CMA Final · Strategic Performance Management and Business Valuation · Risk Management
A bank uses a one-day 99% Value at Risk (VaR) of Rs 4 crore for its trading book, assuming returns are independent and normally distributed. Using the square-root-of-time rule, what is the approximate 9-day 99% VaR?
The 9-day VaR is about Rs 12 crore. Under independent, normally distributed returns, VaR grows with the square root of the horizon, so Rs 4 crore multiplied by the square root of 9, which is 3, gives Rs 12 crore.
- ARs 36 crore
- BRs 12 croreCorrect
- CRs 18 crore
- DRs 4 crore x 81 = Rs 324 crore
Explanation
VaR scales with the square root of time: 4 x sqrt(9) = 4 x 3 = Rs 12 crore. Multiplying by 9 (Rs 36 crore) wrongly scales linearly with time, which would be the error of ignoring diversification of independent daily moves.
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