# Tag Info

Accepted

• 6,394

### Missing data in historical simulation VaR

This issue is incredibly important and I agree there is little practical information about it. To me, the key idea is to find the right matrix completion algorithm that best suits your needs. I work ...
• 171
Accepted

### Parametric VaR, Normality and Subadditivity

Suppose $X\sim N(\mu_X,\sigma_X^2)$ and $Y\sim N(\mu_Y,\sigma_Y^2)$ are correlated jointly normal random variables. Then, $$X+Y\sim N(\mu_X+\mu_Y,\sigma^2_X+\sigma_Y^2+2\rho\sigma_X\sigma_Y).$$ ...
• 14k

### Do people actually use VaR in professional settings?

As discussed, banks do use VaR for risk management. They will have something modified for the specific use (i.e. probably not your VaR from a fitted normal distribution), it's likely more ...
• 5,081

### Imposing Restrictions on Cointegrating Vectors, R example

I know this was asked almost two years ago, but I thought I'd answer the question. It appears that the H that you want to estimate is identical to the values you received from the Johansen test, ...
Accepted

### RiskMetrics VaR Volatility Sample Size

Depending of $\lambda$, pasts observations will be weighted differently, if you compute the volatility at time $t$ , the $t-1$ observation will be weighted by $(1-\lambda)*\lambda^{0}$, the $t-2$ ...
• 2,534
Accepted

### Expected Shortfall Formula in terms of P

Gordon's answer is spot on. Another way to see it though, would be using Bayes formula and a change of variable. \begin{align*} ES_X(p) &=E\left(X \mid X\le Q_X(1-p)\right)\\ &=\int_{-\infty}^...
• 14.1k
Accepted

### 99.97% Percentile VaR Approximation

The 99.97% confidence is somtimes referred to as corresponding to the 1-year probability of default of 3 bps for AA-rated entities. (Here for example https://papers.ssrn.com/sol3/papers.cfm?...
• 1,277
Accepted

### Portfolio VaR with Copula?

You don't really have a multivariate case: we can only define VaR (in its usual sense) for a one-dimensional output. Recall that $$\operatorname{VaR}_\alpha(X) = \inf\{v:F_X(v)\geq \alpha\}$$ and ...
• 1,474

### Stressed Value at Risk vs Value at Risk

The most important difference is that the calculations are based on a "stressed" historical period in the markets as opposed to the most recent X number of years.
• 51
Accepted

Accepted

### Risk Compensation

A linear relationship between expected returns and covariance with a risk factor is a necessary consequence of a linear asset pricing function In theory, a CAPM relationship can be derived when a ...
• 6,394

### Intuitive explanation for expectiles

That picture in the other answer is pretty slick (+1), so I will just add a note on why one can interpret the colors of those areas like that: Blue: Define $Y = (X-x)_+$. This is nonnegative r.v., ...
• 534
Accepted

### 1 day VaR vs 10 day VaR

What are the underlying assumptions for doing this Assumption: Historical returns are lognormally distributed with no autocorrelation. can those assumptions be tested statistically Testing: \$\...
• 3,880

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