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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 information ratio is similar to the Sharpe ratio, the main difference being that the Sharpe ratio uses a risk-free return as benchmark (such as a U.S. Treasury security) whereas the information ratio uses a risky index as benchmark (such as the S&P500). The Sharpe ratio is useful for an attribution of the absolute returns of a portfolio ...
The Brinson model performance attribution can be described as "arithmetic attribution" in the sense that it describes the difference between the portfolio return and the benchmark return. For example, if the portfolio return was 21%, and the benchmark return was 10%, arithmetic attribution would explain 11% of value added. [11]
Thus, for example, it is easy to recognize the magnitude of the difference between two investment portfolios which have M 2 values of 5.2% and of 5.8%. The difference is 0.6 percentage points of risk-adjusted return per year, with the riskiness adjusted to that of the benchmark portfolio (whatever that might be, but usually the market).
The Frankfurt Bond Market, 1988. A bond index or bond market index is a method of measuring the investment performance and characteristics of the bond market.There are numerous indices of differing construction that are designed to measure the aggregate bond market and its various sectors (government, municipal, corporate, etc.)
Usually a broad index, such as the S&P 500 or a national index like the Nikkei 225, is used as a benchmark to determine the expected return. For example, if a stock increased by 5% because of some news that affected the stock price, but the average market only increased by 3% and the stock has a beta of 1, then the abnormal return was 2% (5% ...