Model Parameters Estimation

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Maximum likelihood estimates for means and covariances

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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

. Based on the prices one forms the range of

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:

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: