The tag has no usage guidance.

learn more… | top users | synonyms

0
votes
0answers
41 views

Coherent Risk Measures and VaR

I am working on a problem that is worded exactly as follows: Consider the functions $\rho_{1}$ and $\rho_{2}$, defined on the space of random variables with finite expected value in the following way ...
1
vote
1answer
100 views

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: ...
0
votes
1answer
42 views

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 ...
0
votes
1answer
67 views

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 ...
3
votes
1answer
197 views

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 ...
1
vote
1answer
650 views

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 ...
8
votes
0answers
677 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
1answer
121 views

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 ...
1
vote
2answers
77 views

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 ...
1
vote
1answer
2k views

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 ...
2
votes
1answer
525 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 ...
2
votes
0answers
87 views

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 ...
8
votes
3answers
3k views

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 ...
7
votes
2answers
5k views

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 ...
5
votes
2answers
440 views

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?
7
votes
1answer
333 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 ...
6
votes
1answer
1k 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 ...
12
votes
3answers
2k views

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} ...
16
votes
4answers
4k 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 ...