**2. Strategic and tactical asset allocation**

Asset allocation can be defined as the action of allocating the various components of a financial portfolio in different asset classes according to the investor risk/return profile level. The portfolio construction is an articulated process based on the identification of the optimal asset mix, given a desired time horizon (holding period) and given the investor's risk aversion level. The activity of asset allocation is a 3-phase procedure: analysis of investors' needs, consideration of investor's choices and inclinations, and investor's portfolio performance monitoring. At first, it is necessary to analyze investor's needs in order to understand his/her risk aversion level. The investment subsequent choices depend on the latter analysis, which is not so straightforward and easy to perform. The second phase, illustrated in more detail in the following sections, consists in the actual choice of the asset classes in which to invest, the determination of the relative weights assigned to each asset class and the choice of the securities to be bought and included in the portfolio management process. The third phase consists in the monitoring of the portfolio performance through the utilization of specific indicators enabling the observation of the return and the risk of the managing activity. In this phase, the risk-adjusted return indices (Sharpe Ratio, Sortino Ratio, etc) become important; they specify the return of the portfolio adjusted by the implicit and inherent risk underlying that specific asset management strategy.

As specified herein, the central activity of asset allocation is strictly bound to the investment choices. The portfolio manager first defines the macro asset classes to be considered. The macro asset classes are a set of financial activities or real activities with adequate future potential growth. Upon the definition of such macro asset classes, relative weights shall be determined strategically in order to obtain a diversified portfolio consistent and in line with the return/risk profile of the investor. This asset allocation can be achieved by using quantitative strategies, such as the implementation and utilization of Markowitz's efficient frontier technique (Markowitz, 1952), or qualitative approaches and methodologies based on the individual managers' expectations, experience, and estimates on future market conditions. This primary activity of asset allocation is called strategic asset allocation.

The definition of strategic asset allocation is a component of asset allocation, implemented by the identification of the optimal long-term mix, in compliance with the investor risk/return profile.

A second component of asset allocation is defined as the tactical asset allocation. This is an activity that aims to take, periodically, the most interesting investment opportunities by temporarily and partially deviating from the main strategic portfolio structure.

If in the long term, the adherence to investors' risk profile levels must be maintained; in the short term, the tactical asset allocation manager may deviate from the strategic asset allocation technique aiming to take further advantage from certain market conditions. For example, the tactical asset allocation manager may slightly vary the weights of the various asset classes or the individual securities contained in them, targeting to further increase portfolio returns.

Relative to strategic asset allocation, a fundamental choice to make is the adoption of a particular style of management relative to a benchmark. In defining the strategic asset allocation, the manager must decide which style of management to use relative to a benchmark. In fact, managers differentiate between active and passive strategies by analyzing the portfolio management strategy compared to a benchmark. Passive strategies aim to obtain benchmark returns, structuring a portfolio analogous to the benchmark composition. The asset manager chooses the same asset classes and the same relative or absolute weights as the benchmark. In this case, the risk/return profile level is consistent with the benchmark

Asset allocation can be defined as the action of allocating the various components of a financial portfolio in different asset classes according to the investor risk/return profile level. The portfolio construction is an articulated process based on the identification of the optimal asset mix, given a desired time horizon (holding period) and given the investor's risk aversion level. The activity of asset allocation is a 3-phase procedure: analysis of investors' needs, consideration of investor's choices and inclinations, and investor's portfolio performance monitoring. At first, it is necessary to analyze investor's needs in order to understand his/her risk aversion level. The investment subsequent choices depend on the latter analysis, which is not so straightforward and easy to perform. The second phase, illustrated in more detail in the following sections, consists in the actual choice of the asset classes in which to invest, the determination of the relative weights assigned to each asset class and the choice of the securities to be bought and included in the portfolio management process. The third phase consists in the monitoring of the portfolio performance through the utilization of specific indicators enabling the observation of the return and the risk of the managing activity. In this phase, the risk-adjusted return indices (Sharpe Ratio, Sortino Ratio, etc) become important; they specify the return of the portfolio adjusted by the implicit

As specified herein, the central activity of asset allocation is strictly bound to the investment choices. The portfolio manager first defines the macro asset classes to be considered. The macro asset classes are a set of financial activities or real activities with adequate future potential growth. Upon the definition of such macro asset classes, relative weights shall be determined strategically in order to obtain a diversified portfolio consistent and in line with the return/risk profile of the investor. This asset allocation can be achieved by using quantitative strategies, such as the implementation and utilization of Markowitz's efficient frontier technique (Markowitz, 1952), or qualitative approaches and methodologies based on the individual managers' expectations, experience, and estimates on future market conditions. This primary activity of asset allocation is called strategic asset allocation.

The definition of strategic asset allocation is a component of asset allocation, implemented by the identification of the optimal long-term mix, in compliance with the investor

A second component of asset allocation is defined as the tactical asset allocation. This is an activity that aims to take, periodically, the most interesting investment opportunities by

If in the long term, the adherence to investors' risk profile levels must be maintained; in the short term, the tactical asset allocation manager may deviate from the strategic asset allocation technique aiming to take further advantage from certain market conditions. For example, the tactical asset allocation manager may slightly vary the weights of the various asset classes or the individual securities contained in them, targeting to further increase portfolio returns. Relative to strategic asset allocation, a fundamental choice to make is the adoption of a particular style of management relative to a benchmark. In defining the strategic asset allocation, the manager must decide which style of management to use relative to a benchmark. In fact, managers differentiate between active and passive strategies by analyzing the portfolio management strategy compared to a benchmark. Passive strategies aim to obtain benchmark returns, structuring a portfolio analogous to the benchmark composition. The asset manager chooses the same asset classes and the same relative or absolute weights as the benchmark. In this case, the risk/return profile level is consistent with the benchmark

temporarily and partially deviating from the main strategic portfolio structure.

and inherent risk underlying that specific asset management strategy.

**2. Strategic and tactical asset allocation** 

risk/return profile.

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 effective investment methodology (Gold, 2004).

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 to apply portfolio protection strategies (portfolio insurance).

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,

An Innovative Systematic Approach to Financial Portfolio Management via PID Control 235

In this present work, the following recurrence relation, obtained by discrete time formulation and simple-lag implementation of the integral part (Gandolfi et al., 2007) yields:

<sup>n</sup> p n i n n-1 n-1 d n n-1

(2)

u = + ( - )+ + ( - ) ke k e u u k e e

Fig. 1. PID control block diagram - This figure presents dynamics and processing of the error,

This section presents an original method and system for allocating numerous assets in portfolios, via tactical asset allocation in order to achieve better return and long-term target stability (volatility control) over a desired time horizon. In particular, the present work illustrates a method and system for asset allocation of the 20 securities having each one, its own level of risk and return. The methodology consists in stabilizing the portfolio return . hence the decreasing of portfolio volatility based on the PID feedback control. By applying our strategy to a financial portfolio, financial market assets represent the process plant, controlled by PID controlling action. The assets mix of the portfolio determines the total portfolio return. The action of rebalancing the portfolio alters its return. In various aspects, this work offers methods and systems as an innovative approach to active strategy portfolio management. It is worth noting that the rebalancing of the experimental portfolio (Portfolio "A") is not dictated by a forecast analysis of the various prices of the assets belonging to the portfolio. There is no use of a vector of expected returns and there is no need of determining a variance-covariance matrix. The rebalancing is rather driven by an asset selection

Set-Point and controlled variable while subjected to the PID control action.

**4. Mechanisms of action of the new asset allocation technique** 

Set-point = Desired value. Error = (Output – Set-Point).

n n-1 p i d n n-1

A block diagram of the PID controller follow:

where:

u =output at time n u =output at time n-1 k =Proportional Constant k =Integral Constant k =Derivative Constant e =error at time n e =error at time n-1

used in industrial plant production and engineering, to tactical financial portfolio asset allocation. The goal of their model was to attain long-term performance steadiness over time by controlling the risk adjusted return variable of portfolios. The main attribute to perceive was the achieved constancy and consistency of the Sharpe Ratio of the experimental portfolio (i.e. the portfolio managed by the PID methodology) in comparison to the benchmark. In the present work, the authors build up a new application based on this novel strategy. The target here is to seek a portfolio (Portfolio "A") capable of enhanced long-term risk adjusted performance and risk stability than the Buy-and-Hold portfolio (Portfolio "B").
