Regression Hedging and Principal Component Analysis Flashcards
(15 cards)
What is DV01
DV01 stands for dollar value for a basis point.
It is a sensitivity measure of the bond price to the interest rate.
DV01= Duration X Bond Price X 0.01
What are Treasury Inflation Protected Security?
Also called TIPS, these are bonds where the coupons are dependent on a function of the inflation rate. As a result, this uses real yield.
What is the idea behind this kind of hedging?
When we want to hedge a security/ commodity, which does not have a fully identical security (correlation of 1) to hedge with, we take a similar security/ commodity.
Obviously, the correlation will not be 1.
What is DV01 hedging?
Assumes that when the yield changes by 1 percent in the underlying, the yield will change by 1 percent in the hedging security as well.
Hence, the idea is ;
Face value of bond 1 X DV01 (bond 1) = Face value of bond 2 X DV01(bond 2)
What is the drawback of DV01?
The assumption that the change in yield will be constant.
To combat this assumption, we find something called as the hedge adjustment factor.
What is the hedge adjustment factor?
Given that the change in yield across bonds will not be the same,
We regress the change in bond yields (one we are trying to hedge) to the hedging bond’s yields. The beta is the hedge adjustment factor.
Hence, the formula becomes
Face value of bond 1 X DV01 (bond 1) = Face value of bond 2 X DV01(bond 2) X beta
Advantage of hedge adjustment factor
This considers the changes in the bond yields over time
What is the drawback of hedge adjustment factor
It is considered that the hedge adjustment factor will remain constant over time.
How to gain comfort in hedge adjustment factor
R squared (more the merrier) and Standard error (less the merrier)
How to improve the hedge
By hedging across multiple instruments, hedge adjustment factor is then based on 2 or more independent variables
This provides a better hedge over a single variable approach.
How can we find relationships between yields
- Regress change in yields to change in yields
- Regress yields on yields
Both are okay, but have the problem of serially correlated error terms.
What is reverse regression?
Reversing the dependent and independent variables in a regression
What is the problem with reverse regression when used in regression hedging?
Suggests two different hedging positions with the same two securities.
It is upto the trader what he wants to do.
Regression hedge is ideal for minimizing the variance of hedging the XYZ bond position.
But if the priority is managing treasury exposure while maintaining a fixed treasury position, a reverse regression might be the preferred approach.
What is principal component analysis?
PCA breaks up the term structure of bonds into n pieces, with the following attributes
- Sum of all the principal components equal sum of the variances of the individual rates.
2.They are uncorrelated. - Each principal component is selected with the highest possible variance
With this, first 3 principal components, when summed, give a good approximation of the sum of the variances of all the rates, which simplifies the approach (no nC2 correlations)
Regression analysis vs PCA
Regression analysis focuses on yield changes among a small number of bonds.
Empirical approaches, such as principal component analysis (PCA), take a different
approach by providing a single empirical description of term structure behavior, which
can be applied across all bonds.
