Risk-Based Optimal Portfolio Strategies: A Compendium

140 Pages Posted: 15 Sep 2022

Date Written: August 30, 2022


The paper presents 54 risk-based optimal portfolio strategies. The families of underlining dispersion measures categorize them. We distinguish 5 such families: tail, downside, below threshold, inter-observations distance and central moment dispersion measures. In each case we seek the most general form in terms of $L^p$-norms. Numerical algorithms are presented for p=1 and p=2. In these cases, the portfolio optimizations are formulated as numerically efficient LP (Linear Programming), QP (Quadratic Programming) and SOCP (Second Order Cone Programming) problems. The following dispersion measures are included in this compendium: mCVaR, mSMCR, mMAD, mLSD, mBTAD, mBTSD, Gini, SD, and VAR. The optimal strategies are minimization of risk for targeted expected rate of return value, minimum risk portfolio, maximization of expected rate of return for targeted risk value, maximization of expected rate of return for fixed risk-aversion factor, maximization of generalized Sharpe ratio and minimization of inverse generalized Sharpe ratio. Numerical implementations of these algorithms are available in an open-source Python package called azapy, https://pypi.org/project/azapy. The azapy package technical documentation can be found at https://azapy.readthedocs.io/en/latest and its source code at https://github.com/Mircea-MMXXI/azapy. Simple Python scripts illustrating the use of azapy library accompany the portfolio optimization strategies as well as in-sample and out-of-sample portfolio simulations.

Keywords: portfolio optimization, efficient frontier, CVaR, SMCR, MAD, LSD, BTAD, BTSD, Omega ratio, Sortino ratio, Sharpe ratio, Gini index, mean-variance, LP, QP, SOCP, equal weighted portfolio

JEL Classification: G00, G11

Suggested Citation

Marinescu, Mircea, Risk-Based Optimal Portfolio Strategies: A Compendium (August 30, 2022). Available at SSRN: https://ssrn.com/abstract=4205165 or http://dx.doi.org/10.2139/ssrn.4205165

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