Bonds index tracking

The portfolio is valued at 100,000,000 and has been constructed to track a bond index for which the Euro-Bund Future is a very good hedge instrument. The basis point value (BPV) of the Euro-Bund futures contract is 72.03 and the yield is 5.595% calculated on an annual 360-day year basis. The bond index, which the portfolio has been designed to track, is quoted at 117.80. 

Tracking error is the standard deviation of the difference in returns between a portfolio and a selected benchmark, which is usually a suitable bond index. Assuming a normal distribution of returns, a portfolio manager can expect to deviate by no more than the tracking error amount for 68% of the time during a selected period. 

The first and most straightforward way to calculate tracking error is by using the full covariance model. This method depends heavily on past data for every single instrument in the index and portfolio. Using matrix algebra, the covariance of daily total returns between every pair of assets in the index can be calculated, as well as the variance of total returns for every single asset in the index. A variance-covariance matrix of the bond returns is then constructed based on these calculations. The variance-covariance matrix is then multiplied by the exposures vector, as shown in the equation below ... 

In certain countries, such as the United Kingdom and New Zealand, the central bank has explicit inflation targets, and investors may believe that over the long term those targets will be met. If the monetary authorities have good track records, investors may further believe that inflation is not a significant issue. In such situations, the case for holding index-linked bonds is weakened. 

The H-bond directionality is important in topology optimization. Keeping track of both the existence and direction of the H-bonds in a cluster can be accomplished by using a digraph. The latter can be represented by a directed adjacency matrix D. As with the adjacency matrix, the absence of a bond between monomers i and j is indicated by Dy = 0 and so all diagonal elements vanish, D = 0. If there is a bond in the direction then Dy = 1 and Dy = 0. The D matrix contains, for example, information about the number of donor (don) and acceptor (acc) H-bonds for each molecule = Y,j Dju A cc = S ij- Note that the summation index depends on the definition of the H-bond direction. In a computer program, the sparsity of A and D can be exploited by storing them as linked lists of non-zero elements. 

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