by Dr Alex S.L. Tse, Research Associate, Cambridge Centre for Finance and Cambridge Endowment for Research in Finance
The theoretical modelling of individuals’ consumption and investment behaviours is an important micro-foundation of asset pricing. Despite being a classical problem in the literature of portfolio selection, analytical progress is very limited when we extend the model to a more realistic economy featuring transaction costs. The key obstacle thwarting our understanding in the frictional setup originates from the highly non-linear differential equation associated with the problem.
Using a judicious transformation scheme, Cambridge Centre for Finance (CCFin) research associate Alex Tse and his collaborators David Hobson and Yeqi Zhu show that the underlying equation can be greatly simplified to a first order system. Investigation of the optimal strategies can then be facilitated by a graphical representation involving a simple quadratic function encoding the underlying economic parameters.
The approach offers a powerful tool to unlock a rich set of economic properties behind the problem. Under what economic conditions can we expect a well-defined trading strategy? How does the change in the market parameters affect the purchase and sale decisions of an individual? What are the quantitative impacts of transaction costs on the critical portfolio weights? While some features are known in the literature, there are also a number of surprising phenomena that have not been formally studied to date. For example, the transaction cost for purchase can be irrelevant to the upper boundary of the target portfolio weight in certain economic configurations.
In a follow-up project, the methodology is further extended to a market consisting of a liquid asset and an illiquid asset where transaction costs are payable on the latter. The research findings could serve as the useful building blocks towards a more general theory of investment and asset pricing.