Evaluation metrics

This provides the explanation and equation of the evaluation metrics implemented in the backtester. The code could be found in code/evalaute.py in the repository.

Portfolio return

Definition

Portfolio return is the percentage change in total value of the portfolio.

\[\text{Portfolio return} = \frac{\text{Current portfolio value} - \text{Previous portfolio value}}{\text{Previous portfolio value}} \times 100%\]

Sharpe ratio

Definition

Sharpe ratio computes the ratio of the return of an investment to its risk.

Mathematically, it is the average return earned in excess of the risk-free rate per unit of total volatility.

\[\begin{split}\text{Sharpe Ratio} &= \frac{R_p - R_f}{\sigma_p} \\ \\ R_p &= \text{Portfolio return} \\ R_f &= \text{Risk-free rate} (assumed = 0 in the function)\\ \sigma_p &= \text{Portfolio risk, i.e. standard deviation}\end{split}\]

Maximum drawdown (MDD)

Definition

Maximum drawdown (MDD) measures the maximum observed loss from a peak to a trough of a portfolio. It is an indicator of downside risk over the given time period.

\[\begin{split}\text{MDD} &= \frac{\text{P} - \text{T}}{\text{P}} \\ \\ \text{P} &= \text{Peak value before largest drop} \\ \text{L} &= \text{Lowest value before newest high established}\end{split}\]

Compound Annual Growth Rate (CAGR)

Definition

Compoumd Annual Growth Rate (CAGR) describes the rate at which an investment would have grown if it had grown the same rate every year and the profits were reinvested at the end of each year.

It is used to smooth returns so that they may be more easily understood when compared to alternative investments. Risk is not taken into account.

\[\text{CAGR} = \left(\frac{\text{Ending portfolio value}}{\text{Beginning portfolio value}}\right)^{252 \;\div\; \text{number of days}} - 1\]

Note that “number of days” refers to the time span of the portfolio, and 252 is the total number of trading days in one year.

Standard Deviation

Definition :class: myOwnStyle

Standard Deviation measures the dispersion of the historical portfolio values relative to its mean. A higher standard deviation infers higher volatility.

\[\begin{split}\text{SD} &= \sqrt{\frac{\sum (r_i - r_{avg})^2 }{n-1}} \\ \\ r_i &= \text{Portfolio daily return} \\ r_{avg} &= \text{Mean of portfolio daily returns}\end{split}\]

Note that sample SD is used, and thus the degree of freedom equals n-1 in the equation.

Attention

All investments entail inherent risk. This repository seeks to solely educate people on methodologies to build and evaluate algorithmic trading strategies. All final investment decisions are yours and as a result you could make or lose money.