Efficient frontier construction procedure is a crucial part of investment decision process. Correctly calculated efficient frontier The set of all Efficient portfolios. gives complete description of all rational alternatives being at the investor's disposal. SmartFolio calculates efficient frontier based on a set of portfolios obtained by optimizing CRRA utility functions Class of utility functions which is exhausted by Logarithmic and Power utility functions. These utility functions are characterized by risk bearing proportional to wealth. for different values of relative risk aversion CRRA utility function parameter which determines degree of investor's attitude to risk. For risk aversed investors this parameter takes positive values. The more is the corresponding value, the more is utility function curvature, which leads to more conservative portfolio strategies. Parameter value equal to 0 corresponds to a risk-neutral investor. An investor who is interested only in his portfolio expected growth rate has relative risk aversion equal to 1. It is widely accepted that for most investors this parameter takes values in the range between 2 and 4.. Under the assumptions of the analytical model The financial market model which assumes that all assets collectively follow a random walk in continuous time. This means that distribution of logarithmic returns is normal, returns are serially uncorrelated, and variance of returns grows linearly with a time interval under consideration. the latter set coincides with a set of portfolios which possess minimal variance subject to a given rate of expected return. However, for the historical portfolio As opposed to the Analytical portfolio, which is analyzed based on the assumptions of the Analytical model, historical portfolio is analyzed directly on historical data., when, generally speaking, portfolio returns deviate from normality, these two sets of efficient portfolios might differ. With regard to this observation, the approach implemented in SmartFolio appears more appropriate as it better reflects investor's preferences.
Graphical representation of an efficient frontier is a convex line on Risk-Reward chart. The exact shape of the efficient frontier will depend on exact definitions we give to these measures (portfolio Risk and portfolio Reward). SmartFolio presents the following options:
Volatility The most common measure of risk. Defined as annualized standard deviation of returns.
Normalized semi-volatility Equal to doubled Semi-volatility. Under the assumption of independent normally distributed logarithmic returns it coincides with Volatility. (only for the historical portfolio)
Value-at-Risk Maximum portfolio loss (measured in % of the initial wealth) over a given time interval at a given level of statistical confidence.
Portfolio beta Measure of portfolio sensitivity to changes in price of the only Factor. Under the CAPM assumptions portfolio beta is calculated as the sum of products of individual betas and the corresponding portfolio weights. (only for the analytical portfolio with one factor An asset which plays the role of an independent variable in the context of Factor-based asset pricing models.)
Expected excess growth rate Expected instantaneous rate of return (including Dividend yield) over the risk-free rate.
Excess Mu Equal to Mu plus Dividend yield minus Risk-free rate.
Selection of the latter depends on analysis goals. If your goal is to construct the whole investor's portfolio, including risk-free investments, then it is more informative to use expected excess growth rate as a reward measure. If, on the contrary, the portfolio you are constructing can be considered as a separate asset constituting only a part of the final portfolio, then use excess Mu. In the latter case, as a rule, the efficient frontier is calculated subject to Zero Weight in Riskless Asset constraint.
Efficient Frontier - this table contains data obtained during the efficient frontier construction process.
Risk-reward Analysis - this chart displays the efficient frontier.
Efficient Portfolios - this 3d-area chart shows efficient portfolios In SmartFolio an efficient portfolio is defined as portfolio which is optimal respective to a CRRA utility function with some value of Relative risk aversion. weights structures.