Data and model
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Risk at a glance
Where the risk comes from
Correlation of returns
Stress: the worst stretches in the data
What if? Shocks of your own
Enter how much each asset would move at once, in percent (-10 is a fall of 10%). The effect on the portfolio is the weighted sum, compared with the VaR and the expected shortfall.
Against the benchmark
Rolling beta
Rolling window against a filtered estimate
Multi-period check
Model validation
Growth of 100 and drawdown
Daily return against the VaR forecast
Distribution of returns
Tail shape: QQ plot against the normal
Definitions and assumptions
- Value at risk (VaR)
- The one period return that is not expected to be breached at the chosen confidence level. Losses are negative.
- Expected shortfall (ES)
- The average return on the periods that breach the VaR. Never better than the VaR.
- Breach
- A period whose return is worse than the VaR forecast made before it, from the previous window of returns.
- Kupiec test
- Tests the number of breaches against the confidence level. Rejects too many (risk understated) and too few (overstated).
- Christoffersen independence test
- Tests whether a breach makes another more likely the next period, i.e. whether they cluster.
- Conditional coverage
- Kupiec and independence combined.
- Basel traffic light
- Green, yellow or red from the binomial probability of seeing this many breaches or fewer if the model were right (95% and 99.99% cut-offs).
- Stress window
- The worst compounded return over any 1, 5 or 20 consecutive periods in the data, with its dates. It is what actually happened, not a forecast.
- Share of volatility
- Each asset's weight times its covariance with the portfolio, as a fraction of the portfolio variance. The shares add up to 100%.
- Share of expected shortfall
- The weight times the asset's average return on the periods when the portfolio was in its tail (worse than its VaR). Adds up to 100%.
- Diversification ratio
- The weighted average volatility of the assets divided by the volatility of the portfolio. 1 means no diversification.
- QQ plot
- Sample quantiles, in standard deviations, against normal quantiles. Points on the dashed line mean normal tails; points below it in the left tail mean fatter losses than a normal distribution allows.