Historical var when you have no losses in time period analyzed

[operky1]

Hello,
This is a concept question with historical var. If the time period you are analyzing has no losses can you use historical var? If so would it be zero or just the lowest positive return?

Any help is appreciated! Thank you!

 

[David Harper CFA FRM]

HI @operky1 Sure, as far as HS is concerned, VaR is just the quantile of an (historical) empirical distribution. The zero x-intercept is statistically incidental; if the worst x% quantile happens to be positive, that's a valid statistical outcome. (If you wanted the force the loss viewpoint, you could always "switch" from absolute VaR perspective to relative VaR perspective, effectively, by res-caling your returns as deviations from the distributional mean, rather than zero, which by definition would translate the tails into "losses" relative to the mean). I hope that helps!

 

[operky1]

Thanks for the quick reply! Just had a "duh" moment! Makes total sense.