Abstract
In this manuscript, we introduce asset allocation and portfolio selection techniques based on efficiency condition, Sharpe ratio error condition and order three zero opportunity condition. Investors expect the same level of risk and return from alternative investment options unless they want the advantage of diversification for risk. There are two fundamental investment portfolios. The first one is risk free fundamental portfolio, and the second one is risky fundamental portfolio. Investors use zero opportunity cost to select portfolio objective. In this research, mathematical derivation of portfolio construction approach is described in advance. Historical data of this research show that there is a positive linear relationship between natural logarithm of standard deviation of securities’ return and square of co-variance between securities and market return. Furthermore, it shows that there is a positive linear relationship between Treynor ratio of securities’ return and Sharpe ratio of securities’ return. We use global search optimization tool in MatLab and R software to solve empirical portfolio selection and asset allocation problem. Moreover, we apply direct and indirect mathematical proof methods to prove mathematical facts of this study.
Highlights
Investors optimize investment asset allocation to reduce unnecessary losses based on their investment objectives and constraints
In this manuscript, we introduce asset allocation and portfolio selection techniques based on efficiency condition, Sharpe ratio error condition and order three zero opportunity condition
We have investigated two portfolio selection and asset allocation strategies based on the evidence that there is positive linear relation ship between Treynor ratio of securities and Sharpe ratio of securities and positive linear relation ship between natural logarithm of standard deviation of securities’ return and square of co-variance between securities’ return and market return
Summary
Investors optimize investment asset allocation to reduce unnecessary losses based on their investment objectives and constraints. Practitioners use mean variance model to select portfolio even if the model assumes weights of securities are independent of time parameter. Another problem of mean variance model is that the model does not consider zero opportunity cost between fundamental portfolios. Single index model is developed because mean variance model needs estimations of expected return, risk and covariance of securities. The variance of portfolio can be expressed in terms of expected return due to Sharpe ratio error condition. We determine rtp, wf∗, wp∗ and wm∗ using order three zero opportunity condition, efficiency condition and Sharpe ratio error condition. We use USA s&p500 companies one year daily returns for empirical study
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