Applications of Deep Implicit Layers and Convex Optimization in Portfolio and Risk Management

Abstract

Modern portfolio optimization tactics and frameworks often oversimplify the risks, rewards, and miscellaneous costs of the portfolio with respect to the portfolio’s allocation of assets. Portfolios are often generalized without any product specifications (or they are considered to be all equities). Some of the products’ properties may vary greatly depending on which market sector, such as equities, fixed income, or derivatives. Often, assets within these three markets are combined into one portfolio as instruments in one can hedge the risks of those in another. The allocation of products is extremely important when considering portfolio management, but the diversification of the portfolio is also equally significant, especially if investment in one can balance the risk profile of another. To bridge the gap between theoretical academic propositions and real-world market applications, I incorporate implicit optimization layers with single-period and multiperiod trading into a neural network model to find momentum points of return. These points are those at which it is most appropriate to short or long certain securities given different risk and trading constraints. The model is set to be flexible enough that it caters towards specific market securities rather than a general portfolio, considering each of their unique pricing and risk characteristics. The model is built with the intention of further humanizing algorithmic portfolio management such that end users are able to interpolate their market perspective into the optimization problem that the computer solves. This research is one of a few to attempt cross-market allocation, but I am writing the model in such a way that these products can be either easily replaceable with other similar products or other different types of products can be added to the portfolio.