Portfolio Benchmarking under Drawdown Constraint and Stochastic Sharpe Ratio

Ankush Agarwal () and Ronnie Sircar ()
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Ankush Agarwal: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Ronnie Sircar: Princeton University

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Abstract: We consider an investor who seeks to maximize her expected utility derived from her terminal wealth relative to the maximum performance achieved over a fixed time horizon, and under a portfolio drawdown constraint, in a market with local stochastic volatility (LSV). In the absence of closed-form formulas for the value function and optimal portfolio strategy, we obtain approximations for these quantities through the use of a coefficient expansion technique and nonlinear transformations. We utilize regularity properties of the risk tolerance function to numerically compute the estimates for our approximations. In order to achieve similar value functions, we illustrate that, compared to a constant volatility model, the investor must deploy a quite different portfolio strategy which depends on the current level of volatility in the stochastic volatility model.

Keywords: portfolio optimization; drawdown; stochastic volatility; local volatility; and phrases portfolio optimization; drawdown; stochastic volatility (search for similar items in EconPapers)
Date: 2017-12-22
New Economics Papers: this item is included in nep-upt
Note: View the original document on HAL open archive server: https://polytechnique.hal.science/hal-01388399v2
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