Today’s stock price is $100 × (1 + 10%) = $110
The 95% VaR is given by the 14th worst return, i.e., -6.05%,
N/B: Using 260 days moving window of historical data, the 95% VaR will be r = 260(1 - 95%) + 1 = 14th observation
The new 95% VaR will be $110 × (-6.05/100) = -$6.655

Note. The latest return (10%) does not affect the left tail of the loss distribution. It is higher (more positive) than all the returns given and does not get a spot among the worst 16 observations. In addition, the examiner assumes that the oldest return pushed out the rolling window is not among the entries given. Therefore, today’s worst 16 observations will be the same as yesterday’s.

Things to Remember

• VaR (Value at Risk) is a measure used to assess the potential loss in value of a risky asset or portfolio over a specified time period with a certain level of confidence.
• Historical VaR is calculated based on historical data, while other methods like parametric VaR and Monte Carlo simulation are also used for VaR calculation.
• Confidence level in VaR represents the probability that the actual loss will not exceed the VaR estimate.
• When calculating VaR for a long position, negative returns represent losses, and the VaR value is usually expressed as a positive number.
• The worst returns are used to calculate VaR, and the VaR value is determined based on the historical data and confidence level chosen.