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Thirty Fifth International Conference on Information Systems, Auckland 2014 1

A Formal Model for Investment Strategies to

Enable Automated Stock Portfolio

Management

Completed Research Paper

Jörg Gottschlich

Technische Universität Darmstadt

Hochschulstraße 1

64289 Darmstadt, Germany

gottschlich@emarkets.tu-darmstadt.de

Nikolas Forst

Technische Universität Darmstadt

Hochschulstraße 1

64289 Darmstadt, Germany

nikolas.forst.privat@dmsfactory.com

Oliver Hinz

Technische Universität Darmstadt

Hochschulstraße 1

64289 Darmstadt, Germany

hinz@wi.tu-darmstadt.de

Abstract

In this paper, we develop a formal model to specify a stock investment strategy. Based

on an extensive review of investment literature, we identify determinants for portfolio

performance – such as risk attitude, rebalancing interval or number of portfolio

positions – and formalize them as model components. With this model, we aim to bridge

the gap between pure decision support and algorithmic trading systems by enabling the

implementation of investment approaches into an executable specification which forms

the foundation of an automated portfolio management system. Such a system helps

researchers and practitioners to specify, test, compare and execute investment

approaches with strong automation support. To ensure the technical applicability of our

model, we implement a prototype and use it to show the effectiveness of the model

components on portfolio performance by running several investment scenarios.

Keywords: Investment Decision Support, Investment Strategy, Stock investment,

Portfolio Management, Investment Strategy Model

Introduction

IT increasingly dominates international financial markets and stock exchanges. While stock trading

transactions have taken place via electronic networks for quite some time, recent developments show an

increasing automation of the decision making processes when it comes to stock investments. The

advantages are obvious: machines are able to conduct large-scale analyses 24/7 and neither ask for

commissions nor do they have hidden agendas. Once an investment strategy is defined, they conduct it

rigorously, which might sometimes lead to undesired results such as the Flash Crash on May 6, 2010

(Patterson 2012). But compared to human investors, machines are immune against the influence of

emotions which have shown to spoil the objective judgment of humans (Lucey and Dowling 2005).

However, the human investor is still needed to identify investment opportunities and define strategies to

exploit those opportunities. It seems reasonable to combine the strengths of both actors: use the human

General IS Topics

2 Thirty Fifth International Conference on Information Systems, Auckland 2014

creativity and experience to identify and define investment strategies and then let a machine execute this

strategy automatically to avoid human emotions conflicting with rational strategic decisions. Not

surprisingly, research suggests a range of system designs to support investment decisions (see the

following section for an overview). However, we did not find a flexible and comprehensive framework to

specify an abstract investment strategy in a form machines can understand and execute. Such a generic

model serves researchers as well as practitioners as a conceptual foundation for portfolio management

systems. For researchers, an implementation of the model helps to build a laboratory environment to

analyze investment strategy patterns and test new approaches for stock investment analysis (e.g. using

indicators from Twitter or News analyses). By allowing batch runs on historic stock data with different

parameter settings, researchers can estimate parameter effects on portfolio performance by conducting

sensitivity analysis. For practitioners, the model allows a precise specification of an investment idea

including back-testing and provides strong support to automate portfolio management.

In this paper, we develop a formal model to specify a stock investment strategy. Based on an extensive

review of investment literature, we identify determinants for portfolio performance and describe them

formally to fit in our model. We build the model with the intention to enable the implementation of an

automated portfolio management system, i.e. a system that is able to receive a formal strategic description

and act upon it autonomously for a specified period of time (either a simulation on historic data or a real-

time application with current stock market data). The challenge is to find a way of specification which is

universal and flexible enough to cover the broad range of possible approaches for investment strategies,

but yet formal enough to be executed by a machine. To ensure a maximum flexibility, we integrate a

generic stock ranking mechanism (cf. Gottschlich and Hinz 2014 and section below) based on user-

defined metrics derived from stock analysis (e.g. momentum or volatility). Such a metric or a combination

of several metrics is used as a score to bring the stocks of the investment universe in an order of

preference. Hence, we are able to include a flexible way to express for any investment strategy what makes

a stock more preferable over another form the investor’s point of view. We ensure that our model can be

implemented in software by implementing our model specification as a prototype system and use the

results to show the effectiveness of the model components.

Previous approaches focus on specific aspects of investment decision making, e.g. security price analyses

or News effects, but an overarching framework to integrate those techniques in a flexible way and apply

them for automated portfolio management is not yet available. Application scenarios for such a model are

plentiful though: Investors can simulate and test strategic approaches to stock market investment based

on a variety of indicators on historic data. Once they find a working strategy, they can enable automatic

strategy execution for future transactions within the parameters specified by the investment strategy. Our

approach targets at the gap between professional algo- or high-frequency trading of large institutions and

manual stock selection of private investors. The main intention is to make the analytical capabilities (and

to a less extent the speed advantages) of information systems accessible for stock market investment

decisions in a flexible and agile way to provide a laboratory environment and decision support system for

investors (cf. Gottschlich and Hinz 2014). This paper introduces the model as a “language” to express the

reasoning and restrictions of an investment strategy, but does not aim at finding optimal parameter

settings in terms of portfolio performance. In fact, as we designed the model to be generic for a large

diversity of investment approaches, this would result in the search for an optimal investment approach to

stock markets – though desirable, this exceeds the scope of this paper.

The remainder of the paper is organized as follows: the upcoming section provides an overview of

previous works in the area of investment decision support. Subsequently, we introduce our methodology.

The section “Model Development” introduces all model components based on an extensive body of

investment literature and closes with a formal specification of our model. The extensive evaluation of the

model functionality based on six scenarios follows in the “Model Evaluation” section. We conclude our

work with the final section showing venues for further improvement of this approach.

Investment Decision Support

The majority of previous research on investment decision support strives to provide better insights to

investors by improved information support. Commonly used are methods to model stock price

development utilizing optimization or machine-learning approaches. Specifically, artificial neural

networks show broad coverage in investment decision support literature, often in combination with other

Formal Model for Investment Strategies

Thirty Fifth International Conference on Information Systems, Auckland 2014 3

approaches. Tsaih et al. (1998) combine a neural network approach with a static rule base to predict the

direction of daily price changes in the S&P 500 stock index futures which outperforms a passive buy-and-

hold strategy (Tsaih et al. 1998). Chou et al. (1996) follow a similar approach for the Taiwanese market

(Chou et al. 1996). Liu and Lee (1997) propose an Excel-based tool for technical analysis (Liu and Lee

1997). Kuo et al. (2001) show that they reach a higher prediction accuracy of stock development when

including qualitative factors (e.g. political effect) in addition to quantitative data (Kuo et al. 2001).

More interactive forms of decision support have appeared, e.g. systems providing a laboratory-like

environment for investors to conduct standard as well as customized analyses. Dong et al. (2004) suggest

a framework for a web based DSS which implements a comprehensive approach including support for

rebalancing an investor’s portfolio according to his risk/return profile. They integrated On-Line Analytical

Processing (OLAP) tools for customized multidimensional analyses (Dong et al. 2004). Another approach

for interactive investor support provides the possibility of stepwise model generation such that investors

can start with simple models from a toolbox and incrementally add more building blocks to arrive at more

complex prediction models (Cho 2010).

The impact of news on stock prices can lead to distinct market reactions and hence support for their

evaluation has been subject to several works. Mittermayer (2004) suggests a system which processes news

to predict stock price movements taking a three step approach: extract relevant information from news by

text processing techniques, assign them into three categories (good, bad neutral) and then turn those into

trading recommendations (Mittermayer 2004). Schumaker and Chen (2009) use a similar approach of

news analysis applying different linguistic textual representations to identify their value for investment

decisions (Schumaker and Chen 2009). Muntermann (2009) focuses on more actionable support for

private investors and suggests a system design that estimates price effects of ad hoc notifications for

public companies and sends out text messages to mobile phones including predicted effect size and time

window (Muntermann 2009). This helps private investors to decrease disadvantages in speed or

awareness they usually suffer compared to institutional investors.

Other approaches try to exploit collective intelligence for stock investment decisions. Stock

recommendations from stock voting platforms on the Internet have shown to be a valuable source for

investment decisions (Avery et al. 2009; Hill and Ready-Campbell 2011) and can even be superior to the

advice of institutional analysts (Nofer and Hinz 2014). Therefore, Gottschlich and Hinz (2014) suggest a

decision support system which uses the wisdom-of-crowd concept to automatically select stocks from a

German market and transform this selection into a target portfolio based on a formal investment strategy.

While their approach is close to an automated portfolio management system, their specification of a

formal investment strategy is still at an early stage and not extensively rooted in investment literature

inducing a need for further development.

Surprisingly, there is little coverage of algorithmic trading system designs in scientific literature. This

might be explained by the distinct value such designs have to their (commercial) developers, who have

little incentive to spread this valuable knowledge. However, some recent works also shed some light onto

this field (e.g. Kissel 2013; Narang 2009).

Based on these streams of literature, we are not aware of an integrated model to express investment

strategies in a formal way while allowing for generic and hence flexible investment potential

identification. In this paper, we want to address this gap by providing a formal model which an investor

can use to specify an investment strategy in a formal way so it can be processed by an automated portfolio

management system. We strive for a systematic approach of combining decision support of investors (i.e.

providing insight or information) and stock investment execution (i.e. buying and selling selected stocks).

Such a system derives a target portfolio layout by applying the formal investment strategy on specific

stock data and provides simulation of an investment strategy on historic data or trading a strategy on

current data. Our core question is: How can we formally specify investment strategies to enable automatic

strategy execution? This model is supposed to be a major building block for the development of an

automated portfolio management system.

Methodology

We conduct an extensive literature review of investment literature. From literature, we identify factors

that drive portfolio performance which we formalize and integrate into our model. The goal is to create a

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4 Thirty Fifth International Conference on Information Systems, Auckland 2014

universal model which bridges the gap between the domains of investment strategy formulation and the

detailed instruction level a machine needs to process.

To ensure our model is really executable by a machine, we implement a prototype in the validation section

and analyze the effectiveness of each model component using a scenario analysis. Before we begin to

develop the model, we introduce two central terms needed for understanding throughout this paper.

Risk measure

The risk of a portfolio is the probability of missing an expected return. We can split the total risk of a

portfolio into two components: systematic and unsystematic risk (Evans and Archer 1968; Li et al. 2013).

Unsystematic risk evolves from each of the individual positions in the portfolio and is related to the

specific company (e.g. management errors). An investor can reduce this kind of risk by diversifying his

portfolio (Li et al. 2013; Statman 1987). In contrast, systematic risk affects the market as a whole (e.g.

change in interest rates) and is not affected by portfolio diversion.

We model the risk associated with an investment in a certain security as the volatility of its past returns

measured by the standard deviation. This is a common approach in literature (Markowitz 1991; Sharpe

1992) and easy to understand: if we have two securities yielding the same return, the one with the lower

volatility showed a more steady development and hence a more reliable return potential throughout the

holding period.

Profit/Return measure

The profit or return of an investment is the percentage of value increase (or decrease, if negative) within a

specific period. Formally, we measure profit 𝑅! as:

𝑅!=𝑝!

𝑝!

−1∗100!

with 𝑝! = price of stock at end of period t, 𝑝!= price of stock at beginning of period t. Intuitively, we

measure return as the difference of buying and selling price, while disregarding distributed dividends.

Model Development

In this section we are going to introduce the components of our formal investment strategy model based

on an extensive investment literature research to identify factors relevant for the performance of a

portfolio (cf. Table 1). These components serve as a parameter set which jointly describes an investment

strategy in a formal way. One instance tuple of these parameters describes a specific strategy which an

appropriate software implementation can interpret and process. We integrate each of the identified

components into our formal model which we specify subsequently. Figure 1 shows an overview of the

investment process steps that implement such a strategy and the application of the model components in

each step. The process starts with a computation of a ranking metric from stock data which is

subsequently used to rank the stocks of the investment universe considered by the investor. Based on this

order of preference, the system splits the available capital, determining the sizes of each portfolio

position. Finally, the portfolio is rebalanced such that it reflects the new layout defined in the process.

Formal Model for Investment Strategies

Thirty Fifth International Conference on Information Systems, Auckland 2014 5

Figure 1. Overview of Investment Process and Influence of Model Components on Process Steps

Investor’s Risk Tolerance

One of the fundamental parts of an investor’s strategy is the definition of the target risk-return profile.

The relationship between risk and return has been extensively discussed in literature (cf. Guo and

Whitelaw 2006) and there is evidence of a trade-off between risk and return (Ghysels et al. 2005; Guo and

Whitelaw 2006). Intuitively, it makes sense that investors demand a higher potential return to invest in a

stock with a higher risk. Modern Portfolio Theory states that investors strive to create a portfolio that

maximizes returns at a given risk level or to minimize risk at a given return target (Markowitz 1952).

Hence, it is sufficient to define either a target risk or a target return.

We decide to model the risk-return profile as a maximum acceptable risk level and strive to optimize

portfolio return. This is more intuitively to investors and more convenient when it comes to

implementation because we can compute a good estimate of a security’s risk based on past development

(compared to the difficulty of forecasting expected returns precisely). Of course, the risk computed from

the security’s historic development might not be an appropriate predictor for its future risk – but this is a

general problem in investing which we cannot address ex ante with our model.

Technically, the risk level specified with the investment strategy by the investor serves as the target risk

for the portfolio creation/rebalancing step. Based on this restriction, the goal is to maximize the

prospected return. At the current stage, we model the risk tolerance as the amount of volatility (based on

historic figures) an investor is willing to take when a portfolio is created. When using the Markowitz

portfolio optimization (see section Portfolio Optimization (Markowitz)), we use the risk tolerance as

target risk level which forms a restriction for the portfolio optimization algorithm. Doing so, the risk level

of the target portfolio should likely be in the desired range of the investor. Formally, we denote the

investor’s risk tolerance with r.

This modeling of risk as threshold to volatility is a quite technical and simple approach. More

sophisticated methods for risk management have been proposed and enable investors to express the risk

they take more precisely. Specifically, Value-at-Risk (VaR) is a common measure to express risk

associated with an investment (see e.g. (Linsmeier and Pearson 2000) for an introduction). VaR is the

amount of loss which will be exceeded only with a specified probability p within an observation period t.

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6 Thirty Fifth International Conference on Information Systems, Auckland 2014

There are several common methods to determine VaR: The Historical, the Delta-Normal and the Monte

Carlo Approach (for details see Linsmeier and Pearson 2000). They have in common, that they apply a

distribution of profits/losses of an investment to determine an amount of loss that is only exceeded with a

defined probability, usually 5% or less. For example, if we look at the historic distribution returns for an

investment within the period t, the amount at the 5% quantile is what an investor would lose if the return

would be as bad as it has only been in 5% of historic cases. The rationale is that under “normal

circumstances”, i.e. within the 95%, the loss will be less than the VaR and hence within that confidence,

risk is under control. The definition of p demarks the border between “normal” and “abnormal”

circumstances and depends on the investment universe and the attitude towards risk of the investor. For

more details on how to use VaR for portfolio management, see e.g. (Krokhmal et al. 2002) or (Ogryczak

and Sliwinski 2010).

To apply VaR for our model as an alternative to the target risk level r, we need to exchange r with the

parameters necessary to determine VaR: p which is the quantile to determine the VaR value from the

profit/loss distribution and t, the holding period. In our model, the holding period is connected to the

rebalancing interval (see section Rebalancing Interval or Frequency) because in between rebalancing

events, no changes in the portfolio will occur. This has to be taken into account when using the model for

implementation.

Regarding the method of VaR calculation, we suggest using historical VaR if the necessary data is

available as it should deliver highest accuracy for the price of computation effort – which is convenient for

our intention to create a machine executable model for investment strategies. Alternatively, Delta-Normal

VaR is a simplified method of computation which should be preferred in a portfolio management system

if performance is an issue.

Rebalancing Interval or Frequency

Markowitz initially specified his model only for the case of one period to set up an optimal portfolio at the

beginning (Elton and Gruber 1997), but disregards actions necessary to contain risk or secure

intermediate returns over the course of time, such as checking and re-adjusting portfolio positions (Cohen

and Pogue 1967). However, in reality, when portfolio positions shrink or grow over time due to their price

development, frequent checking and rebalancing of portfolio positions is important to restore the initial

asset allocation and meet the target profile of the portfolio regarding diversification and risk (cf. Buetow

et al. 2002). Such adjustments lead to sell or buy orders for portfolio positions which cause transaction

cost. Hence, an investor needs to maintain a balance between necessary rebalancing and cost for

adjustment (Woodside-Oriakhi et al. 2013).

There are two basic approaches to portfolio rebalancing: Calendar-/Frequency-Rebalancing and Range-

Rebalancing (cf. Buetow et al. 2002; Plaxco and Arnott 2002). Using Calendar-Rebalancing, an investor

checks frequently, e.g. every month, quarter or year, the positions of his portfolio and adjusts them

according to the target layout. This is an easy approach which does not depend on any external triggers,

but is also passive towards dramatic changes in market environment as long as they happen in between

rebalancing intervals.

Range-Rebalancing, in contrast, defines thresholds which specify the tolerance of an investor towards

changes in position size. For example, a tolerance of 5% allows position sizes to deviate up to 5% from the

initial asset allocation (up or down) before a rebalancing of the portfolio is triggered (Buetow et al. 2002).

This allows investors to react immediately on possibly serious changes in portfolio positions and thus

limit losses close to the tolerance interval. However, in reality, this approach needs support by suitable

automatic portfolio surveillance to enable timely reaction.

Plaxco and Arnott (2002) show how important rebalancing is to maintain a defined risk profile: starting

from a portfolio split of 50% in equities and 50% in bonds in 1950 and following a drifting mix strategy

(i.e. re-investing any dividends in equities and interest in bonds), the portfolio would end up at a split of

98% in equities and 2% in bonds over the course of 50 years – resulting in an obviously different risk

profile (Plaxco and Arnott 2002). Buetow et al. (2002) tested a combined approach of Calendar- and

Range-Rebalancing. They defined a threshold for position size deviation and checked this threshold

frequently after a defined time period. They found that especially when markets are turbulent, frequent

Formal Model for Investment Strategies

Thirty Fifth International Conference on Information Systems, Auckland 2014 7

rebalancing is profitable (Buetow et al. 2002). In addition, in most cases range-based rebalancing had

positive effects on portfolio performance over the last five decades (cf. Plaxco and Arnott 2002).

Thus, rebalancing is important to maintain the intended risk profile of an investor over time. We

introduce both Calendar- and Range-Rebalancing into our model and denote the rebalancing frequency

with bf and the threshold for deviations of portfolio size in % with bt.

Number of Portfolio Positions

The number of positions in a portfolio is another determinant of portfolio diversification. Statman (1987)

found that a portfolio’s risk – measured as the standard deviation of returns – drops with every additional

random stock that is added (Statman 1987). Elton and Gruber (1977) found that that 51% of a portfolio’s

standard deviation can be eliminated by increasing the number of positions from 1 to 10. Additional 10

positions only eliminate another 5%. Figure 2 shows the decline of standard deviation (risk) with an

increasing amount of stocks in the portfolio based on a correlation between stocks of 0.08 (as measured

by Campbell et al. (2001)). It confirms that the major part of standard deviation reduction can be

achieved with 10-20 stocks. Statman (1987) recommends 30-40 different positions.

Figure 2. Expected Standard Deviation with Portfolio

Diversification (all stocks have equal weight). The correlation

between the returns of two stocks is 0.08, and the standard

deviation of any stock is 1.0. (Statman 2004)

But an increasing number of portfolio positions increases the average transaction cost per position as well

(Konno and Yamamoto 2003). Hence, to reach at the optimal number of portfolio positions, an investor

should add stocks as long as the marginal transaction cost is lower than the marginal benefit, i.e. the

reduction in risk by diversification (cf. Evans and Archer 1968; Statman 1987). This relationship has been

subject to an extensive body of research. Evans and Archer (1968) found that adding more than 10 stocks

to a portfolio cannot be economically justified (Evans and Archer 1968). In 2004, Statman revised this

analyses and found based on current data that a portfolio can contain up to 300 positions before marginal

cost outweigh marginal benefit (Statman 2004). Shawky and Smith (2005) analyzed U.S. domestic funds

and found they hold a number of 40 to 120 positions and a positive correlation between fund size and

number of positions (Shawky and Smith 2005).

Literature shows that the recommended number of positions increases during the last decades. Campbell

et al. (2001) show that an investor needed 50 positions during 1986-1997 to reach an equal portfolio

standard deviation than one could achieve in 1963-1985 with 20 positions. One reason is that the

standard deviation between stocks dropped from 0.15 in 1984 to 0.08 in 1997 (Statman 2004). In

addition, by the extended use of information technology financial markets became more efficient and

hence transaction cost could be decreased (Hendershott et al. 2011).

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8 Thirty Fifth International Conference on Information Systems, Auckland 2014

Obviously, spreading stock investments over industries is specifically important for diversification. But

nevertheless, risk reduction is actually driven to a larger extent by the number of positions than by

diversification over industries (e.g. Domian et al. 2007; Statman 2004).

Considering this state of research, we include a range for the number of portfolio positions into our

model. Thus, investors are able to express their view on the number of portfolio positions which is an

integral part of an investment approach and hence should be included in an investment strategy. We

denote the minimum number of portfolio positions with n1 and the maximum number with n2.

Stock Ranking Mechanism

At the heart of an investment strategy, and often even considered identical, is the decision which stocks to

choose for a portfolio. When it comes to stock selection, there is a huge variety of approaches derived from

different investment philosophies like fundamental investment, technical analysis and behavioral finance.

The question is: How can we integrate flexible support for such diverse approaches into our model while

preserving its formal character to enable automatic execution of investment strategies? We embrace an

approach suggested in Gottschlich & Hinz (2014), using a scoring mechanism to rank the stocks in the

investment universe by preference. By incorporating the score, or metric, in the investment strategy

specification, we include the knowledge or decision rule which stocks are preferable over others from the

investor’s viewpoint. Depending on the investor’s view of the world, this could be a technical (e.g.

momentum of previous week or moving average for last 200 days) or fundamental (e.g. price/earnings

ratio) indicator or any other metric for which data can be provided. In fact, it is a function that states

which stock is preferable over another based on selected criteria. Combination of metrics, e.g. by building

a weighted sum of several scores, allows for more complex ranking mechanisms. Investors can create a

library as a directed graph of metrics which they can employ in their investment strategies. This graph of

metrics represents the investor’s knowledge and analytical capability for stock selection.

A system implementing our model would compute the score(s) when a portfolio layout needs to be

determined (e.g. at a rebalancing event) and rank all stocks according to their score (cf. Figure 1). For

example, a possible (simple) metric would be the price/earnings ratio. The system would then compute

this metric for every stock at a specific day (when a rebalancing occurs) and sort all stocks by this value

such that stocks with low price/earnings ratios are ranked better than those with higher ratios (assuming

a long strategy)1 and hence preferred for portfolio selection. Ranking can also comprise filtering, i.e.

stocks which should not be taken into account receive prohibitive scores. In the example above, stocks

with price/earnings ratios of e.g. above 50 might be excluded.

By introducing a metric for stock order preference in our model, we can still provide an abstract formal

model description, but allow for flexible specification of stock preference in an application scenario. For

an application example, see the Validation section. We denote the stock preference score in our model

with s.

Distribution of Capital

To arrive at a final portfolio layout from a list of ranked stocks, we need to decide how to split the

available capital among those stocks. How many stocks starting at the top of the list should be considered

and which amount of money should be distributed to each of them? While the first part of the question

can be answered with the help of the model components n1 and n2, specifying the desired range of

portfolio positions, the question of how the capital should be split among selected stocks forms another

dimension of investment decision.

Naïve Diversification (1/N)

The easiest way to split a certain amount of capital to N selected stocks is an equal distribution. With this

method, at every rebalancing event, each portfolio position is adjusted to the same share of total capital C

1 This is a simplified example for illustration purposes which does not necessarily implement a very successful

strategy.

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Thirty Fifth International Conference on Information Systems, Auckland 2014 9

(which is C/N) (cf. DeMiguel et al. 2007; Tu and Zhou 2011). Advantages of this approach are an easy

implementation and independence from biases potentially caused by estimation or optimization

techniques for returns or weights. Also winning and losing positions can be identified at a glance.

Practitioners do use such easy methods of capital spread for their investments and they are able to

compete with more sophisticated methods (DeMiguel et al. 2007).

Portfolio Optimization (Markowitz)

Given a set of stocks the portfolio selection approach as proposed by Markowitz (1952) determines, based

on their historic development, weights for each of the stocks to derive an efficient portfolio. Efficient

means that there is no other stock selection that beats the given solution in terms of risk/return ratio.

Technically, the approach minimizes variance (= risk) for a given return level or maximizes return for a

given risk level. The approach received criticism, partly due to the fact that it maximizes errors in the

estimation of expected return or stock correlation. Those estimates are necessary for the method to

determine position weights (Chopra and Ziemba 1993). In addition, portfolios built using Markowitz’

optimization approach did not necessarily outperform other methods of portfolio construction (cf. Tu and

Zhou 2011). But nevertheless, it is a reasonable approach to determine an optimal portfolio regarding

risk/return trade-off. For our purposes, having an already pre-ranked list of stocks and trying to

determine how much capital should go into which position, the method is a convenient way to determine

optimal weights based on risk/return figures.

Apart from the two capital distribution methods mentioned, investors can specify their own methods, too.

As we have a ranked list of stocks, another reasonable distribution method would be e.g. a diminishing

distribution, assigning most weight to the best-ranked stock and reducing the share while descending the

list. This enables investors to reap the benefits of the ranking to a greater extent than with naïve

diversification. It is obvious that the decision on how to distribute the available capital on the stocks

selected has influence on the portfolio performance outcome and should be included in our investment

strategy model.

We model the capital distribution method as a function that receives the ranked list of stocks and returns

a number of weights for those stocks. For naïve diversification, the function could simply take the top 10

stocks and assign a weight of 10% to each of them. The optimization approach after Markowitz is more

complex and involves running an optimization algorithm. Other approaches are possible, by

implementing an appropriate function and including it in the investment strategy model. We denote such

a function of capital distribution with d.

Model specification

Based on an extensive body of investment literature, we identified several components (cf. Table 1) which

affect portfolio performance and hence are determinants for portfolio creation that should be included in

a formal model for investment strategies. Formally, we specify an investment strategy IS as an instance of

the following tuple of model components:

IS = <r, bf, bt, n1, n2, s, d>

Table 1 summarizes the model components. This model provides a way to specify investment strategies in

a way machines can interpret and execute and hence is an important step towards an automated portfolio

management system (e.g. Gottschlich and Hinz 2014). In the upcoming Evaluation section, we implement

the model and show how different values for strategy parameters affect portfolio performance, thereby

showing the effectiveness of the model.

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10 Thirty Fifth International Conference on Information Systems, Auckland 2014

Table 1. Model Components

IS

Investment strategy

r

Investor’s risk tolerance

bf

Rebalancing frequency

bt

Rebalancing threshold

n1

Minimum number of portfolio positions

n2

Maximum number of portfolio positions

s

Stock ranking metric (score)

d

Capital distribution method

Model Evaluation

In this section, we want to show how the model is applied to formulate an investment strategy which can

be executed by a system to yield a target portfolio layout based on the strategy parameters. To show that

our model provides the intended functionality, we introduce a base scenario and a number of test

scenarios which differ in one of the model parameters to isolate the effect of the specific parameter. We

compare the resulting portfolio of each test scenario with the base scenario to observe the results of the

parameter adjustment. The purpose of this evaluation is not to identify the most profitable parameter

settings, but rather show that changes of parameters have an effect on portfolio performance and hence

there inclusion in the model is justified. The search for optimal parameter settings is subject to further

research which finds strong support by an automated laboratory environment based on our formal

strategy model.

Implementation

To evaluate the functionality of our model, we implemented a prototype system to execute an investment

strategy which is specified using our model. The system takes a specified investment strategy and executes

it over a specified time period while tracking the portfolio layout and performance development. In fact,

the system converts the specified investment strategy into a portfolio layout for a specific day. Besides the

portfolio, the system tracks the amount of cash available for a simulation run. We conduct our simulation

with an initial cash value of 100,000 EUR.

We implemented the prototype in JAVA using the Spring Framework and a MySQL database to store

stock quotes, investment strategies and portfolio layouts. To compute the complex Markowitz

calculations, we integrated the statistical software R which is executed and controlled by the system.

We ran all the scenarios in a time period of two years: January 2009 to December 2010. Stock quotes

were closing prices at Frankfurt Stock Exchange. For transaction cost, we used the cost model of a large

German retail broker who charges 4.90 EUR per transaction plus 0.25% of transaction volume; minimum

fee is 9.90 EUR and maximum fee is 59.90 EUR. Transaction costs were aggregated to an external

account and hence had no effect on the available investment capital. Further, we did not consider

payment of dividends or taxes. One scenario run took approximately between 40 and 70 minutes on an

Intel Core 2 Duo with 2.53 GHz and 4 GB RAM.

Scenarios

We defined 6 scenarios for evaluation purposes (see Table 2). The first scenario serves as a base scenario.

The other scenarios each vary one parameter of the model to show the resulting effect on portfolio

performance. By varying only one parameter at a time, we ensure that observed effects were caused by the

specific manipulated parameter. Thus, we can evaluate the effectiveness of the model parameters. We

keep one parameter fixed: stock selection. For stock selection, we use the score from Gottschlich and Hinz

(2014) (GH). This score is based on a collective estimate of a large crowd on a stock voting platform and

Formal Model for Investment Strategies

Thirty Fifth International Conference on Information Systems, Auckland 2014 11

measures the potential price increase or decrease that the crowd assigns to a certain security on a certain

day. That means for a long strategy (which we apply here), we use this score in a descending order to rank

the stocks with the highest potential first (for details cf. Gottschlich and Hinz 2014). We do not change the

stock selection parameter throughout the test run, because it is not our focus to compare stock selection

mechanisms. We could use any other score as well with its respective results on portfolio performance to

evaluate the effects of the other parameters.

For capital distribution, we use the Markowitz portfolio selection theory (PST) approach to arrive at a

portfolio with optimized risk/return profile in two variants: PST(12) uses price history of the last 12

months to compute the variance of a portfolio position, while PST(6) only uses past 6 months. Thus,

PST(12) should be more stable and react slower to changes of volatility in a security’s development, while

PST(6) reacts quicker, but also more volatile.

Table 2: Model Evaluation Scenarios

Scenario

Risk

Tolerance

r

Rebalancing

Frequency

bf

Rebalancing

Threshold

bt

Min. #

Positions

n1

Max. #

Positions

n2

Stock

selection

score

s

Capital

Distri-

bution

d

S0

30%

weekly

0%

0

10

GH

PST(12)

S1

60%

weekly

0%

0

10

GH

PST(12)

S2

30%

monthly

0%

0

10

GH

PST(12)

S3

30%

weekly

10%

0

10

GH

PST(12)

S4

30%

weekly

0%

0

2

GH

PST(12)

S5

30%

weekly

0%

0

10

GH

PST(6)

Results

As an external benchmark for performance comparison, we show the development of the DAX stock index

which captures the 30 largest German companies (based on market capitalization and turnover). Table 3

shows an overview of all scenario portfolio results, while Figure 3 shows a plot of the scenario portfolio

performances over the whole period. At a first glance, we see that the performances of the different

scenarios differ, giving a first indication that the parameters included in the model are indeed

determinants of portfolio performance and hence should be contained in our model. An exception is the

result of Scenario S3 which performs identical to S0. We will discuss this observation in detail in the

subsection of Scenario S3.

Scenario S0 – Base scenario

The base scenario (cf. Table 2) applies a rather conservative risk tolerance of 30% with a weekly

rebalancing frequency. The rebalancing threshold is 0% which means that every deviation from the

position target weights leads to an adjustment of portfolio position size. We specify no required minimum

of portfolio positions, letting the system decide to invest or keep cash when a rebalancing event occurs.

For this test run, we want to maintain a simple portfolio and hence set the maximum number of positions

to 10. In formal terms, S0 can be specified as:

S0 = <0.3, Weekly, 0%, 0, 10, GH, PST(12)>

Looking at the results (Table 3 or Figure 3, respectively), we see that the DAX benchmark develops

positively with a return of approx. 40%, while S0 clearly outperforms the DAX benchmark with a return

General IS Topics

12 Thirty Fifth International Conference on Information Systems, Auckland 2014

after transaction costs (TC) of app. 126%. These are the absolute results, but for our subject, we are more

interested in the relative results between scenarios.

Table 3: Overview on the Model Evaluation Results (rounded)

Initial

Capital

Resulting

Capital

Return Rate

(rounded)

Transaction

Costs (TC)

Result – TC

Return Rate

– TC

(rounded)

Risk

Dax Benchmark

100,000€

140,551.81€

40.44%

n/a

n/a

n/a

13.92%

Base Scenario S0

100,000€

241,836.86€

141.84%

16,103.97€

225,732.89€

125.73%

27.25%

Evaluation Scenario S1

100,000€

300,544.64€

200.54%

17,187.04€

283,357.6€

183.36%

35.74%

Evaluation Scenario S2

100,000€

181,097.76€

81.10%

4,825.14€

176,272.62€

76.27%

18.46%

Evaluation Scenario S3

100,000€

241,836.86€

141.84%

16,103.97€

225,732.89€

125.73%

27.25%

Evaluation Scenario S4

100,000€

207,683.79€

107.68%

7,293.08€

200,390.7€

100.39%

19.30%

Evaluation Scenario S5

100,000€

370,286.18€

270.29%

21,877.22€

348,408.96€

248.41%

33.01%

Scenario S1 – Risk tolerance

In scenario S1, we change the investor’s risk tolerance to 60%. As we expect a higher risk to yield a higher

return (Ghysels et al. 2005), the Scenario S1 should outperform the base scenario. Formally, we specify S1

as:

S1 = <0.6, Weekly, 0%, 0, 10, GH, PST(12)>

From Table 3, we see that the S1 portfolio indeed outperforms the S0 portfolio by almost 60 points while

the risk associated with the portfolio also increased to 35.74%. As we altered no other parameter except

the risk tolerance, we conclude that the increased risk tolerance led indeed to a higher portfolio

performance at the price of a higher risk. These observations confirm the results of (Ghysels et al. 2005;

Guo and Whitelaw 2006) and show the functionality of this parameter in our model.

Formal Model for Investment Strategies

Thirty Fifth International Conference on Information Systems, Auckland 2014 13

Figure 3. Performance of Scenario Portfolios with Transaction Costs Deducted

Scenario S2 – Rebalancing Frequency

In this scenario, we change the rebalancing frequency from a weekly to a monthly portfolio check and

adjustment. Since Buetow et al. (2002) showed that a smaller rebalancing intervals increase returns, we

expect a negative impact of this parameter change compared to the base scenario S0. The full specification

of S2 is:

S2 = <0.3, Monthly, 0%, 0, 10, GH, PST(12)>

Table 3 shows a performance for the S3 portfolio of 81.10% compared to 141.84% of the base scenario S0.

So changing the rebalancing interval alone from weekly to monthly and keeping everything else equal, the

performance drops by app. 60 points. In addition, due to the less frequent rebalancing interval, there are

less trades to be made (123 trades in contrast to 442 trades in the base scenario), resulting in lower

transaction costs, as Figure 4 shows. However, the lower transaction costs cannot compensate the loss in

price development. All in all, these findings show that the rebalancing interval is an important

determinant of portfolio performance and a necessary part of an investment strategy specification.

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14 Thirty Fifth International Conference on Information Systems, Auckland 2014

Scenario S3 – Rebalancing Threshold

The Rebalancing Threshold defines the maximum deviation a portfolio position may show against the

target weights before its size is re-adjusted. Buetow et al. (2002) reported a positive impact by increasing

the Rebalancing Threshold from 0% to 10%. Another positive effect could arrive from lower transaction

costs, as a higher tolerance towards target weight deviation can lead to a lower number of trades and

hence reduce transaction costs. The formal specification of S3 is as follows:

S3 = <0.3, Weekly, 10%, 0, 10, GH, PST(12)>

The results of Scenario S3 are identical to those of the base scenario S0. Why is that? This is due to a

conflict of parameters: the applied metric for stock selection (GH) is very volatile in its recommendations

leading to a very different list for every rebalancing event. So a rebalancing based on this metric is rather

fundamental exchange of portfolio positions. Because the target weights of portfolio positions and the

positions themselves change so much, this parameter is masked by the stock selection metric and shows

no effect in the current test run. Future evaluations of the model should analyze if this parameter is

effective with different evaluation data.

Scenario S4 – Maximum number of portfolio positions

Because the number of portfolio positions affects diversification of a portfolio which is connected to

portfolio performance and risk, we adjust the maximum number of portfolio positions in Scenario S4

from 10 to 2 and evaluate the effect. Due to the lower diversification, we would expect a higher risk

associated with the portfolio. As we decrease portfolio size by a large extent, we also expect transaction

costs to be lower than in the base scenario. Scenario S4 is specified as follows:

S4 = <0.3, Weekly, 0%, 0, 2, GH, PST(12)>

Figure 4. Development of Transaction Costs

Formal Model for Investment Strategies

Thirty Fifth International Conference on Information Systems, Auckland 2014 15

S4 has a return rate before TC of 107.68% compared to 141.84% in the base scenario (cf. Table 3).

Surprisingly, the risk is not increased compared to the base scenario, but instead dropped to a value of

19.30% compared to 27.25% in the base scenario. This is against the expectations from previous literature,

which predict a higher risk with less diversification. We conclude that this is a random effect with our

evaluation data set. However, in accordance with previous research is the drop in performance compared

to the base scenario which comes with the reduction of risk. In this respect, our results are consistent with

literature.

As expected, the transaction costs also drop from 16,104 EUR in the base scenario to 7,293 EUR (cf. Table

3 and Figure 4) – less than half. However, these savings cannot over-compensate the loss caused by lower

diversification.

Scenario S5 – Capital distribution

For the last evaluation scenario S5, we modify the method of capital distribution. In all previous

scenarios, including the base scenario, we took a history window of 12 months to compute the volatility

and correlation metrics for stocks which are needed for the Markowitz portfolio selection. Now we shorten

this window to 6 months. By doing so, the investment behavior of the system should be more responsive

to recent market developments and act more agile on market changes. Formally, we specify S5 as:

S5 = <0.3, Weekly, 0%, 0, 10, GH, PST(6)>

Scenario S5 shows the strongest performance of all portfolios – 270.29% return compared to 141.84% in

the base scenario. Looking at Figure 3, we see that all other scenarios show no trading activity during the

first few months of the evaluation period. The reason is a rather volatile bear market in 2008, which

ended in 2009 and turned into an upwards trend. The scenarios which use the past 12 months to estimate

stock risk, stick longer to the negative evaluation of stocks before the positive developments allow the

system to invest again instead of keeping a 100% cash position. With a 6-month time window for risk

assessment, the positive market development leads to a quicker pick-up of the bull market by Scenario S5

and hence explains its superior performance compared to the other scenarios.

We confirm that the capital distribution mechanism is a crucial part of an investment strategy and even

slight modification can have large impact on portfolio performance. Hence, we are confident that the

capital distribution method should be an integral part of our formal model for investment strategies.

Conclusion

In this paper, we introduced a formal model to specify investment strategies in a generic way. Based on an

extensive review of current investment literature, we identified determinants of stock portfolio

performance and formalized them as components in our model. To the best of our knowledge, no such

universal and integrated approach of formalizing investment strategies existed before. However, this is a

crucial ingredient to bridge the gap between pure decision support systems, which support a human

decision maker who then executes the decision and fully automated trading systems that are closed (and

often secret) systems and do not allow for an interactive exploration of strategies by an investor. In

contrast, our model serves as a language to express investment strategies by investors and still enable

execution to derive a target portfolio layout automatically when implemented in an appropriate portfolio

management system (cf. Gottschlich and Hinz 2014). This fundamental conceptual framework serves both

researchers and practitioners by providing a generic laboratory environment to model and analyze new

investment ideas and test them in a comparable way with strong automation support. By providing a

“language” to describe an investment strategy formally, we also create a precise way to express,

communicate and store investment approaches. Further, a portfolio management system which

implements the model provides generic support for a wide range of investment approaches which are

applicable to automatic portfolio management. Alternatively, such a system provides decision support up

to the derivation of stock orders which can still be controlled by human investors before execution.

General IS Topics

16 Thirty Fifth International Conference on Information Systems, Auckland 2014

While we provide a first version of an integrated investment strategy model, there is still room for

improvement. First, there might be (and certainly are) other factors which affect portfolio performance

which we have not yet addressed with our model. But we are confident that our suggestion in this paper

already covers the most widely accepted and most common components of investment strategies. In

terms of risk modeling, Value-at-Risk as a common approach used by practitioners should be included in

the implementation of the model to make it more applicable for practical use.

Second, the results of our evaluation were not final with respect to the effect of the rebalancing threshold

(Scenario S3) and the effect of restricting the number of portfolio positions (Scenario S4). While the

effects of these parameters are well founded in theory, based on our data set, we were not able to find

support for this theory. Further improvement efforts of the model should include a re-evaluation of these

parameters to see if their presence in the model is justified. A third venue for improvement is the handling

of conflicts between parameters – as we discovered in Scenario S3, when the stock ranking mechanism

made the rebalancing threshold ineffective. The investor could specify a priority of parameters in case of

conflict to overcome this limitation.

But most exciting future uses will probably comprise a massive sensitivity testing of investment strategies

to apply statistical methods on the significance of strategy parameters. By executing a large number of

slightly different parameter settings and analyze their effect on portfolio performance by applying

statistical methods, new levers for successful investment approaches could be identified and evaluated.

This is an exciting outlook for both, practitioners as well as researchers, as our model would provide the

fundamental building block for such a batch testing of investment approaches in a laboratory

environment or for real money investments.

In conclusion, we are confident that our proposition is a valid and valuable approach to enable a formal

specification of a wide range of investment strategy approaches. We showed by our prototypical

implementation that such specified strategies can be executed by an appropriate portfolio management

system and that our model is suitable to narrow the gap between pure decision support systems and

automated trading systems.

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