# Portfolio intraday statistics¶

## 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¶

Number of Portfolio Intraday Values
The number of all intraday values (stock quotes) is denoted by .
Portfolio Intraday Sum
It is a sum of all intraday portfolio values. Portfolio Intraday Mean
The mean of values is computed as follows: Portfolio Intraday Variance
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. Portfolio Intraday Standard Deviation
The standard deviation estimator of a portfolio values is computed as follows: Portfolio Intraday Skewness
The estimator of a skewness of a portfolio values is computed as follows: Portfolio Intraday Kurtosis
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. 