Portfolio Optimization Model with and without Options under Additional Constraints

T Khodamoradi,M Salahi,Ali Reza Najafi

doi:10.1155/2020/8862435

T Khodamoradi, M Salahi + Show 1 more

Open Access

https://doi.org/10.1155/2020/8862435

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Journal: Mathematical Problems in Engineering	Publication Date: Nov 26, 2020
Citations: 3	License type: CC BY 4.0

Affiliation: University of Guilan

Abstract

In this paper, first, we study mean-absolute deviation (MAD) portfolio optimization model with cardinality constraints, short selling, and risk-neutral interest rate. Then, in order to insure the investment against unfavorable outcomes, an extension of MAD model that includes options is considered. Moreover, since the data in financial models usually involve uncertainties, we apply robust optimization to the MAD model with options. Finally, a data set of S&P index is used to compare the effectiveness of options in the models in terms of returns and Sharpe ratios.

Highlights

Some extensions of the mean-absolute deviation (MAD) model include short selling, threshold, and cardinality constraints
Konno et al used the MAD model with the long-short strategy and showed that the long-short strategy leads to a portfolio with significantly better risk-return structure compared to the portfolio with the long strategy
In 2014, Le i and Moeini [22] extended the MAD model with short selling, cardinality, and the threshold constraints. eir model is reformulated in terms of a DC problem and applied DC algorithms to solve it [23,24,25]

Summary

MAD Model with Options

We use options in the portfolio that ensure the investment against unfavorable outcomes. ey reduce the risk and come, at some costs that decrease the return of the portfolio [35]. ese costs (options prices) are formulated based on the risk-neutral interest rate as follows: Oput max􏼈0, K − ST􏼉 e− rcT,. Ese costs (options prices) are formulated based on the risk-neutral interest rate as follows: Oput max􏼈0, K − ST􏼉 e− rcT,. Ocall max􏼈0, ST − K􏼉 e− rcT, where ST is the stock price vector in the expiration time and K is strike price such that. Where S0 is a vector of stock initial price. Since we use Ocall and Oput for any stock, the total option price is. Using these call and put options under strike price (K), the option payoff functions become. Based on these payoff functions, options returns are as follows:. Erefore, model (4) under the options returns and options prices becomes min x,z,u λ⎛⎝T1.

Robust Model

Numerical Experiments

Findings

Conclusions