Closed-form portfolio optimization under GARCH models

Escobar‐Anel, Marcos; Gollart, Maximilian; Zagst, Rudi

doi:10.1016/j.orp.2021.100216

Cited by 5 publications

(8 citation statements)

References 26 publications

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“…. Using a Taylor approximation of order two, [24] derived an approximated log-wealth process given by:…”

Section: Garch Model and Control Settingsmentioning

confidence: 99%

“…The case without uncertainty and a final time horizon N has already been studied in [24] with a value function describing the maximal expected utility over N periods given by:…”

Section: Garch Model and Control Settingsmentioning

confidence: 99%

“…A useful tool to solve Problem (1) is the value iteration. For this we introduce the following two operators for all admissible functions v : S → R (following [24] a function Φ 0 : S → R is called admissible if there exists a set of functions M ⊂ {v : S → R : E[|v|] < ∞, vs. concave in the first component of S}, such that U : M → M, Φ 0 (s 0 ) ∈ M and that for all v ∈ M there exists an f v ∈ F such that f v (s) maximizes a → Lv(s, a) on A for all s ∈ S):…”

Section: Stochastic Control Modelmentioning

confidence: 99%

“…Nonetheless, to the best of our knowledge, there is no study in the literature addressing GARCH models in portfolio optimization and parameter errors via Bayesian analysis. The Affine GARCH model, pioneered by [23], which permits closed-form pricing of options, has led to recent analytical results within EUT; see [24,25] for extensions to other Affine GARCH models. In these works, the authors did not account for parameter uncertainty.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian Learning in an Affine GARCH Model with Application to Portfolio Optimization

Escobar-Anel,

Speck,

Zagst

2024

Mathematics

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This paper develops a methodology to accommodate uncertainty in a GARCH model with the goal of improving portfolio decisions via Bayesian learning. Given the abundant evidence of uncertainty in estimating expected returns, we focus our analyses on the single parameter driving expected returns. After deriving an Uncertainty-Implied GARCH (UI-GARCH) model, we investigate how learning about uncertainty affects investments in a dynamic portfolio optimization problem. We consider an investor with constant relative risk aversion (CRRA) utility who wants to maximize her expected utility from terminal wealth under an Affine GARCH(1,1) model. The corresponding stock evolution, and therefore, the wealth process, is treated as a Bayesian information model that learns about the expected return with each period. We explore the one- and two-period cases, demonstrating a significant impact of uncertainty on optimal allocation and wealth-equivalent losses, particularly in the case of a small sample size or large standard errors in the parameter estimation. These analyses are conducted under well-documented parametric choices. The methodology can be adapted to other GARCH models and applications beyond portfolio optimization.

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“…. Using a Taylor approximation of order two, [24] derived an approximated log-wealth process given by:…”

Section: Garch Model and Control Settingsmentioning

confidence: 99%

“…The case without uncertainty and a final time horizon N has already been studied in [24] with a value function describing the maximal expected utility over N periods given by:…”

Section: Garch Model and Control Settingsmentioning

confidence: 99%

Section: Stochastic Control Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bayesian Learning in an Affine GARCH Model with Application to Portfolio Optimization

Escobar-Anel,

Speck,

Zagst

2024

Mathematics

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“…F t will also be denoted via the subindex t, e.g., with E t , in the sequel. Note that the moment generating function in (2) can also be formulated for the log return instead of the log price as the first element, making the term uX t−1 in the exponential function vanish. The choice of f 1 , f 2 and f 3 for a particular application shapes the coefficients A and B in Equation ( 2) according to this requirement.…”

Section: Outline Of the Approachmentioning

confidence: 99%

Expected Utility Theory on General Affine GARCH Models

Escobar‐Anel

Spies

Zagst

2021

Applied Mathematical Finance

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Expected utility theory has produced abundant analytical results in continuous-time finance, but with very little success for discrete-time models. Assuming the underlying asset price follows a general affine GARCH model which allows for non-Gaussian innovations, our work produces an approximate closed-form recursive representation for the optimal strategy under a constant relative risk aversion (CRRA) utility function. We provide conditions for optimality and demonstrate that the optimal wealth is also an affine GARCH. In particular, we fully develop the application to the IG-GARCH model hence accommodating negatively skewed and leptokurtic asset returns. Relying on two popular daily parametric estimations, our numerical analyses give a first window into the impact of the interaction of heteroscedasticity, skewness and kurtosis on optimal portfolio solutions. We find that losses arising from following Gaussian (suboptimal) strategies, or Merton's static solution, can be up to 2.5% and 5%, respectively, assuming low-risk aversion of the investor and using a five-years time horizon.

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