11 Total = 5 marks Having studied Fixed Income Securities, you are now working as an analyst for a well known band 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-BONDL 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 M-BOND L-BOND Aggregate-bond index M-BOND 0.0051% 0.0065% 0.0047% L-BOND 0.0065% 0.0121% 0.006956 Aggregate bond index 0.0047% 0.0069% 0.005056 Note: As usual, variances are given on the diagonal, e.g. the variance of M-BOND is 0.0051%. As usual, covariances appear in the non-diagonal elements, eg the covariance of M-BOND and L-BOND is 0.0065%.

(a) (1 mark) It can be shown that the optimal weights for the replicating portfolio are 80.95% for M- BOND and 19.05% for L-BOND. Carefully explain what it means for this portfolio to be the optimal replicating portfolio

(b) (1 mark] Now suppose that L-BOND S considered to be illiquid so that your optimal replicating portfolio consists of M-90ND only. Based on the data above, what is the correlation of the replicating portfolio with the aggregate bond index?

(c) (2 marks] Explain what is meant by a rebalancing of a passively managed portfolio and explain when a rebalancing is required.

(d) (1 mark) You implement the tracking error minimization approach with a weight of 80.95% for M- BOND and 19.05% for L-BOND. for the replicating portfolio. You then observe that in the first month your replicating portfolio outperforms the index by 35 basis points. In the second months, your replicating portfolio underperforms the index by 25 basis points. In the third month your replicating portfolio outperforms the index by basis points. Based on these observations, what is the out-of-sample tracking error for your portfolio?