Question

Assume the following: 1 yr rate = +10, 2 yr rate = +4, 3 yr rate = -8 PC1 factors: 1yr = 0.32, 2 yr = 0.35, 3 yr = 0.36 PC2 factors: 1 yr = -0.32, 2 yr = -0.1, 3 yr = 0.02 What are the factor scores (in bps) and what is the change in portfolio value approximated by?

Answer 1

The question asks for the calculation of factor scores from given rates and principal component factors and how these scores relate to the change in portfolio value. The factor scores are obtained by multiplying the rates with the principal component factors, while the change in portfolio value depends on the portfolio's factor exposures, which are not provided.

Step-by-step explanation:

The student's question involves calculating factor scores in basis points (bps) and approximating the change in the value of a portfolio given certain interest rates and principal component factors (PC1 and PC2). To find the factor scores, we multiply the given rates by their respective principal component factors. The formula for the factor score for each principal component is (Yearly Rate) x (PC Factor). Then sum the obtained products for PC1 and PC2 separately to get the factor scores in bps.

The approximation of the change in portfolio value can be derived by multiplying the portfolio's exposure to each factor by the respective factor score. If the portfolio's exposure to PC1 and PC2 is not given, this portion of the question cannot be completed without additional information.