VRM13 - Modelling Non-Parallel Term Structure Shifts and Hedging

Question 1

Describe principal component analysis and explain its use in understanding term structure movements

Answer 1

Finds multiple factors and estimates their relative importance in describing movements in a term structure

Factor loadings used to interpret PCA, i.e. first three factors explain 95% of variance in the data

Term structure can be approximated by three factors:
1. factor where all rates move in same direction but not by same amount
2. factor where structure steepens or flattens
3. factor where there is bowing

Question 2

Define key rate exposures and know the characteristics of key rate exposure factors, including partial 01s and forward bucket 01a

Answer 2

KR01 is reduction in portfolios value from a one-basis-point increase in the two year spot rate
KR02 is increase in five-year
KR03 is increase in ten-year

Question 3

Describe key-rate shift analysis

Answer 3

Banks required to analyse risks to their portfolio considering 10 kr01s. Have to calculate VaR based off of the KR01s and standard deviations

Question 4

Define, calculate, and interpret key rate 01 and key rate duration

Answer 4

KR01j = sum dPji * d Sji where S is change in spot rate

Question 5

Compute the positions in hedging instruments necessary to hedge the key rate risks of a portfolio

Answer 5

Set portfolio value for KR0j and hedging instruments = 0 and solve for weights on the instruments

Question 6

Relate key rates, partial 01s, and forward-bucket 01s and calculate the forward-bucket 01 for a shift in rates in one or more buckets

Answer 6

To calculate forward bucket:
1. calculate value of bond as is
2. apply a 1 basis point increase to rates JUST IN BUCKET YEARS to value portfolio again
3. FB01 = difference