Here you will find our research papers which we make publicly available in the spirit of openness and transparency. Many of these papers are motivated by our internal research & development and serve as helpful reference material for specific capabilities on the D3X platform. You will also find articles here that raise interesting or unexpected findings in the realm of portfolio optimization, risk-return attribution, and other investment management topics.

QuantHub Custom Factor Attribution

Author: Scott Shaffer, PhD, CFA

This document describes the mathematical formulation of the custom factor attribution in the QuantHub application. We begin in Section 2 by reviewing the mathematics of factor-replicating portfolios for linearly independent factors. Section 3 introduces the additional machinery required to compute factor returns and replicating portfolios when the factor model contains linearly dependent factors. This is a common feature of multi-country models, where country and industry factors are both linearly dependent in the presence of a global market factor. Section 4 discusses computational issues that must be addressed for efficient factor risk and return estimation. In Section 5, we describe three options for computing returns and replicating portfolios for user-defined custom factors in the presence of a previously-estimated reference risk model (typically a third-party commercial model). We conclude in Section 7 by describing the custom risk attribution. Readers seeking a quick overview of the available functionality may start with Section 5 and use Sections 2–4 as reference material.

QuantHub Multi-Period Return Attribution

Author: Scott Shaffer, PhD, CFA

This document describes the multi-period factor return attribution functionality provided on the QuantHub platform. In a multi-period attribution, a sequence of daily attributions are aggregated into a single composite that decomposes the total portfolio return into individual factor contributions for the entire time period. Unfortunately, the geometric nature of return compounding prevents us from defining a unique multi-period aggregation. The purpose of this document is to describe two methods for linking single-period attribution contributions into the multi-period aggregate.

QuantHub Multiple-Account Optimization

Author: Scott Shaffer, PhD, CFA

This document describes the optimization of multiple accounts on the QuantHub platform. We consider a scenario in which separate client accounts are managed using the same quantitative investment model or strategy. The trade lists will be correlated, and as a result, the accounts will compete for liquidity and short availability. The optimization must allocate these resources across accounts in a manner that is fair to all clients and satisfies all regulatory requirements.

QuantHub Index Tracking With Cash Reserves

Author: Scott Shaffer, PhD, CFA

Investment managers running index-tracking portfolios must often maintain a small cash balance to meet client redemptions or to ensure that incomplete or imbalanced trade executions do not incur an overdraft. This document derives an analytical solution for the optimal index tracking portfolio given a required cash reserve but no other constraints or transaction costs. This ideal case may serve as a reference for more complex optimizations that include asset holding bounds, transaction costs, and trading constraints.

The Surprisingly Large Contribution of Specific Risk...

Author: Scott Shaffer, PhD, CFA

This document presents a simple framework to explore the relative contributions of factor and specific risk in custom attribution reports. It is motivated by the unexpected observation that asset-specific risk often contributes more than custom factor risk even for portfolios with large exposures to the custom factors and near zero exposures to factors in the parent risk model.

QuantHub "L1" Risk for Portfolio Optimization

Author: Scott Shaffer, PhD, CFA

This document introduces a new risk metric that we call "L1" risk for use in the proprietary D3X portfolio optimizer. It has two main advantages over traditional mean/variance optimization. The first advantage is conceptual: the L1 risk measure is formulated around the absolute values of active asset weights and factor exposures, rather than the square of those values that occur in the standard variance formulation. Absolute values are more robust to outliers than squared values, and we expect the L1 risk formulation to be more robust than the traditional variance formulation in a way analogous to the robustness of median-absolute deviation regression compared to traditional least-squares regression. The second advantage is computational: The L1 risk formulation is strictly linear and can be optimized with high-performance open-source linear programming solvers without the need to license commercial third-party convex solvers.


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