Comparing Trading Strategies with Risk, Return, and Diversification Metrics

# How to compare algorithmic trading strategy risk/reward performance?


# How to compare algorithmic trading strategy risk/reward performance?












I am setting up different algorithmic trading strategies with varying performance characteristics. I am new to this. The strategies vary greatly with their aggressiveness. I would like to find a way to look their

Currently, I am mostly looking at the following:

- Annual return

- Maximum drawdown

- Sharpe

What would be good metrics to determine if the risk/reward is balanced? What are the other metrics that traders use outside these common ones? How would one benchmark low profitability/low-risk strategy against high profit/volatile ones? How would one balance between a suite of strategies that are both high-risk and low-risk?

## Answer by Hans-Peter Schrei (score 5, accepted)

https://quant.stackexchange.com/a/75378

As you will probably read in the documentation of many packages for algorithmic trading, there is a standard list of well known metrics outside of the ones you already mention:



$\text{Sortino Ratio}=\frac{R_p-R_f}{\sigma_d}$



$\text{Sterling Ratio}=\frac{\text{Annualized Return}}{\text{Max Drawdown}}$



$\text{Calmar Ratio}=\frac{\text{Annualized Return}}{\text{Average Max Drawdown over}\,N\,\text{years}}$



$\text{Omega Ratio}=\frac{\text{Prob of Returns > Target Return}}{\text{Prob of Returns < Target Return}}$



$\text{Treynor Ratio}=\frac{R_p-R_f}{\beta}$

Other, more specific metrics include:

- Effective Number of Bets (ENB): The Effective Number of Bets measures the diversification of a portfolio by considering the correlation between its components. A higher ENB indicates a better-diversified portfolio.

$ENB = \frac{(\sum_{i=1}^n w_i)^2}{\sum_{i=1}^n w_i^2}$



$\text{Diversification Ratio} = \frac{\sqrt{\sum_{i=1}^n (w_i \cdot \sigma_i)^2}}{\sum_{i=1}^n w_i \cdot \sigma_i}$

- Conditional Value-at-Risk (CVaR): Also known as Expected Shortfall, CVaR measures the expected loss during extreme market conditions, beyond a certain confidence level. It is more sensitive to the tail risk than the widely used Value-at-Risk (VaR) metric. $\alpha$ is the confidence level, $VaR_\alpha$ is the Value-at-Risk at the given confidence level, and $f(x)$ is the probability density function of the portfolio returns.

$CVaR = \frac{1}{(1-\alpha)} \int_{-\infty}^{VaR_\alpha} x \cdot f(x) \, dx$

- Gain-Loss Ratio (GLR): The Gain-Loss Ratio measures the average gain relative to the average loss, providing an indication of the strategy's ability to generate positive returns versus negative returns.

$GLR = \frac{\text{Average of Positive Returns}}{\text{Average of Negative Returns}}$



$\text{Pain Index} = \frac{\sum_{i=1}^{n} Loss_i \cdot Length_i}{\sum_{i=1}^{n} Length_i}$

This is just a selection of metrics though, for your specific use case there might be additional metrics that are more appropriate.