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

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?

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:

• Sortino Ratio: Similar to the Sharpe ratio, the Sortino ratio measures the risk-adjusted return but only considers downside volatility. This can provide a better assessment of the strategy's performance, as it focuses on the negative volatility that you typically find most undesirable.

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

• Sterling Ratio: This is the ratio of the average annual rate of return to the maximum drawdown, which can help you evaluate the strategy's performance relative to its most significant losses.

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

• Calmar Ratio: Similar to the Sterling ratio, the Calmar ratio divides the average annual return by the average maximum drawdown over a specific period (commonly 3 years). It helps measure a strategy's consistency and ability to recover from drawdowns.

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

• Omega Ratio: The Omega ratio measures the ratio of the likelihood of achieving a given target return to the likelihood of falling below that target. It considers both upside and downside potential and can help in determining if a strategy is more likely to achieve a particular return level.

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

• Treynor Ratio: This ratio measures the strategy's return per unit of systematic risk (beta). It helps in understanding how much return the strategy is generating for the level of market risk it's taking.

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

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.

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

• Diversification Ratio: The Diversification Ratio measures the extent to which a portfolio is diversified by comparing the portfolio's volatility to the weighted average volatility of its individual components. A higher Diversification Ratio indicates a better-diversified portfolio, as it shows that the portfolio's overall volatility is lower than the weighted average of its individual components.

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

• 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.

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

• Pain Index: The Pain Index measures the average length, depth, and frequency of losing periods. A lower Pain Index indicates a more favorable investment experience, with shorter and less severe drawdowns. $$Loss_i$$ is the loss during drawdown $$i$$, $$Length_i$$ is the length of drawdown $$i$$, and $$n$$ is the number of drawdowns.

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

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