Final answer:
To calculate the SD of the change in Portfolio, use the formula sqrt((SD(PC1))^2 + (SD(PC2))^2). For the 1 day 99% VaR, multiply the SD by the z-score.
Step-by-step explanation:
To calculate the change in Portfolio, we need to find the standard deviation (SD) of the factor scores for PC1 and PC2. The SD of the change in Portfolio can be calculated using the formula:
SD = sqrt((SD(PC1))^2 + (SD(PC2))^2)
Substituting the given values, the SD of the change in Portfolio is sqrt((17.49)^2 + (6.05)^2) = 18.47.
To calculate the 1 day 99% VaR (Value at Risk), we multiply the SD of the change in Portfolio by the z-score corresponding to the desired confidence level:
VaR = SD * z-score
For a 1 day 99% VaR, the z-score is approximately 2.33. Therefore, the 1 day 99% VaR is 18.47 * 2.33 = 43.05.