Cross-Selling Investment Products with a Win-Win Perspective in Portfolio Optimization

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 Yapı 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.