Cross-selling investment products with a win-win perspective in portfolio optimization

Abstract

We propose a novel approach to cross-selling investment products that considers both the customers' and the bank's interests. Our goal is to improve the risk-return profile of the customer's portfolio and the bank's profitability concurrently, essentially creating a win-win situation, while deepening the relationship with an acceptable product. Our cross-selling approach takes the customer's status quo bias into account by starting from the existing customer portfolio, rather than forming an efficient portfolio from scratch. We estimate a customer's probability of accepting a product offer with a predictive model using readily available data. Then, we model the investment product cross-selling problem as a nonlinear mixed-integer program that maximizes a customer's expected return from the proposed portfolio, while ensuring that the bank's profitability improves by a certain factor. We implemented our methodology at the private banking division of Yapi Kredi, the fourth-largest private bank in Turkey. Empirical results from this application illustrate that (1) a traditional mean-variance portfolio optimization approach does not increase portfolio returns and reduces overall bank profits, (2) a standard cross-selling approach increases bank profits at the expense of the customers' portfolio returns, and (3) our win-win approach increases the expected portfolio returns of customers without increasing their variances, while simultaneously improving bank profits substantially.