Term
| When can the mean-variance framework be applied? one key assumption... |
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Definition
| only under the assumption of an elliptical distribution such as the normal distribution |
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Term
| If the return is non elliptical what is a more robust measure than VaR? |
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Definition
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Term
| What does the traditional mean-variance model estimate? |
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Definition
| the amount of financial risk for portfolios in terms of the portfolios expected return (i.e. mean) and risk (i.e. standard deviation). |
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Term
| Can VAR calculate risk nor non-normal distributions? |
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Definition
| It can but the results may be unreliable |
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Term
| What properties should coherent risk measures exhibit? |
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Definition
- Monotonicity : a portfolio with greater future returns will likely have less risk
R1 > R2 then std dev R1 < std dev R2
- Subaddivity: the risk of a portfolio is at most equal to the risk of the assets within the portfolio
- Positive homogenieity: the size of a portfolio will impact the size of it's risk
- Translation invariance: the risk of a portfolio is dependent on the assets within teh portfolio for all constants
m s p t
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Term
| What is expected shortfall? |
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Definition
the expected loss given that the portfolio return already lies below the pre-specified worst case quantile return
it's the mean percent loss among the returns falling below the q-quantile (also known as conditional VAR or expected tail loss) |
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Term
| Why is ES a more appropriate risk measure than VAR? |
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Definition
- ES satisfies all of the properties of coherent risk measurements (M, T, P S). VAR only satisfies these properties for normal distributions
- the portfolio risk surface for ES is convex because the property of subadditivity is met. Thus ES is more appropriate for solving portfolio optimization problems than VAR.
- ES gives an estimate of the magnitidue of a loss for unfavourable events - VAR doesn't estimate how large the loss may be.
- ES has less restrictive assumptions regarding risk/return decision rules. |
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