# Questions tagged [coherent-risk-measure]

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### Standard Deviation and Monotonicity property

I just read that standard deviation is a coherent risk measure, and therefore it should satisfy the monotonicity property: $X_1 \geq X_2 \implies \rho(X_1) \leq \rho(X_2)$ where $X_1,X_2$ are asset ...
75 views

### How to calculate the ex-ante beta of a portfolio between several rebalancing?

I have a portfolio composed of $N$ assets. I know the one-year beta of these assets, I also know the past (ex-post) beta ($\beta$) of my portfolio. My portfolio changes allocation every month. So I ...
30 views

### Is there a formal notion of a "reward measure"?

A risk measure, as defined in the Wikipedia page, is a function that maps random variables to real numbers and satisfies the normalized, translative, and monotone properties. There are many other ...
1 vote
300 views

### Showing that VaR is not sub additive

I found on pages 2 and 3 of Martin Haugh's "Risk Measures, Risk Aggregation and Capital Allocation" from 2010 an example showing non sub-additivity of VaR (excerpts given at the end). I ...
169 views

### 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 ...
1 vote
42 views

### 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 ...
610 views

### 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 ...
179 views

### 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 ...
365 views

### 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 $F_X(a-)<1$....
1k views

### 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 ...
129 views

### 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 ...
13k views

### 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 ...
77 views

### Choquet integral risk measure

I have one question that cannot fully understand why. What is the definition of the Choquet integral risk measure?
92 views

### 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 ...
2k views

### 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 ...
1 vote
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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 ...
86 views

### 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 ...
1 vote
3k views