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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.
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. It was proved by Jensen in 1906, [ 1 ] building on an earlier proof of the same inequality for doubly-differentiable functions by Otto Hölder in 1889. [ 2 ]
Subtracting from both sides and dividing by 2 by two yields the power-reduction formula for sine: = ( ()). The half-angle formula for sine can be obtained by replacing θ {\displaystyle \theta } with θ / 2 {\displaystyle \theta /2} and taking the square-root of both sides: sin ( θ / 2 ) = ± ( 1 − cos θ ) / 2 ...
Michael Cole Jensen (November 30, 1939 – April 2, 2024) was an American economist who worked in the field of financial economics. From 1967-1988, he was on the University of Rochester's faculty. [1] Between 2000 and 2009 he worked for the Monitor Company Group, [2] a strategy-consulting firm which became
The information ratio is often annualized. While it is then common for the numerator to be calculated as the arithmetic difference between the annualized portfolio return and the annualized benchmark return, this is an approximation because the annualization of an arithmetic difference between terms is not the arithmetic difference of the annualized terms. [6]
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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
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 ...