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Sharpe Ratio What differentiates a ‘good’ manager from one who is not as good? One of the earliest measures proposed and still one of the most popular is called the Sharpe Ratio, and it is defined as follows:
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Sharpe Ratio The Sharpe ratio or reward-to-variability ratio is a measure of the excess return (or Risk Premium) per unit of risk in an investment asset or a trading strategy Named after William Forsyth Sharpe (1990 Nobel Memorial Prize in Economic Sciences)
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Sharpe Ratio Sharpe Ratio = (Rp – rf ) / σ p where: Rp= the return of the portfolio, rf = the risk-free rate, usually chosen as a 3 month BA rate σ p = the volatility of the portfolio , usually calculated as the standard deviation of returns. Risk Premuim
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Sharpe Ratio The basic idea is that an investment with a higher Sharpe ratio is a better investment. A higher ratio indicates more return per unit of risk assumed by the manager
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Sortino Ratio The Sortino ratio is closely related to the Sharpe ratio. It compares the return of a portfolio with a chosen Minimum Acceptable Return (which could be the risk free rate but need not be), and divides it by the downside semi-standard deviation, which measures only the volatility of returns below the MAR:
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Sortino Ratio Downside deviation Similar to the loss standard deviation except the downside deviation considers only returns that fall below a defined Minimum Acceptable Return (MAR) rather then the arithmetic mean
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Sortino Ratio Sortinoratio = Rp – MAR / σDDMAR Rp = the return of the portfolio MAR = Minimum Acceptable Return σDD= Downside deviation of return.
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Sortino Ratio Where the Sharpe Ratio measures return per unit of total risk the Sortino Ratio measures the return per measure of downside risk. Thus what is the chance a manager’s portfolio will go below the MAR which is usually the risk free rate of return.
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Information Ratio IR attempts to measure not just the excess return to a benchmark, but also how consistent that performance is. Is a manager beating the benchmark by a little every period, or a lot in a few particular periods? Most investors would prefer the former, and the IR measures this degree of consistency.
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Information Ratio To define the IR we first have to define a related concept called the tracking error. The tracking error is defined as the volatility, or standard deviation, of excess return. The excess return is calculated as the unit trust’s return minus the benchmark return The IR is then defined as the excess return divided by the tracking error.
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Information Ratio Information Ratio = (Rp-Ri) / σ p-i σ p-i =Tracking error Rp = Unit Trust Return Ri = Benchmark return
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Example The following information is given for 2 Unit trusts A and B The benchmark for these unit trusts is the JSE ALSI The AVERAGE risk free rate rf = 5%. The Minimum Acceptable Return (MAR) = 5% = rf
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InformatonRatio (5 Year) Information Ratio A = (-2.14) / 6.98 = -0.31 Information Ratio B = 0.52 / 2.62 = 0.2
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Example According to the Information Ratio Unit Trust B performs better than the benchmark (JSE ALSI) on a more consistent basis than Unit Trust A.
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