# Tag Archives: Expected Shortfall

## Historical Value at Risk versus historical Expected Shortfall

Comparing the behavior of the two on the S&P 500. Previously There have been a few posts about Value at Risk (VaR) and Expected Shortfall (ES) including an introduction to Value at Risk and Expected Shortfall. Data and model The underlying data are daily returns for the S&P 500 from 1950 to the present. The VaR and … Continue reading

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## The scaling of Expected Shortfall

Getting Expected Shortfall given the standard deviation or Value at Risk. Previously There have been a few posts about Value at Risk and Expected Shortfall. Properties of the stable distribution were discussed. Scaling One way of thinking of Expected Shortfall is that it is just some number times the standard deviation, or some other number … Continue reading

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## An infelicity with Value at Risk

More risk does not necessarily mean bigger Value at Risk. Previously “The incoherence of risk coherence” suggested that the failure of Value at Risk (VaR) to be coherent is of little practical importance. Here we look at an attribute that is not a part of the definition of coherence yet is a desirable quality. Thought … Continue reading

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## The incoherence of risk coherence

What coherent risk measures are, why some people think coherence is important, and why I don’t. The rules A risk measure is considered to be coherent if it satisfies some mathematical properties.  They are formulated in various ways — here is one set: (monotonicity) If the value of portfolio X is always bigger than the … Continue reading

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## The estimation of Value at Risk and Expected Shortfall

An introduction to estimating Value at Risk and Expected Shortfall, and some hints for doing it with R. Previously “The basics of Value at Risk and Expected Shortfall” provides an introduction to the subject. Starting ingredients Value at Risk (VaR) and Expected Shortfall (ES) are always about a portfolio. There are two basic ingredients that … Continue reading

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## The basics of Value at Risk and Expected Shortfall

Value at Risk and Expected Shortfall are common risk measures.  Here is a quick explanation. Ingredients The first two ingredients are each a number: The time horizon — how many days do we look ahead? The probability level — how far in the tail are we looking? Ingredient number 3 is a prediction distribution of … Continue reading

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