FPGA Acceleration of Mean Variance Framework for Optimal Asset Allocation

      Asset allocation is the core part of portfolio management. With asset allocation, an investor distributes his wealth across different asset classes which include different securities such as bonds, equities, investment funds, derivatives, etc. in a given market to form a portfolio. Because each asset class responds differently to shifts in financial markets, an investor can minimize the risk of loss and maximize the return of his portfolio by diversifying his assets.
      Increasing the number of diversified assets in a financial portfolio significantly improves the optimal allocation of different assets giving better investment opportunities. The goal of the portfolio manager in a financial institution is to provide the asset allocation with the greatest return for some level of risk for investors.

Adding new assets to a portfolio shifts the frontier to the upper left which gives better return opportunities with less risk compared to the lower number of assets portfolios.

      The most popular approximation approach for optimal asset allocation is Markowitz's mean variance framework. In this framework, the investor tries to maximize the portfolio's expected return for a given risk and investment constraints. Mean variance framework is a two-step approach: the first step of the mean variance optimization selects efficient allocations for different risks among all the possible combinations of assets to form the efficient frontier; and the second step searches for the best allocation among all efficient allocations found in the first step.

The required steps for optimal asset allocation are shown in (a), (b) and (c). After the required inputs to the mean variance are generated in (a), computation of the efficient frontier and determination of the highest utility portfolio are shown in (b) and (c) respectively. This figure also presents the inputs and outputs provided to the user.

      However, a large number of assets require a significant amount of computation that only high performance computing can currently provide. Because of the highly parallel nature of Markowitz' mean variance framework an FPGA implementation of the framework can also provide the performance necessary to compute the optimal asset allocation with a large number of assets.

      In this work, we present:
1) A detailed description of the mean variance framework for optimal asset allocation, incorporating investor objectives and satisfaction indices used in practical implementations;

The procedure to generate required inputs is described. The numbers 1-5 refers to these computation steps which are explained in paper subsections in more detail.

2) Identification of bottlenecks for the mean variance framework which can be adapted to work in hardware;

We run two different test while holding all but one variable constant. We determined that generation of the required input does not consume significant amount of time. On the other hand, step 1 and 2 of the mean variance framework consumes significant amount of time.

3) Design of the proposed hardware for the FPGA implementation of the mean variance framework;

Parallel parameterizable hardware architecture for the mean variance framework step 2. The Monte-Carlo block, Utility Calculation Block, and Satisfaction Function Calculator IP core can be easily parallelized.

4) A study of potential performance improvements through simulations of the hardware architectures and a comparison between a software implementation running on two 2.4 Ghz Pentium-4 CPUs, and an FPGA architecture, showing potential performance ratios of 9.6 × and 221 × for different steps.

Possible speed-ups for "generation of the required inputs - phase 5" and "mean variance framework Step 2".

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