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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.
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.
The return on domestically held short-dated government bonds is normally perceived as a good proxy for the risk-free rate. In business valuation the long-term yield on the US Treasury coupon bonds is generally accepted as the risk-free rate of return. However, theoretically this is only correct if there is no perceived risk of default ...
With a risk-free asset, the straight capital allocation line is the efficient frontier. 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 ...
[citation needed] equity risk premium (ERP) is the difference between the return on a market portfolio or a stock with average market risk and the risk-free rate of return. From this definition, it is clear that the market average equity return is the expected "threshold" for investors to engage in investment activities in the market, and if ...
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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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 ...