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The main idea is that the riskiness of one portfolio's returns is being adjusted for comparison to another portfolio's returns. 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 ...
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]
The ex-post Sharpe ratio uses the same equation as the one above but with realized returns of the asset and benchmark rather than expected returns; see the second example below. The information ratio is a generalization of the Sharpe ratio that uses as benchmark some other, typically risky index rather than using risk-free returns.
The portfolio performance was 4.60%, compared with a benchmark return of 2.40%. Thus the portfolio outperformed the benchmark by 220 basis points.The task of performance attribution is to explain the decisions that the portfolio manager took to generate this 220 basis points of value added.
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.
In finance, Jensen's alpha [1] (or Jensen's Performance Index, ex-post alpha) is used to determine the abnormal return of a security or portfolio of securities over the theoretical expected return. It is a version of the standard alpha based on a theoretical performance instead of a market index .