**1. Introduction**

Portfolio management is the art and science of modifying the asset allocation of a financial portfolio in response to and/or in anticipation of market conditions and dynamics of financial markets. The modification of the asset allocation is obtained by rebalancing and varying the relative weights of the assets comprising the portfolio on a periodic basis. The asset manager considers two distinct portfolios: the financial portfolio subject to his management technique (referred to here as the experimental portfolio, or Portfolio "A"), and a benchmark (or comparison) portfolio called Portfolio "B". The asset manager composes his experimental portfolio, also referred to as the benchmark-based portfolio, following, generally, two different types of strategies: active and passive (indexed) strategy. In this work, we analyze a fundamental aspect of portfolio management: the active asset allocation. The objective of this writing is to illustrate a new asset allocation technique to compose an experimental portfolio, which uses the Proportional, Integral, Derivative (PID) controller aiming to overcome a benchmarked portfolio. Therefore, the two portfolios taken into consideration are the experimental portfolio subject to the PID controlling methodology and a buy-and-hold diversified portfolio as the benchmark portfolio. The technique consists in managing portfolio asset-allocation revisions through PID control, a tool that is highly utilized and implemented in the engineering, industrial processing units and in production plants. The goal is to achieve a good portfolio performance trying to control volatility; in other words, the goal is to obtain good performance of risk adjusted returns. Thus, in finance, financial market assets forming a portfolio or a market benchmark represent the process plant controlled by the PID controller.

A brief literature review covering the comparison between strategic and tactical asset allocation introduces the topic, followed by some examples of tactical asset allocation techniques. Subsequently, this article illustrates how the PID controller functions. Then, it exemplifies the new asset allocation technique, functioning, and methodology. This work shows how a portfolio managed by this new technique attains fine results of risk adjusted returns compared with a benchmark.

An Innovative Systematic Approach to Financial Portfolio Management via PID Control 233

risk/return level. On the contrary, an active strategy aims to reach an active return compared to the benchmark. The active manager can select different asset classes relative to the benchmark, or different weights. In this case, it is the manager's responsibility to construct the portfolio based on his expectations. In literature, a vivid debate about the superiority of passive vs. active strategies and vice versa, comes forwards. The issue starts with the Efficient Market Hypothesis (Fama, 1965, 1970). This theory assumes that under strong efficient information conditions, it is not possible to have mispriced securities; all prices in the market are fair and balanced; therefore, it is impossible to outperform the market by using active strategies (Samuelson, 1974). Another important factor to consider is the transaction costs (Sharpe, 1991). In fact, even if active and passive strategies are able to achieve the same returns (market returns), the first strategy has unavoidably a diminished total performance, since transaction costs and research costs worsen the outcome. Normally, many active managers manage portfolios formed by index asset classes and liquidity; hence, outperformance compared to the benchmark results. When the market makes a severe downtrend, active portfolios achieve a better performance than the market thanks to the liquidity portion of the portfolios. Not all authors concur in the use and benefits of active strategies. Some authors (Gruber, 1996; Carhart, 1997) state that the active strategies' outperformance has no persistence and exhibits random behavior. Other authors confirm that active strategies produce an

In order to implement an active strategy, asset managers can apply different tactical asset allocation methods. Each of these active strategies aims to take opportunities when markets are non-aligned (Anson, 2004). Tactical asset allocation can be defined as "active strategies which seek to enhance performance by opportunistically shifting the asset mix of a portfolio in response to changing patterns of reward available in capital market" (Arnott & Fabozzi, 1988). Tactical asset allocation establishes the variations in the asset weights in a portfolio. The rebalancing is performed at different time intervals: on a monthly basis, quarterly or annually. Tactical asset allocation methodologies can be divided into two macro categories: dynamic asset allocation and pure tactical asset allocation (Sampagnaro, 2006). Dynamic asset allocation consists in a series of modifications following a set of precise rules (algorithms). The manager implements such rules such that the portfolio weight rebalancing allows the manager to achieve a predetermined target: to regain alignment to the strategic asset allocation weights, or

Pure strategies of tactical asset allocation, on the other hand, include all those methodologies in which the manager aims to maximize the absolute return of the portfolio or the relative return of the portfolio compared to a benchmark. The manager could change the portfolio composition by removing securities and adding others, selecting those securities that present the best expected future returns. The manager could also modify the weights of the current securities producing a distance from the original strategic allocation weight determination. In literature, an extensive variation of methodologies to take advantage of financial markets is available. Some authors (MacBeth & Emanuel, 1993) suggest to use dividend yield price/earning ratio and price/book ratio to estimate market overvaluation or undervaluation. Others use the spreads between the earning/price ratio of the S&P 500 index and interest rates (Shen, 2003), or present the use of Beta drivers to decide the exposure to the financial market and Alpha drivers to underweight or overweight relative to the benchmark (Anson, 2004). As a final point, a research paper (Gandolfi et al., 2007) pioneers an innovative tactical asset allocation technique. The novelty embedded in this model consists in the application of the well-known PID feedback controlling mechanism,

effective investment methodology (Gold, 2004).

to apply portfolio protection strategies (portfolio insurance).
