How to compare market efficiency? The Sharpe ratio based on the ARMA-GARCH forecast

This paper derives a new method for comparing the weak-form efficiency of markets.The author derives the formula of the Sharpe ratio from the ARMA-GARCH model and finds that the Sharpe ratio just depends on the coefficients of the AR and MA terms and is not affected by the GARCH process.For empirical purposes,the Sharpe ratio can be formulated with a monotonic increasing function of R-squared if the sample size is large enough.One can utilize the Sharpe ratio to compare weak-form efficiency among different markets.The results of stochastic simulation demonstrate the validity of the proposed method.The author also constructs empirical AR-GARCH models and computes the Sharpe ratio for S&P 500 Index and the SSE Composite Index.

The term structure of Sharpe ratios and arbitragefree asset pricing in continuous time

Motivated by financial and empirical arguments and in order to introduce a more flexible methodology of pricing,we provide a new approach to asset pricing based on Backward Volterra equations.The approach relies on an arbitrage-free and incomplete market setting in continuous time by choosing non-unique pricing measures depending either on the time of evaluation or on the maturity of payoffs.We show that in the latter case the dynamics can be captured by a time-delayed backward stochastic Volterra integral equation here introduced which,to the best of our knowledge,has not yet been studied.We then prove an existence and uniqueness result for time-delayed backward stochastic Volterra integral equations.Finally,we present a Lucas-type consumption-based asset pricing model that justifies the emergence of stochastic discount factors matching the term structure of Sharpe ratios.

Evaluating the Performance of Investment Funds in Turkey

It is important to determine the most appropriate levels of risk and return for small investors. For that purpose, the investment funds are very important tools to create a portfolio for small investors, to deploy the potential risks in optimal proportions, and to direct investors. In this study, the performance of 83 pieces of investment funds will be evaluated which are treated in Turkey dates from January 1, 2010 to December 31, 2012 with performance evaluation methods such as Sharpe, Modigliani （M2） that is based on the standard deviation, and Treynor, T2, Jensen that is based on systematic risk （beta）, and the highest and lowest performance investment funds will be presented. The aim of the study is to examine the success of the investment fund managers whether they could estimate the course of the market well or not regarding time period. The empirical results show that the investors who invest on the funds that have negative risk premium by investing in the investment funds getting under the risk cannot get more excess return than getting the return from the risk-free interest rate as treasury bills. The result implies that it could be said that the systematic and total risks of all investment funds are low and they are not sensitive to the developments in the market, and thus, regarding funds could be called as conservative funds.

Portfolio Selection Using Double GAs Searching for Cardinality and Integer Multiplied Optimal Weights

This paper studied cardinality constrained portfolio with integer weight.We suggested two optimization models and used two genetic algorithms to solve them.In this paper,after finding well matching stocks,according to investor’s target by using first genetic algorithm,we gave optimal integer weight of portfolio with well matching stocks by using second genetic algorithm.Through numerical comparisons with other feasible portfolios,we verified advantages of designed portfolio with two genetic algorithms.For a numerical comparison,we used a prepared data consisted of 18 stocks listed in S&P 500 and numerical example strongly supported the designed portfolio in this paper.Also,we made all comparisons visible through all feasible efficient frontiers.

A Correction for Classic Performance Measures

Non-normality in asset returns is now a common feature of financial markets. However, many practitioners as well as investors do still refer to classic risk adjusted performance measures to assess their investment. For example, Sharpe and Treynor ratios are designed for a Gaussian world. Then, employing them for a performance assessment prospect relative to the risk borne is a biased approach. If we look for consistency in risk assessment and in asset performance valuation, we need to look for robust methods or tools. Moreover, the well-known mathematical consistency and numerical tractability concerns drive our preference for simple methods. Under this setting, we propose to account in a simple way and to some extent for the skewness and kurtosis patterns describing the deviations from normality. We adjust therefore the classic Sharpe and Treynor ratios to asymmetries in the downside and upside deviations from the mean values of asset returns. Specifically, the adjusted Sharpe and Treynor ratios are weighted by the upside and downside deviation risks. Accounting for skewness and kurtosis changes generally the ranking of hedge fund performance. Moreover, the obtained adjusted performance measures capture well the skewness and/or kurtosis patterns in hedge fund returns depending on the targeted investment strategy

Optimal algorithms and intuitive explanations for Markowitz's portfolio selection model and Sharpe's ratio with no short-selling

Most of the previous researches about portfolio analysis focus on short-selling. In fact, no short-selling is also important because short-selling is not allowed in stock markets of some countries. This paper gives the sufficient and necessary conditions and proposes an optimal algorithm for Markowitz’s mean-variance models and Sharpe’s ratio with no short-selling. The optimal algorithm makes it easier to obtain the efficient frontiers with no short-selling.

Solving constrained portfolio optimization model using stochastic fractal search approach

Purpose-Optimum utilization of investments has always been considered one of the most crucial aspects of capital markets.Investment into various securities is the subject of portfolio optimization intent to maximize return at minimum risk.In this series,a population-based evolutionary approach,stochastic fractal search(SFS),is derived from the natural growth phenomenon.This study aims to develop portfolio selection model using SFS approach to construct an efficient portfolio by optimizing the Sharpe ratio with risk budgeting constraints.Design/methodology/approach-This paper proposes a constrained portfolio optimization model using the SFS approach with risk-budgeting constraints.SFS is an evolutionary method inspired by the natural growth process which has been modeled using the fractal theory.Experimental analysis has been conducted to determine the effectiveness of the proposed model by making comparisons with state-of-the-art from domain such as genetic algorithm,particle swarm optimization,simulated annealing and differential evolution.The real datasets of the Indian stock exchanges and datasets of global stock exchanges such as Nikkei 225,DAX 100,FTSE 100,Hang Seng31 and S&P 100 have been taken in the study.Findings-The study confirms the better performance of the SFS model among its peers.Also,statistical analysis has been done using SPSS 20 to confirm the hypothesis developed in the experimental analysis.Originality/value-In the recent past,researchers have already proposed a significant number of models to solve portfolio selection problems using the meta-heuristic approach.However,this is the first attempt to apply the SFS optimization approach to the problem.