Abstract. We propose a novel approach to handle cardinality in portfolio selection, by means of a biobjective cardinality/mean-variance problem, allowing the investor to analyze the efficient tradeoff between returnrisk and number of active positions. Recent progress in multiobjective optimization without derivatives allow us to robustly compute (in-sample) the whole cardinality/mean-variance efficient frontier, for a variety of data sets and mean-variance models. Our results show that a significant number of efficient cardinality/mean-variance portfolios can overcome (out-of-sample) the naive strategy, while keeping transaction costs relatively low.
This paper suggests a new approach for portfolio choice. In this framework, the investor, with CRRA preferences, has two objectives: the maximization of the expected utility and the minimization of the portfolio expected illiquidity. The CRRA utility is measured using the portfolio realized volatility, realized skewness and realized kurtosis, while the portfolio illiquidity is measured using the well-known Amihud illiquidity ratio. Therefore, the investor is able to make her choices directly in the expected utility/liquidity (EU/L) bi-dimensional space. We conduct an empirical analysis in a set of fourteen stocks of the CAC 40 stock market index, using high frequency data for the time span from January 1999 to December 2005 (seven years). The robustness of the proposed model is checked according to the out-of-sample performance of different EU/L portfolios relative to the minimum variance and equally weighted portfolios. For different risk aversion levels, the EU/L portfolios are quite competitive and in several cases consistently outperform those benchmarks, in terms of utility, liquidity and certainty equivalent.
This paper extends the study of the cardinality impact on portfolio performance, from the traditional mean‐variance framework to more general frameworks that include higher moments. For each framework, we propose a biobjective model that allows the investor to explicitly analyze the efficient trade‐off between expected utility and cardinality. We applied the proposed methodology to data from the Portuguese Stock Index (PSI20 index). The empirical results show that, in‐sample, the certainty equivalent and the Sharpe ratio increase with the cardinality level in all frameworks. The results also suggest that there are no performance gains, in‐sample, in terms of certainty equivalent, when higher moments are considered. Out of sample, the turnover increases up to a certain cardinality level, then decreases. For certain cardinality levels, there are gains in terms of out‐of‐sample certainty equivalent and Sharpe ratio, when skewness and kurtosis are considered. Finally, we check the robustness of these results in a large dataset from the EUROSTOXX50 index.
In this paper, we devise a forward-looking methodology to determine efficient credit portfolios under the IFRS 9 framework. We define and implement a credit loss model based on prospective point-in-time probabilities of default. We determine these probabilities of default and the credits' stage allocation through a credit stochastic simulation. This simulation is based on the estimation of transition matrices. Using data from 1981 to 2019, in a non-homogeneous Markov chain setting, we estimate transition matrices conditional on the global real gross domestic product growth. This allows considering the effects of the economic cycle, which are of great importance in bank management. Finally, we develop a robust optimization model that allows the bank manager to analyze the tradeoff between the annual average portfolio income and the corresponding portfolio volatility. According to the proposed bi-objective model, we compute the efficient credit portfolios constructed based on 10-year maturity credits. We compare their structure to those generated by the IAS 39 and CECL accounting frameworks. The results indicate that the IFRS 9 and CECL frameworks generate efficient credit portfolios whose structure penalizes riskier-rated credits. In turn, the riskier efficient credit portfolios under the IAS 39 framework concentrate entirely on speculative-grade credits. This pattern is also encountered in efficient credit portfolios constructed based on credits with different maturities, namely 5 and 15 years. Moreover, the longer the maturity of the credits that enter into the composition of the efficient portfolios, the more the speculative-grade credits tend to be penalized.
This article proposes a flexible methodology for portfolio selection using a skewness/semivariance biobjective optimisation framework. The solutions of this biobjective optimisation problem allow the investor to analyse the efficient trade-off between skewness and semivariance. This methodology is used empirically on four data sets, collected from the Fama/French data library. The out-of-sample performance of the skewness/semivariance model was assessed by choosing three portfolios belonging to each in-sample Pareto frontier and measuring their performance in terms of skewness per semivariance ratio, Sharpe ratio and Sortino ratio. Both the in-sample and the out-of-sample performance analyses were conducted using three different target returns for the semivariance computations. The results show that the efficient skewness/semivariance portfolios are consistently competitive when compared with several benchmark portfolios.
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