Portfolio optimization with asset selection and risk parity control

After the 2008 financial crisis, risk management has become more important than performance management and an alternative portfolio design, referred to as risk parity portfolio, has been receiving significant attention from both theoretical and practical fields due to its advantage in diversification of (ex-ante) risk contributions among assets. Usually, this approach results in a portfolio with nonzero weights in all the assets. Investors, however, could not lay out the capital among all the assets listed on the markets, which results in unrealistically high transaction costs, and therefore, reduction of the return of the designed portfolio. To overcome this drawback, in this paper, we propose a method to jointly select only some of the assets and distribute the capital among the selected assets such that the risk is diversified enough.