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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.
Sharpe ratios, along with Treynor ratios and Jensen's alphas, are often used to rank the performance of portfolio or mutual fund managers. Berkshire Hathaway had a Sharpe ratio of 0.79 for the period 1976 to 2017, higher than any other stock or mutual fund with a history of more than 30 years.
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.
A positive Jensen's alpha indicates that managers of the fund have been able to extract higher returns than the market. Skip to main content. Sign in. Mail. 24/7 Help. For premium support please ...
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 ...
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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
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 ...