QUESTION 4

Having studied Fixed Income Securities, you are now working as an analyst for a well known bond fund. Your manager asks you to replicate the JP Morgan T-Bond Index using a tracking error minimization approach. You are to replicate this index as closely as possible using a medium duration Treasury bond (M-BOND) and a long duration Treasury bond (L-BOND). These expire in approximately 5.6 years' and 29.1 years' time respectively. The following variance-covariance matrix, based on daily returns over the preceding six months, is given to you to use in your replication. Also assume that the weights, in order to replicate the index, for M-BOND and L-BOND are 0.65 and 0.35 respectively.

M-BOND L-BOND Aggregate-bond index

M-BOND 0.0059% 0.0074% 0.0054%

L-BOND 0.0074% 0.0138% 0.0079%

Aggregate-bond index 0.0054% 0.0079% 0.0058%

Note: As usual, variances are given on the diagonal, e.g. the variance of M-BOND is 0.0059%. As usual, covariances appear in the non-diagonal elements, e.g. the covariance of M-BOND and L-BOND is 0.0074%.

(a) What is the correlation of M-BOND with L-BOND?

(b) What is the correlation of M-BOND with the Aggregate Bond Index?

(c) What is the correlation of L-BOND with the Aggregate-Bond Index?

(d) What is the variance of the replicating portfolio where the weight on M-BOND is 0.65 and the weight on L-BOND is 0.35?

(e) What is the covariance of the replicating portfolio (where the weight on M-BOND is 0.65 and the weight on L-BOND is 0.35), with the index?

(f) What is the tracking error of the replicating portfolio (where the weight on M-BOND is 0.65 and the weight on L-BOND is 0.35), with respect to the index?

(g) What is the correlation of the replicating portfolio (where the weight on M-BOND is 0.65 and the weight on L-BOND is 0.35), with the index?