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The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio, or strategy. [1] It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target or required rate of return , while the Sharpe ratio penalizes both upside and downside volatility equally.
The following table shows that this ratio is demonstrably superior to the traditional Sharpe ratio as a means for ranking investment results. The table shows risk-adjusted ratios for several major indexes using both Sortino and Sharpe ratios. The data cover the five years 1992-1996 and are based on monthly total returns.
The ex-post Sharpe ratio uses the same equation as the one above but with realized returns of the asset and benchmark rather than expected returns; see the second example below. The information ratio is a generalization of the Sharpe ratio that uses as benchmark some other, typically risky index rather than using risk-free returns.
The standard form of the Omega ratio is a non-convex function, but it is possible to optimize a transformed version using linear programming. [4] To begin with, Kapsos et al. show that the Omega ratio of a portfolio is: = [() +] + The optimization problem that maximizes the Omega ratio is given by: [() +], (), =, The objective function is non-convex, so several ...
Modern portfolio theory (MPT), or mean-variance analysis, is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk. It is a formalization and extension of diversification in investing, the idea that owning different kinds of financial assets is less risky than owning ...
The risk parity approach asserts that when asset allocations are adjusted (leveraged or deleveraged) to the same risk level, the risk parity portfolio can achieve a higher Sharpe ratio and can be more resistant to market downturns than the traditional portfolio. Risk parity is vulnerable to significant shifts in correlation regimes, such as ...
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For example, what does it mean if one investment has a Sharpe ratio of 0.50 and another has a Sharpe ratio of −0.50? How much worse was the second portfolio than the first? These downsides apply to all risk-adjusted return measures that are ratios (e.g., Sortino ratio, Treynor ratio, upside-potential ratio, etc.).