# Definitions

## Dashboard

### Stats

#### Profit

The net profit of your trading account after all transaction costs in the currency of a trading account.

#### Equity

The net liquidation balance of your account in the accounts base currency. It is the cash balance plus the mark-to-market profit and loss of all open positions.

#### Return

Change in equity between the two time periods relative to the opening equity at the beginning of the time period. For example, if equity at time $t$ is $12,000 and equity at time $(t-1)$ is$10,000 the return is equal to $r_t = (12,000-10,000)/10,000 = 0.2$.

If a deposit or withdrawal is recorded between the time periods $t$ and $(t-1)$ it is accounted for in a denominator. For instance, if in the previous example, there was a deposit of \$1,000 between the time $(t-1)$ and $t$ – the return is equal to $r_t = (12,000-10,000)/(10,000 + 1,000) = 0.18$.

#### Performance

The mark-to-market cumulative profit an account has accumulated from inception-to-date using periodical returns. The mathematical formula for performance is $p = \prod_{t=1}^T (1 + r_t) - 1$, where $r_t$ is the return for the period $t$, and $t$ takes on values of each period from inception to T, which is the moment of measurement. Given a performance value and a subsequent return, the following formula gives the updated performance: $p= (1+p_{T-1})(1+r_T)-1$, where $p_{T-1}$ is the performance and $r_{T}$ is the subsequent return.
So once performance reaches -1, no subsequent returns can affect it, because $(1 + (-1))$ will always be zero.

For example, if a trading account has three daily returns of $0.01$, $0.02$, and $-0.01$ respectively – the performance of a trading account would be computed as $p = (1+0.01)(1+0.02)(1-0.01) - 1 = 1.01 \cdot 1.02 \cdot 0.99 - 1 = 0.0199 \sim 2\%$.

#### Maximal Drawdown (MaxDD)

The maximal drawdown is a maximal loss from a peak to a valley divided by the peak value. The maximal drawdown is a downside risk measure.

The mathematical formula for maximal drawdown can be derived as follows. If $e_t$ are the timeseries of account equity, we may define the running maximum as $M_t = \max_{s \lt t} e_s$. In this case, the maximal drawdown is just $MaxDD = \max_t \{ (e_t - M_t)/M_t \}$.

Imagine the following scenario: your account equity started at 10,000, went down to 6,000, then increased to 15,000 and dropped to 8,000. There are two candidates for the max drawdown – going down from 10,000 to 6,000 and going down from 15,000 to 8,000. In the first case the drawdown is $(6,000 - 10,000)/10,000 = -40\%$ and in the latter case it is $(8,000 - 15,000)/15,000 = -46\%$. Therefore, your max drawdown is$-46\%$.

#### VaR, Open Positions

Value at Risk is defined as the daily loss that is expected to be exceeded on about 5% of all trading days, or said differently the loss you can expect in 1 of the next 20 trading days. The way it is calculated in PsyQuation is based on the VaR of each open position. This takes into account the current risk in the account not simply the VaR of the historic account equity curve.

#### VaR

Value at Risk, Value at Risk is defined as the daily loss that is expected to be exceeded on about 5% of all trading days, or said differently the loss you can expect in 1 of the next 20 trading days. The way it is calculated in PsyQuation is based on the VaR of each open position. This takes into account the current risk in the account not simply the VaR of the historic account equity curve.

For example, if you see equity value at 10,000 USD and your VaR is 9.000 USD then it means that your open portfolio (trades which are opened at time T (axis X) ) has probability of 5% to lose 1,000 USD or more in price during next day (or in other words, it is the typical value of loss during 1 of 20 days).

### Current Portfolio

Current portfolio tab displays your open positions grouped by symbol

#### Instrument

Instrument or symbol, for example EUR/USD or AUD/NZD.

#### Quantity

A sum of lots of your open positions (negative if SELL and positive if BUY).

#### Dollar Exposure

Is the ratio between the total volume of open positions in a given instrument relative to the total volume of all open positions.

#### Risk Contribution

Is the contribution of the sum of open positions in the instrument to the total risk of portfolio. For example, risk contribution of 20% for AUD/USD means that this instrument’s price fluctuations are responsible for 20% of your portfolio risks.

### Statistics

#### Skill

Is a component of the score measuring traders edge and profitability.

#### Risk

Is a component of the score that compares your risk level to the risks of other trading accounts in PsyQuation’s universe.

#### Behaviour

Is a component of the score related to your affinity to behavioral biases.

#### Profit Factor

Profit factor is a gross profit divided by the gross loss (including commissions) for the entire trading period. Profit factor needs to be greater than one for a profitable account. The mathematical formula for profit factor is

#### Sharpe Ratio

Sharpe ratio is a measure of portfolio return relative to its standard deviation. Any Sharpe ratio greater than one is considered good by investors. For accounts with negative performance Sharpe Ratio is less than zero.

Sharpe ratio (annualized) is defined mathematically as $SR = P/V$ where $P$ is an (annualized) trading performance and $V$ is an (annualized) volatility.

#### One Day Return

Is a return on your equity since the end of the previous day.

#### Annualised Return

is a return over a period scaled down to a 12-month period. If $T$ is an age of your trading account and $r_t$ are your daily returns, then annualized return is given by $R_{ann} = \prod_t (1 + r_t)^{252/T} - 1$.

#### Annualised Volatility

Volatility Annualized equals to $\sqrt{252} \sigma$ where $\sigma$ is a standard deviation of your daily returns. It is a measure of variability of returns – higher volatility means greater returns fluctuation around the mean value.

#### Sortino Ratio

Sortino ratio measures the performance of the investment relative to the downside deviation. Unlike the Sharpe ratio, it doesn’t take into account the upside volatility of returns.

#### Omega Ratio

Is a Omega ratio is a probability-weighted ratio of gains versus losses. Unlike the Sharpe ratio, Omega also takes into account the so-called higher moments of the distribution.

Mathematically, if $r_t$ are the daily returns – denote by $r_t^{+} = \max (0, r_t)$ and by $r_t^{-} = \min (0, r_t)$. Omega ratio is defined as the ratio $\Omega = \mathbb{E}r^{+}/\mathbb{E} r^{-}$.

#### Chance of Profit

Is a probability to achieve positive return in the next trading period on the basis of your history over the last 30 days.

#### Account Age

Is the difference between the date of the last known equity and the equity begin date.

Is a total amount of lots traded.

#### Commissions

Is a total amount of money you paid to the broker as commissions across all trades.

#### Swaps

Is a total amount of money you paid to the broker as swaps.

#### Total Deposits

Is a total amount of money deposited to your account.

#### Total Withdrawals

Is a total amount of money withdrawn from your account.

#### Expectancy

Is a mathematical expectation of trader’s profits.

### Winners

#### Best Win

Is the largest profit among your trades expressed both as an absolute number in your account currency and as a percentage relative to the value of equity at the trade open.

#### Average Win

Is an average value among the profitable trades in absolute numbers and relative to the account equity at the trades open.

#### Win Duration

Is an average duration of your winning trades. For open positions duration is computed as a difference between the current time and the time of the trade open.

### Losers

#### Worst Loss

Is the largest loss among your trades expressed both as an absolute number in your account currency and as a percentage relative to the value of equity at the trade open.

#### Average Loss

Is an average value among the losing trades in absolute numbers and relative to the account equity at the trades open.

#### Loss Duration

Is an average duration of your losing trades. For open positions duration is computed as a difference between the current time and the time of the trade open.