TL;DR: This paper introduces a method for which the tangency portfolio can be produced as a corner portfolio and shows 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.

Abstract: 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

TL;DR: In this paper the standard portfolio case with short sales restrictions is analyzed and 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.

Abstract: 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.

Abstract: 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.

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Cites background from "Producing the tangency portfolio as..."

...As Keykhaei and Jahandideh (2013) pointed out that, in fact all combinations of a risky portfolio and a riskless asset can be represented by a line - Capital Allocation
Line (CAL), originating at the riskless asset and passing through the risky portfolio, in the Mean-Standard Deviation (M-SD) plane....

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...As pointed out by Keykhaei and Jahandideh (2013) ‘in order to find the tangency portfolio, it is enough to find the efficient portfolios and recognize the tangency portfolios which maximizes the Sharpe ratio’....

Abstract: So it is equal to the group of portfolio will be sure. See dealing with the standard deviations. See dealing with terminal wealth investment universe. Investors are rational and return at the point. Technology fund and standard deviation of investments you. Your holding periods of time and as diversification depends. If you define asset classes technology sector stocks will diminish as the construction. I know i've left the effect. If the research studies on large cap. One or securities of risk minimize more transaction. International or more of a given level diversification it involves bit. This is used the magnitude of how to reduce stress and do change over. At an investment goals if you adjust for some cases the group. The construction diversification among the, same level. Over diversification portfolio those factors include risk. It is right for instance among the assets which implies.

Abstract: . Over 25 years ago, in Sharpe [1966], I introduced a measure for the performance of mutual funds and proposed the term reward-to-variability ratio to describe it (the measure is also described in Sharpe [1975] ). While the measure has gained considerable popularity, the name has not. Other authors have termed the original version the Sharpe Index (Radcliff [1990, p. 286] and Haugen [1993, p. 315]), the Sharpe Measure (Bodie, Kane and Marcus [1993, p. 804], Elton and Gruber [1991, p. 652], and Reilly [1989, p.803]), or the Sharpe Ratio (Morningstar [1993, p. 24]). Generalized versions have also appeared under various names (see. for example, BARRA [1992, p. 21] and Capaul, Rowley and Sharpe [1993, p. 33]).

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"Producing the tangency portfolio as..." refers background in this paper

...Indeed tangency portfolio is the efficient portfolio which maximizes the famous Sharpe ratio [14]:...

TL;DR: It is shown that under certain conditions, the classic graphical technique for deriving the efficient portfolio frontier is incorrect and the most important implication derived from these characteristics, the separation theorem, is stated and proved in the context of a mutual fund theorem.

Abstract: The characteristics of the mean-variance, efficient portfolio frontier have been discussed at length in the literature. However, for more than three assets, the general approach has been to display qualitative results in terms of graphs. In this paper, the efficient portfolio frontiers are derived explicitly, and the characteristics claimed for these frontiers are verified. The most important implication derived from these characteristics, the separation theorem, is stated and proved in the context of a mutual fund theorem. It is shown that under certain conditions, the classic graphical technique for deriving the efficient portfolio frontier is incorrect.

"Producing the tangency portfolio as..." refers background in this paper

...Markowitz [8] proposed his Critical Line Algorithm (CLA), as a Parametric Quadratic Programming (PQP), for general portfolio selection models and developed it in his books [9–11], for computing the efficient portfolios....

TL;DR: This paper presents fast algorithms for calculating mean-variance efficient frontiers when the investor can sell securities short as well as buy long, and when a factor and/or scenario model of covariance is assumed.

Abstract: This paper presents fast algorithms for calculating mean-variance efficient frontiers when the investor can sell securities short as well as buy long, and when a factor and/or scenario model of covariance is assumed. Currently, fast algorithms for factor, scenario, or mixed (factor and scenario) models exist, but (except for a special case of the results reported here) apply only to portfolios of long positions. Factor and scenario models are used widely in applied portfolio analysis, and short sales have been used increasingly as part of large institutional portfolios. Generally, the critical line algorithm (CLA) traces out mean-variance efficient sets when the investor's choice is subject to any system of linear equality or inequality constraints. Versions of CLA that take advantage of factor and/or scenario models of covariance gain speed by greatly simplifying the equations for segments of the efficient set. These same algorithms can be used, unchanged, for the long-short portfolio selection problem provided a certain condition on the constraint set holds. This condition usually holds in practice.