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For example, if the stock market went up by 20% in a given year, and a manager had a portfolio with a market-beta of 2.0, this portfolio should have returned 40% in the absence of specific stock picking skills. This is measured by the alpha in the market-model, holding beta constant. Occasionally, other betas than market-betas are used.
The rate of return on a portfolio can be calculated indirectly as the weighted average rate of return on the various assets within the portfolio. [3] The weights are proportional to the value of the assets within the portfolio, to take into account what portion of the portfolio each individual return represents in calculating the contribution of that asset to the return on the portfolio.
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 ...
To calculate beta, investors divide the covariance of an individual stock (say, Apple) with the overall market, often represented by the Standard & Poor’s 500 Index, by the variance of the ...
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The term () represents the movement of the market modified by the stock's beta, while represents the unsystematic risk of the security due to firm-specific factors. Macroeconomic events, such as changes in interest rates or the cost of labor, causes the systematic risk that affects the returns of all stocks, and the firm-specific events are the ...