Parameters estimation procedure is started automatically during the portfolio construction process. However, you also can launch this procedure afterwards. Obtained results are then stored in the MODEL table. One separate technique, which is not included in the range of methods presented in the Parameter Estimation dialog, is the Black-Litterman model.
The key prerequisite of successful portfolio analysis under the analytical model of the financial market 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. is a choice of correct values for model parameters: Mu Vector parameter of the Analytical model. Asset Mu can be viewed as the expected simple annual rate of return in the asset, as opposed to the expected geometric rate of return, measured by the expected growth rate. and the covariance matrix Symmetric matrix containing covariances between portfolio components annual returns. Its diagonal elements are equal to squared volatilities of corresponding assets.. As a rule, these parameters are estimated based on available data of historical returns. The most common estimates used here are maximum-likelihood estimates of means and covariances calculated for multivariate normal distribution. However, in recent years several new estimation methods appeared that were specially designed for financial applications. Below we list those estimation techniques which are included in SmartFolio Professional Edition.
This technique provides an extension of commonly used MLE's of expected returns and the covariance matrix to a case of "combined sample", in which the lengths of return histories differ across assets. [Stambaugh; 1997]. This method is of a particular importance when portfolio contains assets with short return histories.
The following three estimates are based on statistical tradeoff between estimation error and bias. Such estimates are called shrinking estimates An estimate which is obtained via a "shrinkage" of sample unbiased estimate towards some biased target with lower estimation error..
This estimate is a weighted average of the sample excess Mu (this estimate is unbiased, but it has significant estimation error) and excess Mu of the global minimum variance portfolio The less volatile portfolio among all fully-invested portfolios. (this estimate is biased, but it has small estimation error). [Jorion; 1986].
The final estimate is obtained as a mix of the sample covariance matrix and the constant correlations matrix. [O. Ledoit, M. Wolf; 2003].
This method assumes that some portfolio components are used as factors An asset which plays the role of an independent variable in the context of Factor-based asset pricing models.. The final estimate is obtained as a mix of the corresponding sample estimate and the estimate which is implied by the assumptions of the corresponding asset pricing model A regression model which imposes additional structure on the parameters of the Analytical model. This is achieved by imposing conditions on regression coefficients. The one-factor case corresponds to CAPM. Fama-French 3-factor model is another commonly used asset pricing model.. [Pastor, Stambaugh; 2000], [Wang; 2003].
This technique can be applied in a situation when there are reasons to believe that the dynamics of the portfolio assets is determined by influence of one factor only, however, the factor itself is "unobservable", i.e. the structure of the latter is unknown [MacKinlay, Pastor; 2000].