## Definitions¶

The sum of profit/loss of all trades up to -th quote. Concerns only already closed position at last at moment of -th quote.
The estimated value of all open positions at the -th moment.
Profit/Loss: .
Portfolio value at the end of day : .
The return of the portfolio at the time when the i-th stock quote is received: .
The number all of positive returns: .
The number all of negative returns: .

## Simple statistics¶

The number of all intraday values (stock quotes) is denoted by .
It is a sum of all intraday portfolio values.

The mean of values is computed as follows:

The estimator of a variance of a portfolio values is computed as follows, the denominator of the below fractional is because this estimator is unbiased.

The standard deviation estimator of a portfolio values is computed as follows:

The estimator of a skewness of a portfolio values is computed as follows:

The estimator of a kurtosis of a portfolio values is computed as follows:

## Returns statistics¶

Highest Period Return
It is the maximum of all portfolio returns. It is defined as follows:

Lowest Period Return
It is the minimum of all portfolio returns. It is defined as follows:

Standard deviation negative returns
The estimator of a standard deviation of all negative returns is computed in the following way. Estimator is unbiased, so the denominator is . Moreover, .

Standard deviation positive returns
The estimator of a standard deviation of all positive returns is computed in the following way. Moreover, .

Max Drawdown Portfolio Return
The maximum drawdown of a portfolio return is computed in the following way:

## Other statistics¶

Max Drawdown Portfolio
The maximum drawdown of a portfolio value is computed in the following way:

Calmar Ratio
The Calmar ratio of a portfolio is a risk index which presents a relation between a mean return and an absolute value of a return drawdown.