## Description of the Daily risk forecast methods

Daily risk forecasts for some exchange rates and the SP-500 index. Estimation window is 1000 days, and probability is 99%, with portfolio value €1000 for the FX and \$1000 for the SP-500. Returns are log returns, $y_t=\log(p_t/p_{t-1})$.

### Tables

There are four tables, first two showing VaR and ES, along with model risk calculated by the risk ratio method. The last two tables show the implied probability of a 5% and 15% drop in the euro exchange rate. We cannot calculate the probability for HS and it is not relevant to calculate model risk in this case. The risk is for a €1000 portfolio. Freq. -5% in years shows how frequently (in years) the model thinks a 5% drop will happen.

### Plots of returns and VaRs

Here we show the returns times 1000, the black line, and VaR for each of the risk forecast methods. Actually, the plot shows negative VaRs, because after all, VaR is about losses, and showing the negative VaR is more natural on the plot. Again, the portfolio value is thousand euros.