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The risk–return spectrum (also called the risk–return tradeoff or risk–reward) is the relationship between the amount of return gained on an investment and the amount of risk undertaken in that investment. The more return sought, the more risk that must be undertaken.
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 ...
Here, the risk-return spectrum is relevant, as it results largely from this type of risk aversion. Here risk is measured as the standard deviation of the return on investment, i.e. the square root of its variance. In advanced portfolio theory, different kinds of risk are taken into consideration.
A Spectral risk measure is a risk measure given as a weighted average of outcomes where bad outcomes are, typically, included with larger weights. A spectral risk measure is a function of portfolio returns and outputs the amount of the numeraire (typically a currency ) to be kept in reserve.
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In modern portfolio theory, the efficient frontier (or portfolio frontier) is an investment portfolio which occupies the "efficient" parts of the risk–return spectrum. Formally, it is the set of portfolios which satisfy the condition that no other portfolio exists with a higher expected return but with the same standard deviation of return (i ...
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Economic capital is a function of market risk, credit risk, and operational risk, and is often calculated by VaR. This use of capital based on risk improves the capital allocation across different functional areas of banks, insurance companies, or any business in which capital is placed at risk for an expected return above the risk-free rate.