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: