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3 votes
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What are the advantages of $EVaR$ over $CVaR$?

The entropic value at risk (EVaR) is a coherent risk measure, developed to tackle some computational inefficiencies of the CVaR. It is the tightest possible upper bound for traditional VaR and CVaR, ...
develarist's user avatar
  • 3,040
3 votes
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Calculating Expected Shortfall of combined portfolios

Since the bonds are independent we have one of three things that can happen (1) With probability 0.98*0.98 both bonds lose 1 Million, the total loss is 2 Million (2) With probability 2*0.98*0.02 one ...
Alex C's user avatar
  • 9,382
3 votes

Bregman Mean of a Distribution

Note that \begin{align*} f(m) &= \int d_{\gamma}(m,x)\mu(dx)\\ &=\int \big[\gamma(m)-\gamma(x)-\gamma'(x)(m-x)\big]\mu(dx)\\ &=\gamma(m) - \int \big[\gamma(x)+\gamma'(x)(m-x)\big]\mu(dx). \...
Gordon's user avatar
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2 votes
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Industry or academic standard frequency to report the return, standard deviation, and Sharpe ratio?

Insofar as a standard exists, it would be a Sharpe ratio from monthly returns using arithmetic rather than log returns. As a rule of thumb, arithmetic returns should always be used in any kind of ...
Chris's user avatar
  • 1,643
2 votes

Industry or academic standard frequency to report the return, standard deviation, and Sharpe ratio?

The question isn't simply answered and the short answer is it depends on a number of factors. The GIPS standard for investment managers is the only performance reporting standard AFAIK and it can be ...
pyCthon's user avatar
  • 2,131
2 votes
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Expected Shortfall monotonicity

$E(X|X\geq b)=\frac{\int_b^{\infty}X dP}{P(X\geq b)}=\frac{\int_b^{a}X dP+\int_a^{\infty}X dP}{P(X\geq b)} \leq \frac{a\int_b^{a} dP+\int_a^{\infty}X dP}{P(X\geq b)}=\frac{a\int_b^{a} dP+\int_a^{\...
CABLE's user avatar
  • 443
2 votes

What are the advantages of $EVaR$ over $CVaR$?

Two other important properties: $ EVaR $ is strictly monotone over continuous distributions, and strongly monotone over all distributions. Formulations involving $ EVaR $ are diffrentiable without ...
Amir's user avatar
  • 21
2 votes
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How to calculate the distortion function for CVaR?

I have solved it myself. The key was to realize that for $X \geq 0$ and $S_X(t) = \mathbb{P}(X>t)$ $$ \int_0^\infty S(t) dt = \int_0^1 F_X^{-1}(u) du = \mathbb{E}\left[X \right].$$ This is ...
T-at-R's user avatar
  • 81
2 votes

Proof for expected shortfall sub additivity

As per your previous question, please provide more details in your question. A quick hint: It seems to me that on the LHS you have the worst $\omega$ realizations of $X + Y$ and on the RHS you have ...
Bob Jansen's user avatar
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1 vote

Showing that VaR is not sub additive

What Alper says but from a quick look, I'll give you hint: They figured out that (by trail and error for B) these bounds result in the various $P(\cdot)$ to have value close to the desired VaR levels ...
Bob Jansen's user avatar
  • 8,582
1 vote

How to calculate the distortion function for CVaR?

Maybe prove that $$CVaR_\alpha (X) = \frac{1}{\alpha} \int_0^\alpha F^{-1}_X(u) du$$ has the distortion function $$ g(u)= \begin{cases} \frac{u}{\alpha}, \quad \; u \leq \alpha \\ 1, \qquad ...
CaffeRistretto's user avatar
1 vote

Examples of Spectral Risk Measures

As I know, I think that spectral risk measure is a new kind of measure developed from the CVaR (weighted average value of VaR) and in the framework of coherent risk measures. If you can prove that a ...
David Nguyen's user avatar
1 vote

Examples of Spectral Risk Measures

I believe that Prospect Theory (as defined by Kahneman, Amos, and Tversky) implicitly makes use spectral risk measures. Though I am not able to find any literature linking the two, I think there is ...
David Addison's user avatar

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