Questions tagged [coherent-risk-measure]

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Proof for expected shortfall sub additivity

I found on pag 5 https://faculty.washington.edu/ezivot/econ589/acertasc.pdf the proof about the sub additivity of expected shortfall. I understood the demonstration on the whole, but I would like to ...
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Showing that VaR is not sub additive

I found on pag 2 and 3 of Martin Haugh's Risk Measures, Risk Aggregation and Capital Allocation, 2010 (in this file http://www.columbia.edu/~mh2078/RiskMeasures.pdf ) an example showing non sub ...
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How to use coherent risk measure for evaluating price?

Coherent risk measures are defined by number of axioms (see e.g. Coherent Risk Measure) but a question that does not seem well studied is how to use them. Let's take a coherent risk measure $\rho$ and ...
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Industry or academic standard frequency to report the return, standard deviation, and Sharpe ratio?

Everyone (funds, banks, academics, financial information sites etc.) reports the annualized return, standard deviation, and Sharpe ratio. Yet we never get to know what the basis of their computation ...
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Expected Shortfall monotonicity

I have to show monotonicity for a more general case than the expected shortfall. I have to show that $E(X|X \geq a) \geq E(X|X \geq b), \forall a,b \in \mathbb{R}$ so that $a\geq b$ and $F_X(a-)<1$....
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Chorent risk measure with superaddative

In some definition of chorent risk measure Superadditive is one of the properties I don't understand Why? With subadditivity and homogeneous CvaR is convex, but if we assume another definition for ...
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Choquet integral risk measure

I have one question that cannot fully understand why. What is the definition of the Choquet integral risk measure?
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Bregman Mean of a Distribution

In a paper (link), author writes, given that $\gamma:R\rightarrow \bar{R}$ is a convex function, $dom_{\gamma}:=\{x\in R:\gamma(x)<+\infty\}$ is a non-empty open set and $\gamma$ a closed proper ...
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Risk Measure-identication

Let X be a variable with existing moment generating function $M_x(z)=E[e^{zX}]$. Define the following risk measure: $\rho_{\alpha}(X)=inf_{z>0}(z^{-1}ln(\frac{M_x(z)}{1-\alpha}))$ Does anyone know ...
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Example of Coherent Risk measure with Compact Representation

Every coherent risk measure $\rho$ can be represented as $$ \rho(X)\triangleq \sup_{Q \in \mathcal{Q}} \mathbb{E}\left[ -X \right], $$ for a set of probability measures $\mathcal{Q}$ defined on the ...
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What are the advantages of $EVaR$ over $CVaR$?

$CVaR$, which is short for Conditional Value-at-Risk, has long been accepted by both academe and practice as a good coherent risk measure. Entropic value-at-risk ($EVaR$) is a comparative new coherent ...
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Calculating Expected Shortfall of combined portfolios

So I am reading lecture notes here: https://courses.edx.org/c4x/DelftX/TW3421x/asset/Week3_var_3_slides.pdf The example is this: We have two independent portfolios of bonds. They both have a ...
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How to calculate the distortion function for CVaR?

Can anyone give me some hints as to how to prove that $$g(x) = \begin{cases} \frac{x}{1-\alpha}, &0 \leq x \leq 1-\alpha\\ 1 , &1-\alpha \leq x \leq 1 \end{cases}$$ ...
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Is Value-at-Risk translation invariant?

Let: $X=V_1-V_0R_0$ where $R_0$ is the interest rate. Then, is it so that this risk measure is Translation Invariant as: $\textit{VaR}_{\alpha}(X)=\textit{VaR}_{\alpha}(V_1-V_0R_0)=V_0+\textit{VaR}_{\...
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Convex risk measure and a coherent risk measure?

A coherent risk measure is: $\rho(\lambda X_1+(1-\lambda X_2))$ How can it be shown that everey convex risk measure is indeed a coherent risk measure? I assume that it is enough to show that a ...
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Good book about replicating portfolios

I want to know if anybody can suggest me a good textbook which explains in detail and in an understandable way how to create replicating portfolios of financial instruments like options "cash or ...
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Is volatility really a coherent risk measure?

Why people say that volatility is a coherent risk measure? I don't see it clearly because what happen if the two assets are correlated positively? subadditivity would not be preserved. That ...
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Elicitability of risk measures

I read that CVaR (Conditional Value-at-Risk, also Expected Shortfall), satisfies coherence, but not Elicitability. On the other hand, VaR satisfies Elicitability, but not coherence. What is ...
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12 votes
2 answers
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Examples of Spectral Risk Measures

Let's take the usual definition of a spectral risk measure. If we look at the integral we see that spectral risk measures have the property that the risk measure of a random variable $X$ can be ...
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right benchmark for an incompletely diversified international portfolio (for a CAPM): MSCI World or MSCI ACWI IMI?

I want to calculate annual excess returns on portfolios using monthly returns for a CAPM (for the assets in the portfolio as well as for the benchmark), in order to have more information on the ...
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different amount of information on return correlations from shorter and longer periods?

I want to calculate annual excess returns on portfolios using monthly (total) returns for a CAPM (for the assets in the portfolio as well as for the benchmark), in order to have more information on ...
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1 answer
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how to chain monthly excess returns into annual?

I want to calculate annual excess returns on portfolios using monthly returns for a CAPM (for the assets in the portfolio as well as for the benchmark), in order to have more information on the ...
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2 votes
1 answer
1k views

annual excess returns from CAPM on monthly total returns

I want to calculate annual excess returns on portfolios using monthly returns for a CAPM (for the assets in the portfolio as well as for the benchmark), in order to have more information on the ...
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2 votes
0 answers
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Portfolio insurance with a coherent risk measure (CVaR)

I would like to analysis of portfolio insurance under a coherent risk-measure method (CVaR), How can I achieve that? Is there a way to turn the problem into a linear programming problem? or to ...
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16 votes
3 answers
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Gamma vs. Volatility Risk

Original Question: What is the link between Gamma and the Volatility Risk? It leads me to ask: - What is the Volatility Risk definition and what are the good practices to measure it? Thinking about ...
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What is the meaning of subadditivity in a risk measure?

The subadditivity reads: $\rho(X_1+X_2) \leq \rho(X_1) + \rho(X_2)$ What is the meaning of this condition? I can vaguely accept that one should diversify the investment portfolio. Or, I can ...
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7 votes
2 answers
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Does a coherent risk measure satisfy the four axioms of von Neumann–Morgenstern?

What is the relationship between the axioms of Artzner et al (1999) for coherent risk measures and the axioms of von Neumann-Morgenstern (1944) for the expected utility theory?
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8 votes
1 answer
547 views

Which is a more appropriate choice of risk measurement in a utility function, CVaR or VaR?

What is the consensus on which risk measure to use in measuring portfolio risk? I am researching what is the best risk measure to use in a portfolio construction process for a long/short option-free ...
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8 votes
1 answer
2k views

Value at Risk backtesting (kupiec)

I m doing my research on estimating Value at risk using different assumptions on volatility and then compare my results based on backtesting. I obtained results and just on question based on my ...
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18 votes
3 answers
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Is Conditional Value-at-Risk (CVaR) coherent?

When the risk is defined by a discrete random variable, is CVaR a coherent risk measure? I stick to the following definition of CVaR: $$ CVaR_\alpha(R) = \min_v \quad \left\{ v + \frac{1}{1-\alpha} \...
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24 votes
3 answers
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What is a "coherent" risk measure?

What is a coherent risk measure, and why do we care? Can you give a simple example of a coherent risk measure as opposed to a non-coherent one, and the problems that a coherent measure addresses in ...
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