No Arabic abstract
In this paper, we solve portfolio rebalancing problem when security returns are represented by uncertain variables considering transaction costs. The performance of the proposed model is studied using constant-proportion portfolio insurance (CPPI) as rebalancing strategy. Numerical results showed that uncertain parameters and different belief degrees will produce different efficient frontiers, and affect the performance of the proposed model. Moreover, CPPI strategy performs as an insurance mechanism and limits downside risk in bear markets while it allows potential benefit in bull markets. Finally, using a globally optimization solver and genetic algorithm (GA) for solving the model, we concluded that the problem size is an important factor in solving portfolio rebalancing problem with uncertain parameters and to gain better results, it is recommended to use a meta-heuristic algorithm rather than a global solver.
The paper solves the problem of optimal portfolio choice when the parameters of the asset returns distribution, like the mean vector and the covariance matrix are unknown and have to be estimated by using historical data of the asset returns. The new approach employs the Bayesian posterior predictive distribution which is the distribution of the future realization of the asset returns given the observable sample. The parameters of the posterior predictive distributions are functions of the observed data values and, consequently, the solution of the optimization problem is expressed in terms of data only and does not depend on unknown quantities. In contrast, the optimization problem of the traditional approach is based on unknown quantities which are estimated in the second step leading to a suboptimal solution. We also derive a very useful stochastic representation of the posterior predictive distribution whose application leads not only to the solution of the considered optimization problem, but provides the posterior predictive distribution of the optimal portfolio return used to construct a prediction interval. A Bayesian efficient frontier, a set of optimal portfolios obtained by employing the posterior predictive distribution, is constructed as well. Theoretically and using real data we show that the Bayesian efficient frontier outperforms the sample efficient frontier, a common estimator of the set of optimal portfolios known to be overoptimistic.
We implement momentum strategies using reward-risk measures as ranking criteria based on classical tempered stable distribution. Performances and risk characteristics for the alternative portfolios are obtained in various asset classes and markets. The reward-risk momentum strategies with lower volatility levels outperform the traditional momentum strategy regardless of asset class and market. Additionally, the alternative portfolios are not only less riskier in risk measures such as VaR, CVaR and maximum drawdown but also characterized by thinner downside tails. Similar patterns in performance and risk profile are also found at the level of each ranking basket in the reward-risk portfolios. Higher factor-neutral returns achieved by the reward-risk momentum strategies are statistically significant and large portions of the performances are not explained by the Carhart four-factor model.
This paper develops the first closed-form optimal portfolio allocation formula for a spot asset whose variance follows a GARCH(1,1) process. We consider an investor with constant relative risk aversion (CRRA) utility who wants to maximize the expected utility from terminal wealth under a Heston and Nandi (2000) GARCH (HN-GARCH) model. We obtain closed formulas for the optimal investment strategy, the value function and the optimal terminal wealth. We find the optimal strategy is independent of the development of the risky asset, and the solution converges to that of a continuous-time Heston stochastic volatility model, albeit under additional conditions. For a daily trading scenario, the optimal solutions are quite robust to variations in the parameters, while the numerical wealth equivalent loss (WEL) analysis shows good performance of the Heston solution, with a quite inferior performance of the Merton solution.
We find economically and statistically significant gains when using machine learning for portfolio allocation between the market index and risk-free asset. Optimal portfolio rules for time-varying expected returns and volatility are implemented with two Random Forest models. One model is employed in forecasting the sign probabilities of the excess return with payout yields. The second is used to construct an optimized volatility estimate. Reward-risk timing with machine learning provides substantial improvements over the buy-and-hold in utility, risk-adjusted returns, and maximum drawdowns. This paper presents a new theoretical basis and unifying framework for machine learning applied to both return- and volatility-timing.
We consider an investor with constant absolute risk aversion who trades a risky asset with general Ito dynamics, in the presence of small proportional transaction costs. Kallsen and Muhle-Karbe (2012) formally derived the leading-order optimal trading policy and the associated welfare impact of transaction costs. In the present paper, we carry out a convex duality approach facilitated by the concept of shadow price processes in order to verify the main results of Kallsen and Muhle-Karbe under well-defined regularity conditions.