A linear programming research project

The aim of this project is to construct a portfolio that replicates a fixed-income index within Corporate Investment Grade - companies with good credit rating, by using linear programming. The portfolio must have the possibility to deviate from the index in a controlled manner (to take active positions), in order to exceed the market index over time. The replication will be restricted to determine the minimum number of key figures in an fixed income portfolio (credit portfolio within IG) to achieve an acceptable replication of indices with the same return dynamics. By minimizing the requirement for the number of key figures a flexibility is created that results in opportunities. Quantitative analysis and tools will be used to manage and analyze data and will form the basis of the design of a portfolio that replicates the market index. The first step in that quantitative process is to determine the quality of the replication. The portfolio should not be given the possibility to take its own positions, which will provide the performance of its ability to understand the underlying return dynamics in terms of risk factors. Creating a sparse portfolio that can reproduce the performance of the fixed-income index can be viewed as a linear optimization problem, since measures such as duration, convexity and DTS (Duration Times Spread) are used in the process. Research question • What is the minimum number of key figures in a fixed income portfolio (credit portfolio within Investment Grade) in order to achieve a replication of indices that in long-term exceed the market index? Data The data used for this report consists of information on all assets included in the index EUR Investment grade (ER00), EUR High Yield (HE00), USD Investment Grade (C0A0) and USD high yield (H0A0). The data goes back five years and contains values for all bonds. Methodology The first step is to replicate the index. Then by using linear programming and lasso try to find as few key figures as possible to possibly surpass the index during this period. It is important to also be able to have a diversified portfolio regarding the area of ​​assets.