While portfolio optimisation is commonplace in equities, it is more complex in the fixed-income space, partly because of trading lot sizes. Implementing the portfolio composition by converting weights into holdings is easy for equities due to small lot sizes.
If we consider bonds, the difference between the model and the resulting portfolio may be significant, especially when the notional amount at stake is not large. In previous research, we have approched bond-index tracking by using genetic algorithms. In this research, we explore the use of mixed-integer optimisation techniques and show that it is straightforward to implement in either corporate or government bond portfolios for any given portfolio size, subscriptions, redemptions, and portfolio rebalancing. In particular, we prove that linear constraints implying one to several bond characteristics or cardinality constraints can be handled without prior stability or convergence tests.
You can now read the full whitepaper at the link below