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Jensen's alpha is a statistic that is commonly used in empirical finance to assess the marginal return associated with unit exposure to a given strategy. Generalizing the above definition to the multifactor setting, Jensen's alpha is a measure of the marginal return associated with an additional strategy that is not explained by existing factors.
Jensen's inequality generalizes the statement that a secant line of a convex function lies above its graph. Visualizing convexity and Jensen's inequality. In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function.
Using Jensen's formula, it can be proved that this measure is also equal to the geometric mean of | | for on the unit circle (i.e., | | =): = ( (| |)). By extension, the Mahler measure of an algebraic number α {\displaystyle \alpha } is defined as the Mahler measure of the minimal polynomial of α {\displaystyle \alpha } over Q ...
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
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This measure became known as Jensen's alpha, and became widely used to measure the performance of mutual funds and other investments by both academics and practitioners. Jensen's best-known work is the 1976 Journal of Financial Economics article he co-authored with William H. Meckling , "Theory of the Firm: Managerial Behavior, Agency Costs and ...
Jensen's formula can be used to estimate the number of zeros of an analytic function in a circle. Namely, if is a function analytic in a disk of radius centered at and if | | is bounded by on the boundary of that disk, then the number of zeros of in a circle of radius < centered at the same point does not exceed
Virtually any benchmark return (e.g., an index or a particular portfolio) could be used for risk adjustment, though usually it is the market return. For example, if you were comparing performance of endowments, it might make sense to compare all such endowments to a benchmark portfolio of 60% stocks and 40% bonds.