  In the last few years, the financial advisory industry has been impacted by
the emergence of digitalization and robo-advisors. This phenomenon affects
major financial services, including wealth management, employee savings plans,
asset managers, etc. Since the robo-advisory model is in its early stages, we
estimate that robo-advisors will help to manage around $1 trillion of assets in
2020 (OECD, 2017). And this trend is not going to stop with future generations,
who will live in a technology-driven and social media-based world. In the
investment industry, robo-advisors face different challenges: client profiling,
customization, asset pooling, liability constraints, etc. In its primary sense,
robo-advisory is a term for defining automated portfolio management. This
includes automated trading and rebalancing, but also automated portfolio
allocation. And this last issue is certainly the most important challenge for
robo-advisory over the next five years. Today, in many robo-advisors, asset
allocation is rather human-based and very far from being computer-based. The
reason is that portfolio optimization is a very difficult task, and can lead to
optimized mathematical solutions that are not optimal from a financial point of
view (Michaud, 1989). The big challenge for robo-advisors is therefore to be
able to optimize and rebalance hundreds of optimal portfolios without human
intervention. In this paper, we show that the mean-variance optimization
approach is mainly driven by arbitrage factors that are related to the concept
of hedging portfolios. This is why regularization and sparsity are necessary to
define robust asset allocation. However, this mathematical framework is more
complex and requires understanding how norm penalties impacts portfolio
optimization. From a numerical point of view, it also requires the
implementation of non-traditional algorithms based on ADMM methods.
