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The modern theory of portfolio, or simply the portfolio theory, explains how the rational investors to use the principle of the diversification to optimize its portfolios of investment, and as risk assets must have a price. The development of models of portfolio optimization has its origin in the financial area.
The pioneering work in the scope of the optimization of the portfolio is the proposal of the model of average-variance of Markowitz (1952). The theory of the portfolio that the decisions on the selection of investments must become on the base of relation risk-return. In order to help in this process, the models of optimization of the portfolio have been developed. With the purpose of to be effective, these models must be able to quantify the risk levels and return of the investment.
The student of Markowitz, William Sharpe, along with John and Jack Treynor Lintner, what is called developed the Model for the Evaluation of Financial Assets - Capital Asset Pricing Model or CAPM, in which the determining factor of the waited for yield of an action is the coefficient β (beta) of action, defined by the covariance of their price in the world-wide market. The fundamental hypothesis was that of diversification of idiosyncratic risks (specific) of a certain action it can be diverse, although the risk the fluctuations of the world-wide market of generic (systemic). The rational investors then are necessary that he increases the benefits waited for to maintain existence with β high, in contrast to the actions of β down. The sprouting of the modern financial theory is part of a revolution that had a great impact in the old of financing, to a great extent pre-theoretical zone, and, often based on a world of explicit relations.
Thus, the basic concepts of the portfolio theory are the waited for yield, the risk, the diversification, efficient border, the coefficients alpha and beta, the line of the market of capitals, the market of the security in line and the model of valuation of financial assets.
Theory of the portfolio considers the yield of the assets like a variate, and a portfolio like an average combination of the assets, so that the return of a portfolio is an average combination of yield of the assets. In addition, the return of the portfolio is a variate and therefore it has an awaited value and the variance. The risk in this model is the standard deviation of the return. Risk and yield
The model supposes that the investors have aversion to the risk, which means that, given two assets who offer the same waited for yield, the investors prefer less risk. Therefore, an investor will only increase the risk if compensated by the increase of the awaited yields. On the contrary, an investor who wishes to obtain a greater yield must accept more risks. The precise measurement of this compensation will be different for each one of the investing on the base from the aversion from the individual risk. As a result of a rational investor it will not invest in a portfolio, if there is one second alternative with a risk greater ratio of more favorable return - that is to say, for the same risk level it is a portfolio of alternatives that the greater awaited yield. In summary, the investors know that one of the principles that must consider at the time of making an investment, is the type of risk that goes with her, and the yield that could come with this investment. The risk can be greater or smaller, and give rise to losses or gains. Whichever major is the investment risk, major will be its return. There are no absolute guarantees of which a risk investment to satisfy the expectations with the investor, the benefit could be significantly smaller than the awaited thing. The risk is in fact one uncertainty and they extend in the time becomes more uncertain. If the investment is applied to the actions, the risk is directly tie to unpredictable situations, such as the speculation, the monetary fluctuations, the political factors, the economic factors. Like preventive measure, the investments must be diversified, the investment in diverse types of assets will allow the different types from yield and to reduce the risk, reason why the investment will be safer and the security will be greater. The variance
The risk preference assumes in addition that/return that the investor can be described by a function of quadratic utility. The effect of this supposition is that only the awaited yield and volatileness (that is to say, the yield average and standard deviation) are important for the investor. The investor is indifferent to other characteristics of the distribution of return, such as the asymmetry or curtosis.
He considers that the theory uses a parameter, volatileness like proxy for the risk, whereas the yield is an expectation on the future. This is in accordance with the hypothesis of the efficiency of the market and the most classic studies of the modern finances, like the model of Negro and Scholes of fixation of prices of European options (Marting model: in average the short one that the best prognosis for morning is the price nowadays). The recent innovations in the theory of the portfolio, especially the call Theory of the post-modern one of portfolio, has shown several faults in the examination of the variance like a financial indicator of the risk of the investors:
The theory uses an historical parameter, volatileness, like proxy for the risk, whereas the yield is an expectation on the future. (It considers that this is consistent with the hypothesis of the efficiency and the majority of the classic findings of financing, like Negro and Scholes, which they use the model of martingi, that is to say, the assumption that the best prognosis for morning is the price of today).
The affirmation of which “the investor is indifferent to the other characteristics� does not seem to be certain since the risk asymmetry seems to be a price by the market.
According to the model:
The return of the portfolio is the average combination of the rate of return on the assets constitute that it. The volatileness of the portfolio is a function of Ï? of correlation of the active components. The change in volatileness changes nonlinear in the consideration of the active components. These models are used to help to determine the portfolio of financial assets to provide the best yield against the risks from the point of view of an investor. The main motivation for the development of these models is related to the reduction of the risk to that the investor is exhibited, through the diversification and the balance of the portfolio. The diversification is an effective form to reduce the risk, because the yields offered by the different assets do not move together.
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