John Flag, the manager of a USD 150 million distressed bond portfolio, conducts stress tests on the portfolio. The portfolio's annualized return is 12%, with an annualized return volatility of 25%. In the past two years, the portfolio encountered several days when the daily value change of the portfolio was more than 3 standard deviations. If the portfolio would suffer a 4-sigma daily event, estimate the change in the value of this portfolio. Daily volatility is equal to 0.25 * sqrt (1/250) = 0.0158. A 4-sigma event therefore implies a loss equal to 4*0.0158*150 = 9,486,832 Why it shouldn't be (.12-0.25) * sqrt (1/250)?

Relative VaR & Absolute VaR One has drift, the other does not. Depends on application but usually use relative VaR, especially when horizon is short.