In this paper the standard portfolio case with short sales restrictions is analyzed.Dybvig pointed out that if there is a kink at a risky portfolio on the efficient frontier, then the securities in this portfolio have equal expected return and the converse of this statement is false.For the existence of kinks at the efficient frontier the sufficient condition is given here and a new procedure is used to derive the efficient frontier, i.e. the characteristics of the mean variance frontier.

A Note on the Kinks at the Mean Variance Frontier

Basically this is an empirical study which aims to test the Markowitz Modern portfolio theory (MPT) or the mean-variance analysis. Fund managers and general investors seek a portfolio that yields maximum return with minimum risk. The problem of investors is dual in nature, as Markowitz showed, i.e., the indifferent choice of risk and return. Though, diversification reduces non-systematic risk but due to limited resources one cannot afford to invest in all stocks, therefore it is pertinent to know that what should be the minimum level of stocks in a portfolio that produces maximum return and minimum risk. The theoretical framework of Markowitz MPT tested by computed 134 months expected the return of thirtytwo stocks, thirty-one variances and 465 co-variances, in order to evaluate efficient portfolio frontier.

Determinants Of Stocks For Optimal Portfolio

Various reward-risk performance measures and ratios have been considered in reward-risk portfolio selection problems. This paper investigates the optimal portfolio corresponding to the CVaR (STARR) ratio. Considering the LP solvability of CVaR, a method is proposed for detecting the optimal portfolio by using the corresponding Mean-CVaR optimization problem. By applying LP tools, a method is suggested for producing the optimal portfolio as a by-product during the procedure of computing the efficient frontier of the Mean-CVaR problem.

A note on optimal portfolio corresponding to the CVaR ratio

We propose a novel portfolio evaluation method, a distance-based approach, which directly evaluates the portfolio composition rather than portfolio returns. In this approach, we consider a portfolio as an estimator for an in-sample tangency portfolio, which we define as the optimal reference portfolio. We then evaluate the portfolio by computing its vector distance to the optimal reference portfolio. In search of the proper distance-based performance measure, we choose four representative vector distances and compare their suitability as a new portfolio performance measure. Through extensive statistical analysis, we find that the Euclidean distance is the most proper distance-based performance measure of the four representative vector distances. We further verify that a portfolio with a large Euclidean distance is not desirable because not only does it provide a low utility implied by the first four moments of portfolio returns, but also it is not likely to maintain its long-term performance. Hence, the Euclidean distance can complement the return-based performance measures by confirming the reliability of a portfolio in its investment performance.

/pdf/portfolio-evaluation-with-the-vector-distance-based-on-3pm2ayfw.pdf

Portfolio Evaluation with the Vector Distance Based on Portfolio Composition

A risk measure in a portfolio selection problem is linear programming (LP) solvable, if
 it has a linear formulation when the asset returns are represented by discrete random
 variables, i.e. , they are defined by their realizations under specified
 scenarios. The efficient frontier corresponding to an LP solvable model is a piecewise
 linear curve. In this paper we describe a method which realizes and produces a tangency
 portfolio as a by-product during the procedure of tracing out of the efficient frontier of
 risky assets in an LP solvable model, when our portfolio contains some risky assets and a
 riskless asset, using nonsmooth optimization methods. We show that the test of finding the
 tangency portfolio can be limited only for two portfolios. Also, we describe that how this
 method can be employed to trace out the efficient frontier corresponding to a portfolio
 selection problem in the presence of a riskless asset.

/pdf/tangency-portfolios-in-the-lp-solvable-portfolio-selection-1s9o91w58f.pdf

Tangency portfolios in the LP solvable portfolio selection models

One-fund theorem states that an efficient portfolio in a Mean-Variance (M-V) portfolio selection problem for a set of some risky assets and a riskless asset can be represented by a combination of a unique risky fund (tangency portfolio) and the riskless asset In this paper, we introduce a method for which the tangency portfolio can be produced as a corner portfolio So, the tangency portfolio can be computed easily and fast by any algorithm designed for tracing out the M-V efficient frontier via computing the corner portfolios Moreover, we show that how this method can be used for tracing out the M-V efficient frontier when problem contains a riskless asset in which the borrowing is not allowed

/pdf/producing-the-tangency-portfolio-as-a-corner-portfolio-1s5gzr2ogs.pdf

Mohamad Taghi Jahandideh

Papers

Tangency portfolios in the LP solvable portfolio selection models

Producing the tangency portfolio as a corner portfolio