Sharpe Ratio or Sortino Ratio - which one is better?

Sharpe Ratio Versus Sortino Ratio – Which one is Better?

the Sharpe Ratio and Sortino Ratio as Measures of Risk-Adjusted Returns

In financial and investment management, the assessment and quantification of risk-adjusted returns is important for judging portfolio performance. The evaluation process is significantly aided by the utilization of two metrics - the Sharpe Ratio and the Sortino Ratio.

Regarded highly within the financial industry, these ratios give investors differentiated insights into the counterplay of risk versus return. The Sharpe and Sortino Ratios are employed in the computation of risk-adjusted returns of a diverse range of investment portfolios, with their primary function being the evaluation of whether the projected returns justify the associated risks.

Despite the shared objective, these ratios incorporate and quantify risk through distinct methodologies, thereby rendering them appropriate for different circumstances and investment strategies. We will look at these two ratios, focusing on their shared aspects, where they differ, and distinct applications within the broader framework of risk-adjusted performance measurement.

An Examination of the Sharpe Ratio

Originating from modern portfolio theory, the Sharpe Ratio, brought into existence by Nobel Laureate William F. Sharpe, provides an essential measure for the assessment of risk-adjusted returns. Conceptually, the Sharpe Ratio calculates the excess return, often denoted as the risk premium, of an investment or a portfolio, per unit of total risk or volatility.

Mathematically, the Sharpe Ratio is represented as:

Sharpe Ratio = (Expected portfolio return – Risk-free rate) / Standard deviation of the portfolio's excess return.

In this calculation, the risk-free rate typically corresponds to a secure government bond, reflecting the return an investor might expect from an investment devoid of risk. The expected portfolio return, subtracted by the risk-free rate, provides the excess return. This value, once divided by the standard deviation of the portfolio's excess return, gives the Sharpe Ratio. The higher the ratio, the better the portfolio's risk-adjusted performance.

However, the Sharpe Ratio is not without its limitations. Most notably, the ratio presumes all volatility, whether upwards or downwards, as equally detrimental. This broad-brush approach to risk, considering all deviations from the mean return (positive or negative) as risk, tends to simplify the risk-return landscape excessively. It is especially less ideal for asymmetric return distributions or strategies with significant skewness. This critical limitation creates the idea for the introduction of the Sortino Ratio, a refinement of the Sharpe Ratio, which considers only downside risk.

An Examination of the Sortino Ratio

Emerging from the critical examination of the Sharpe Ratio's limitations, we encounter a more nuanced measure of risk-adjusted return, the Sortino Ratio. Named after Frank A. Sortino, this metric retains the fundamental principles of the Sharpe Ratio, with a key difference: it penalizes only downside volatility, thereby distinguishing harmful volatility from overall volatility.

Conceptually, the Sortino Ratio calculates the return earned over and above a certain 'desired rate' for each unit of bad or downside risk. This ratio stands as a testament to the fact that investors are primarily concerned with the potential for their investments to underperform, rather than just the sheer volatility of returns.

The Sortino Ratio is mathematically expressed as:

Sortino Ratio = (Expected portfolio return – Target return) / Downside deviation

Here, 'target return' or 'desired rate' stands for the minimum return expected by an investor. The downside deviation, in contrast to the standard deviation used in the Sharpe Ratio, measures only the variability of returns that are below the target.

Incorporating only the downside risk into the equation, the Sortino Ratio provides a more relevant assessment of risk for investors, as it discerns between 'good' and 'bad' volatility. This discernment is a significant advantage over the Sharpe Ratio, as it provides a clearer representation of the risk associated with negative returns, making it particularly advantageous for portfolios or strategies that do not adhere to a normal distribution of returns.

Comparing the Sharpe and Sortino Ratios

Dissecting the Sharpe and Sortino Ratios, it is the treatment of volatility that delineates the primary distinction between them. The Sharpe Ratio, as established earlier, adopts an all-encompassing view of volatility, interpreting both upward and downward price fluctuations as risk. This assumption inherently positions it on the premise that all volatility is detrimental and all risk is symmetrical, which may not accurately represent the investor's perspective.

On the contrary, the Sortino Ratio discerns between detrimental (downside) volatility and overall volatility. This crucial differentiation stems from the understanding that investors are typically more perturbed by potential losses (downside risk) than equivalent gains (upside risk). Consequently, by penalizing only downside volatility, the Sortino Ratio presents a measure of risk-adjusted performance that aligns more intuitively with the investor's concerns.

This distinction between the ratios significantly influences the interpretation of investment risk. The Sharpe Ratio's view of risk, being comprehensive, could potentially penalize risk-taking even when the volatility might lead to positive returns. In contrast, the Sortino Ratio’s selective approach to volatility provides a more tailored risk assessment, particularly beneficial when considering strategies prone to negative skewness or those exhibiting high kurtosis. Therefore, the Sortino Ratio's focus on negative volatility offers a more nuanced and practical gauge of the risk an investor is likely to care about most.

Practical Applications: When to Utilize Which Ratio

Understanding the differences between the Sharpe and Sortino Ratios allows investors to make informed decisions about when to employ each one.

The Sharpe Ratio, being a measure of total risk, might be a preferable metric in circumstances where a broad view of volatility is appropriate. This could be particularly relevant for symmetrically distributed returns or where the investor is equally concerned with upside and downside volatility. The Sharpe Ratio is straightforward, widely recognized, and provides a broad-brush perspective of risk-adjusted performance, making it suitable for comparing diverse investment opportunities or strategies on a general level.

Conversely, the Sortino Ratio emerges as a more suitable choice in scenarios where downside risk is a principal concern. This could be the case for asymmetric strategies with a focus on capital preservation or for strategies that aim to exploit the positive skewness of returns. Moreover, the Sortino Ratio might be a superior choice when comparing strategies that have similar Sharpe Ratios but differing downside risks, as it more accurately reflects the risk of substantial losses.

Conclusion

The Sharpe Ratio, by considering total volatility, provides a broader view of the investment's risk-relative returns. In contrast, the Sortino Ratio, by focusing exclusively on negative volatility or downside risk, offers a more precise tool for analyzing strategies where downside protection is a priority.

The importance of these metrics is underpinned by their capacity to deepen our understanding of risk and return in investment analysis. They offer investors a sophisticated means of evaluating and comparing investment strategies on a risk-adjusted basis, thereby fostering more informed decision-making.

Ultimately, the choice between using the Sharpe Ratio or Sortino Ratio hinges upon the investor's perspective on risk. Are they concerned with total volatility, both upside and downside, or is their focus primarily on downside volatility? This discernment fundamentally shapes which of these metrics is most appropriate.

However, in the context of systematic trading strategy development, we would advocate for the Sortino Ratio. Given that most trading systems aim to control downside risk tightly while exploiting upward movements, the Sortino Ratio’s focus on downside volatility aligns well with these objectives. The Sortino Ratio, thus, allows for a more nuanced assessment of a system's risk-adjusted performance, making it a valuable tool for traders seeking to maximize their strategies' effectiveness.