019
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Ingår i: Risks. - : MDPI AG. - 2227-9091. ; 7:2
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Tidskriftsartikel (refereegranskat)abstract
- The beta coefficient plays a crucial role in finance as a risk measure of a portfolio in comparison to the benchmark portfolio. In the paper, we investigate statistical properties of the sample estimator for the beta coefficient. Assuming that both the holding portfolio and the benchmark portfolio consist of the same assets whose returns are multivariate normally distributed, we provide the finite sample and the asymptotic distributions of the sample estimator for the beta coefficient. These findings are used to derive a statistical test for the beta coefficient and to construct a confidence interval for the beta coefficient. Moreover, we show that the sample estimator is an unbiased estimator for the beta coefficient. The theoretical results are implemented in an empirical study.
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| 6. |
- Alfelt, Gustav
(författare)
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Modeling Realized Covariance of Asset Returns
- 2019
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis, which consists of two papers, we consider the modeling of positive definitive symmetric matrices, in particular covariance matrices of financial asset returns. The return covariance matrix describes the magnitude in which prices of financial assets tend to change over time, and how price changes between different assets are related. It is an instrumental quantity in many financial applications, and furthermore, an important component in understanding the dynamics present prior to and during times of financial turbulence, such as the 2008 financial crisis.In the first paper, we provide several goodness-of-fit tests applicable to models driven by a centralized Wishart process. To apply such a distributional assumption has become a popular way of modeling the stochastic properties of time-series of realized covariance matrices for asset returns. The paper includes a simulation study that aims to investigate how the tests perform under model uncertainty stemming from parameter estimation. In addition, the presented methods are used to evaluate the fit of a typical model of realized covariance adapted to real data on six stocks traded on the New York Stock Exchange.The second paper considers positive definite and symmetric random matrices of the exponential family. Under certain conditions for this class of distributions, we derive the Stein-Haff identity. Furthermore, we determine this identity in the case of the matrix-variate gamma distribution and apply it in order to present an estimator that outperforms the maximum likelihood estimator in terms of Stein's loss function. Finally, a small simulation study is conducted to support the theoretical results.
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| 7. |
- Bauder, David, et al.
(författare)
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Bayesian inference for the tangent portfolio
- 2018
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Ingår i: International Journal of Theoretical and Applied Finance. - : World Scientific Publishing Co. Pte. Ltd.. - 0219-0249. ; 21:8
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we consider the estimation of the weights of tangent portfolios from the Bayesian point of view assuming normal conditional distributions of the logarithmic returns. For diffuse and conjugate priors for the mean vector and the covariance matrix, we derive stochastic representations for the posterior distributions of the weights of tangent portfolio and their linear combinations. Separately we provide the mean and variance of the posterior distributions, which are of key importance for portfolio selection. The analytic results are evaluated within a simulation study, where the precision of coverage intervals is assessed.
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| 8. |
- Bodnar, Taras, et al.
(författare)
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A closed-form solution of the multi-period portfolio choice problem for a quadratic utility function
- 2015
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Ingår i: Annals of Operations Research. - : Springer Science and Business Media LLC. - 0254-5330 .- 1572-9338. ; 229:1, s. 121-158
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Tidskriftsartikel (refereegranskat)abstract
- In the present paper, we derive a closed-form solution of the multi-period portfolio choice problem for a quadratic utility function with and without a riskless asset. All results are derived under weak conditions on the asset returns. No assumption on the correlation structure between different time points is needed and no assumption on the distribution is imposed. All expressions are presented in terms of the conditional mean vectors and the conditional covariance matrices. If the multivariate process of the asset returns is independent, it is shown that in the case without a riskless asset the solution is presented as a sequence of optimal portfolio weights obtained by solving the single-period Markowitz optimization problem. The process dynamics are included only in the shape parameter of the utility function. If a riskless asset is present, then the multi-period optimal portfolio weights are proportional to the single-period solutions multiplied by time-varying constants which are dependent on the process dynamics. Remarkably, in the case of a portfolio selection with the tangency portfolio the multi-period solution coincides with the sequence of the single-period solutions. Finally, we compare the suggested strategies with existing multi-period portfolio allocation methods on real data.
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| 9. |
- Bodnar, Taras, et al.
(författare)
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A linear test for the global minimum variance portfolio for small sample and singular covariance
- 2015
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Bodnar and Schmid (2008) derived the distribution of the global minimum variance portfolio weights and obtained the distribution of the test statistics for the general linear hypothesis. Their results are obtained in the case when the number of observations n is bigger or equal than the size of portfolio k. In the present paper, we extend the result by analyzing the portfolio weights in a small sample case of n < k, with the singular covariance matrix. The results are illustrated using actual stock returns. A discussion of practical relevance of the model is presented.
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| 10. |
- Bodnar, Taras, et al.
(författare)
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A test for the global minimum variance portfolio for small sample and singular covariance
- 2017
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Ingår i: AStA Advances in Statistical Analysis. - : Springer. - 1863-8171 .- 1863-818X. ; 101:3, s. 253-265
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Tidskriftsartikel (refereegranskat)abstract
- Recently, a test dealing with the linear hypothesis for the global minimum variance portfolio weights was obtained under the assumption of non-singular covariance matrix. However, the problem of potential multicollinearity and correlations of assets constitutes a limitation of the classical portfolio theory. Therefore, there is an interest in developing theory in the presence of singularities in the covariance matrix. In this paper, we extend the test by analyzing the portfolio weights in the small sample case with a singular population covariance matrix. The results are illustrated using actual stock returns and a discussion of practical relevance of the model is presented.
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