# 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.