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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.
Performance attribution, or investment performance attribution is a set of techniques that performance analysts use to explain why a portfolio's performance differed from the benchmark. This difference between the portfolio return and the benchmark return is known as the active return .
Even if a PME can be calculated, while the investment stays negative, every increase in the index will be interpreted as a hit in the performance of the theoretical investment : on the above example, the value of the index went back up to 120, which had a negative impact on the value of the theoretical investment.
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 ...
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).
To begin, define to be: = () where is the vector of active weights for each asset relative to the benchmark index and is the covariance matrix for the assets in the index. While creating an index fund could involve holding all N {\displaystyle N} investable assets in the index, it is sometimes better practice to only invest in a subset K ...
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