In another forum, someone posted an interview question asking candidates how to compute 10-day VaR.The candidate replies with c*sqrt(10)*SD where c is the critical value (e.g. 2.33 for 99%) and SD is the standard deviation.The interviewer said that in practice, this formula works well with 1-day VaR but not 10-day VaR. Does anyone know why the interviewer say so? What book should I read to understand this (apparently not the Hull book)?Thanks in advance

If you calculated 1-day V@R,formula works everytime well.Just control your last V@R values.Only take 1-Day V@R*sqrt(10 or any Holding Period)You Can read Implementing Value at Risk Philip Best or Paul Wilmott Quantitative Finance books.

If you multiply the 1-day VaR by sqrt(10), then isn't it the same as the formula c*sqrt(10)*SD?Supposedly this is not the VaR value for 10 days according to that interviewer, why?

the sqrt-rule is valid if you assume independent p/l-distributions with identical stddev (then Variance(X1+X2+...+X10) = SUM Variance(Xi) = 10 * Variance(X1), so stddev(sum Xi) = sqrt(10)*stddev(X1)). Perhaps the interviewer is not happy with the independence assumption.

QuoteOriginally posted by: pcaspersthe sqrt-rule is valid if you assume independent p/l-distributions with identical stddev (then Variance(X1+X2+...+X10) = SUM Variance(Xi) = 10 * Variance(X1), so stddev(sum Xi) = sqrt(10)*stddev(X1)). Perhaps the interviewer is not happy with the independence assumption.I think that probably is what the interviewer thought. So usually what kind of volatility model people actually use to calculate VaR in practice?

The point about independence is one possible answer. However it is more likely that the interviewer wanted you to also scale the mean by 10 days to avoid overestimating the VaR as outlined in Kevin Dowd's book Measuring Market Risk. The original RiskMetrics papers all used the assumption of a 0 daily mean which is statistically defensible for equities but may nor be appropriate for other assets or longer time frames. Once you start to consider higher order statistics such as in the Cornish Fisher or 'Modified' VaR the time scaling of these higher moments also becomes a significant factor that is in general applied incorrectly.

VaR is such a hack.

Even for one-day var you don't calculate it as c*sd as the underlying Normality assumption is too naive. You have to take into account the tail behaviour.For 10-day var you need to study the rolling 10-day PnL vs. the underlying risk factors.However, given the exact one-day var but no further information, it is OK to scale it up by sqaure root of 10 to get the approximated 10-day var - this is equivalent to derive the "implied volality" from the one-day var and then assume indepdendent Normal: NOT the same as what the candidate has said.