May 28

Translating value at risk (VaR) - Reader question

by David Harper, CFA, FRM, CIPM

FRM |

Question from P. K.,

Dear David: I read through article on Intro to VAR (both parts). I was wondering whether you have any document (that you can share) on how the conversion takes place at various confidence levels with examples. For example: Goldman Sach's reports its VAR on 95% confidence levels at 1-day trading whereas JP Morgan reports VAR at 90% confidence levels at 1-day trading period. To make the analysis we need to convert them. How does one make this conversion to make the figures comparable (apples-to-apples match)? I would appreciate if you could help me in this regard. Regards

This is related to a question on the forum yesterday about the use of parametric versus non-parametric VaR. Why do we use parametric VaR (specifically the flavor where normality is assumed) when it has been deemed such a failure? For at least two reasons:

  • It is incredibly convenient; e.g., we can convert per the question. When portfolios get complicated, this is a big deal.
  • It's not a standalone metric. It's a tool in the toolbox. A metric to be considered in tandem with other things; e.g., stress testing.

The translation of normal parametric VaR is given by:

Translated VaR = [VaR]*[NORMSINV(new confidence)/NORMSINV(old confidence)]*SQRT[new time horizon/old time horizon]

Please see the EditGrid below for a simple worksheet (open into Excel with File > Export As). Note it is just two adjustments:

  • The ratio of the inverse standard normal cumulative distributions
  • The square root of the time difference. This is the "square root rule" that says variance scales directly with time.

But, keep in mind, this translation only holds under restrictive assumptions. In fact, we can pretty much assume the restrictions will not be met. Ergo, the translation is invalid. Does that make it useless? Not even! This is the nature of quantitative finance: models simplify reality (Black-Scholes, CAPM), they have tough assumptions, we break them, some breaks are deadly, some not so much.

The specifically problematic assumption here is that returns are not independent: we know volatility variously clusters and mean reverts (and, okay, sure returns are fat tailed. Pile on, will you?).

The EditGrid:

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