  The Theory \ Details \ parameters estimation \ sample estimates

# Model Parameters Estimation

## Maximum likelihood estimates for means and covariances

Consider segment with observations of the discounted prices: , where . Proceeding from practical reasons, we shall assume that the above prices don’t take into account the dividend yields and the risk-free rate. Based on the prices one forms the range of logarithmic returns of length by means of the formula ### Sample Expected Growth Rate The MLE for expected growth rate is the annualized average of . Sample estimate for expected excess growth rate is where denotes risk-free rate; denotes vector of dividend yields; stands for vector of ones.

### Sample Covariance matrix The Covariance matrix estimate , calculated in SmartFolio, is an annualized sample covariance matrixof the range . ### Sample Mu vector To estimate one should resort to the following expression: Note. If price process satisfies the analytical model assumptions, then sample Mu vector can be calculated in alternative way from a sample expected growth rate and a sample covariance matrix : Corresponding sample estimate for excess Mu has the following form:   