Journal of Robotics, Networking and Artificial Life, Vol. 2, No. 4 (March 2016), 272-275

Momentum and Its Implications in Corporate Management
Tsutomu Ito*, Katsuhiko Takahashi, Katsumi Morikawa, Takao Ito

Graduate School of Engineering, Hiroshima University, 1-4-1 Kagamiyama
Higashi-Hiroshima, Hiroshima 739-8527, JapanRajiv Mehta
School of Management, New Jersey Institute of Technology University Height
Newark, NJ 07102-1982 USA
Sakamoto Makoto, Satoshi Ikeda

Faculty of Engineering University of Miyazaki 1-1, Gakuenkibanadai-nishiMiyazaki, 889-2192 JAPAN*

Corresponding author, E-mail: fw.eldorado.500cuin@gmail.com
Tel: +81-82-424-5594, Fax: +81-82-424-5594

Abstract
The current manuscript reviews the literature associated with corporate strategy, and proposes a new approach ofacceleration to measure momentum based on limited cycle theory. Thus, this research manuscript makes acontribution to extant thought by: 1) Defining momentum, 2) Discussing the nature of the relationship between
momentum to its external environment, and company scale, 3) Ascertaining the momentum period, and 4)
Proposing a four-cell model composed of momentum and company scale for judging a firm’s position.
Additionally, the relationship between momentum and the impact of 2007-2008 financial crises is addressed. Basedon the findings, the study limitations are identified and directions for further research are suggested.
Keywords: Momentum, velocity, limit cycle theory, four cell model, strategy

1. Introduction
The basis of corporate strategy stems from two
seminal books: The Art of War, and On War written by
Sun Tzu in the late sixth century BC and Carl vonClausewitz in 1827, respectively. In comparing thesetwo books, especially the Art of War, with extant
strategic theories, discussions on momentum, animportant concept, have been sparse, although in thecontext of current management strategies, the pivotal
nature of momentum recently has been operationalized
and discussed in research on marketing, and finance.
This paper reviews the literature associated withcorporate strategy to propose a new approach ofacceleration for measuring momentum based on limited
cycle theory. This research also attempts to shed lighton the relationship between sales revenue andmomentum, and offers an explanation why the businesscycle in Japan’s automobile industry changed to afour-year period. Furthermore, the paper also develops afour cell model comprising momentum and firm scale asan effective approach for improving corporateperformance.
This paper is structured as follows. Section 2 reviews
the literature focusing on the momentum and corporatemanagement. In section 3, the paper explicates thecalculation process of momentum and data collection.
Section 4 discusses our findings and managerial
implications based upon our calculation. The study
limitations are identified and directions for further
research are proffered in Section 5.

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Tsutomu Ito, Katsuhiko Takahashi, Katsumi Morikawa, Takao Ito, Sakamoto Makoto, Satoshi Ikeda

2. Background
Momentum is a term to express power, force andspeed of organizational movement. The originaldescription of momentum appears in Art of War written
by famous strategist Sun Tzu. Indicating the importanceof momentum at the beginning of his book, Sun Tzu
famously asserts: It is important to “look for advantages
when applying my principles and you will gather
sufficient force to take on unforeseen situations. Forceis tilting the balance of power to your side by gathering
advantages” to win any battle [1, 01.11-01.12]. He
continued to explain the meaning of momentum inchapter five as force. In this context, he asserts “the rushof torrential waters tossing boulders illustrates force.
The strike of a bird of prey breaking the body of its
target illustrates timing. Therefore, the force of thoseskilled in warfare is overwhelming and their timing
precise. Their force is like a drawn crossbow and theirtiming is like the release of the trigger” [1,05.08-05.10]. Furthermore, in analyzing the relationshipbetween the momentum and war, Sun Tzu, posits“Those skilled in warfare seek victory through force anddo not require too much from individuals. Therefore,
they are able to select the right men and exploit force.
One who exploits force commands men into battle likerolling logs and boulders. Logs and boulders are stillwhen on flat ground, but roll when on steep ground.
Square shapes are still, but round shapes roll. Therefore,
those skilled in warfare use force by making the troops
in battle like boulders rolling down a steep mountain.
This is force” [1, 05.16-05.18].
It is widely acknowledged that military strategy
forms the basis of corporate strategy. But in the strategic
management literature, surprisingly there is no
theoretical description nor application of momentum,
which plays an important role in the performance ofbusiness activities. An on-line browse of the term“strategy
momentum”(inJapanese)yieldedapproximately 932,000 hits which suggest that it
obviously is an important concept in corporate strategy.
Momentum expresses a force or speed of movement.
In this paper, momentum is defined as a force orimpetus of firms to maintain firm’s development
durability in certain period. Why is momentum
becoming more and more important? A possible
explanation is that inherent uncertainty is in-built within
the dynamic, high-speed global economy. With the highrate of innovation, the speed of decision-making has
become a condition for successful performance.
In 1995, as a new method applying business to U.S.
army logistics, velocity management focused on
improving the speed and accuracy with which materials
and information flow from providers to users. Meanwhile, velocity management is an emergent scientificfield that conflates army’ operations and business
together to reflect the new realities of the globalenvironment. Mourier observed that velocity management is decision making at speeds consistent withtoday’s competitive environment and technology [2].
It is noteworthy that momentum has been the subjectof study in finance and marketing. Momentum in stockand securities is used to illustrate that their price is more
likely to keep moving in the same direction than tochange directions. In technical analysis, momentum isconsidered as an oscillator and is used to help identify
trend lines. It is the empirically observed tendency forrising asset prices to rise further, and falling prices tokeep falling. One of the important achievements infinance is that stocks with strong past performancecontinue to outperform stocks with poor past
performance in the next period with an average excess
return of about 1% per month [3].
However, to our best knowledge, this is the first workthat shows how to calculate momentum using velocity
for corporate strategy. The basic reasons why we haveto calculate momentum using limit cycle theory because
the global economy is becoming increasingly uncertain
and most of the corporate behaviors are non-linear. Thisbody of thought is important as it will help increase ourunderstanding and provide guidance that strategic
management practitioners can use to increaseorganizational performance. Thus, this study addresses
the paucity in the strategic management literature andmakes a contribution to the filed by being the first,
initial, investigation that illustrates how to measure
momentum using velocity, and its observed importancefor corporate strategy.
3.

Measurement and Data Collection

In this section, previous studies have showed thatchaos, which is generally described as a disorder state,is driven by deterministic nonlinear processes, such as
hydraulic flow and astronomical phenomena. Findingsin physics and biology have discovered some examplesof chaos. For example, Tsuda et al, found a chaotic

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Momentum and Its Implications

pulsation in a finger’s capillary vessels in normal
subjects and psychiatric patients, as well as cardiac
chaos [4].
Additional research illustrated that chaotic movement
is not only applicable in physics and biology, but also insociology and management science. For instance,
Priesmeyer and Baik proposed a new method todiscover the pattern of chaos in 1989. They noticed thatorganization have characteristics limit cycle like thehuman heart. They indicated “Company data tend toadhere to an attractor as they collect their quarterly sales
and drive their quarterly profits. One can almost hear
the organizational heartbeat pounding out ‘Quarter 1,Quarter 2, Quarter 3, Quarter 4’” [5]. Furthermore, Itoand Sakamoto shed light on the nature of therelationship between economic development and thevelocity history of the typical companies in Japan [6].
Because most of the behaviors of the firms are
nonlinear, momentum should be calculated based oncomplex systems theory. In this paper, momentum isconceptualized as a force that composed of sales andprofit movement, and is calculated based upon limit
cycle theory because of its non-linear movement.
In order to calculate and assess the impact ofmomentum on corporate performance, data werecollected from 35 selected companies, including 10 car
makers and 25 parts suppliers. In order to understandthe impacts of the Lehman shock on momentum, thedata includes sales and profit from 2003 to 2013.

decreased in 2009, and recovered in 2010. Other car
makers, such as Nissan and Mitsubishi, reacted
similarly. Second, the financial crisis had an impact
over three years on the Japanese car market. In otherwords, momentum could be considered as an effective
index to calculate the environmental changes.
ToyotaMomentumNissanFig. 1.

One-year momentum of each firm (2005-2013).

Next, the multiple year momentum was calculated,which is illustrated in Fig. 2.
1600000000000

Momentum

1400000000000
1200000000000
1000000000000
800000000000
600000000000
400000000000

4. Discussions and Analysis

Toyota Motor Corp.
Mitsubishi Motors
Mazda Motor Corp.
Daihatsu Motor Co., Ltd.
Hino Motors, Ltd.
Kawasaki Heavy Industries, Ltd.
Musashi Seimitsu Industry Co., Ltd.
Jidosha Buhin Kogyo Co., Ltd.
NOKKeihin Corporation
Aishin Seiki Co., Ltd.
Showa Corporation
Mitsuba CorporationAisan Industry Co., Ltd.
Nihon Plast Co., Ltd.
Yorozu Corporation
TS Tech Co., Ltd.
TBK

Nissan Moto Co., Ltd.
Honda Motor
Suzuki Motor Corp.
Isuzu Motors LimitedFuji Heavy Industries Ltd.
F-Tech Inc.
Nissan Shatai Co., Ltd.
Tachi-S Co., Ltd.
Shiroki Corporation
Kasai Kogyo Co., Ltd.
Ikuyo Co., Ltd.
Koito Manufacturing Co., Ltd.
Toyoda Gosei Co., Ltd.
Meiwa Corporation
Murakami Corporation
Yachiyo Industry Co., Ltd.
Akebono Brake Industry Co., Ltd.

ToyotaHonda

200000000000

The t in Momentum equation may vary depending on
different analysis proposed. For instance, one-year
momentum is calculated when t is equal to 1, andtwo-year momentum is calculated when t is equal to 2.
To understand the movement of the momentum within ashort period, one-year momentum is calculated as
below.
All momentum looks very stable except the period
from 2007 to 2010. As a well-known fact, 2007-2008
financial crisis resulted from subprime lending
practices. The prospects of Japan’s economy areunpredictable and the sales of new decreased. The
unstable momentum could be considered as a reactionof the financial crisis. Therefore, two conclusions are
made based on observing Fig. 1. First, momentum isvery sensitive to external changes. Another important
fact is that momentum of Toyota increased in 2008,

0

1-YearMomentum-200000000000

2-YearMomentum

3-YearMomentum

4-YearMomentum

5-YearMomentum

6-YearMomentum

7-YearMomentum

8-YearMomentum

9-YearMomentum

Mitsubishi-400000000000

Fig. 2. 1-9 year Momentum of each firm (2005-2013).

In Fig. 2, Toyota is seen to have the biggest value formomentum over 9-years. The second is Honda, and theleast is Mitsubishi. As time t becomes longer,momentum of a big scale company grows larger. The
third conclusion is that the reaction is apparently
pronounced if the scale of the company is large.
The momentum of big scale companies shows largechange, but all the others show stable change or
marginal change. The four-year momentum has thehighest effect on the sales in Fig. 3. Our conclusion isthat this research offers an explanation why the modelchange cycle in Japan automobile industry changed to afour-year period.

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Tsutomu Ito, Katsuhiko Takahashi, Katsumi Morikawa, Takao Ito, Sakamoto Makoto, Satoshi Ikeda

Momentum

into four different groups. Our next conclusion is thatthe four-cell model is appropriate to judge a firm’sposition.

4-year momentum
5-year momentum
6-year momentum

0.8
0.6

8-year momentum

0.4
0.2

3-Year Momentum

4-Year Momentum

8-Year Momentum

9-Year Momentum

Fig. 3.

TBK

TS Tech Co., Ltd.

Yorozu Corporation

Yachiyo Industry Co., Ltd.

5. Conclusion
Akebono Brake Industry Co., Ltd.

2-Year Momentum
7-Year Momentum

Nihon Plast Co., Ltd.

Meiwa Corporation

1-Year Momentum
6-Year Momentum

Murakami Corporation

Mitsuba Corporation

Toyoda Gosei Co., Ltd.

Ikuyo Co., Ltd.

Aishin Seiki Co., Ltd.

Kasai Kogyo Co., Ltd.

NOK

Keihin Corporation

Tachi-S Co., Ltd.

Shiroki Corporation

Jidosha Buhin Kogyo Co., Ltd.

F-Tech Inc.

Nissan Shatai Co., Ltd.

Musashi Seimitsu Industry Co., Ltd.

Hino Motors, Ltd.

Kawasaki Heavy Industries, Ltd.

Isuzu Motors Limited

Fuji Heavy Industries Ltd.

Daihatsu Motor Co., Ltd.

Honda Motor

Suzuki Motor Corp.

Mitsubishi Motors

Mazda Motor Corp.

Toyota Motor Corp.

Nissan Moto Co., Ltd.

Aisan Industry Co., Ltd.

1-year momentum

0Showa Corporation

1

Koito Manufacturing Co., Ltd.

1.2

Firm

5-Year Momentum

Different Momentum of each firm (2005-2013).

Based on the results, it is also possible to identify
successful companies as well as firms with impaired
performance using momentum measurements. Based on
the findings, momentum is influenced by the externalenvironment, company scales, and corporateperformance. Thus a four-cell model is proposed in thispaper. Comprising of momentum and scale should beeffective. The four-cell model of momentum (‘13/’05)
and sales13 is illustrated in Fig. 4.

ProblemChildPoorGood
PerformanceThis paper proposed a new approach for using
momentum based on the limit cycle theory afterreviewing the relevant literature. The relationshipbetween momentum and its external changes,
momentum and company scale were analyzed overvarious momentum periods. Furthermore, the four-cellmodel composed of momentum and company salesconfirmed that it is effective for judging firm’s position.
Additionally, the impact of the financial crisis was also
considered.
Sales and profit, as indices of corporate performance,
is insufficient. Additional indices, such as aggregate
market value and ROI (return on investment), should beinvestigated. What’s more, in the future these models
should be tested using data drawn from other settings,
such as, information technology, the ship-building
industry for comparative research as well as replicating
the current findings.

References

Potential Development

Fig. 4. A four-cell model of momentum (‘13/’05) and Sales ’13.

The reference line of x axis and y axis are the medianof momentum and sales ‘13 respectively in Fig. 4. Thefirms located in the 1st quadrant and the 3rd quadrant
are good firms and poorly performing firms,respectively, because they have appropriate relationshipbetween momentum and sales’13. The firm is called
developing company with high development potential if
it is located in 4th quadrant, while the firm is called
problem child if it is located in 2nd quadrant. A firm
moving from 3rd quadrant to 2nd or 4th quadrant, or
further from 2nd and 4th to 1st quadrant would beconsidered positive signs. All the companies are divided

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2. Pierre Mourier, (2001), Velocity management: ‐creating organizational instinct, Strategy & Leadership,Vol. 29 Issue 2, pp.24 – 28.
3. Chakrabarti Gagari (2015) Time-series momentum
trading strategies in the global stock market, Business,
http://www.thefreelibrary.com/Time-series+momentum+
trading+strategies+in+the+global+stock+market-a042323
4977, Retrieved October 22, 2015.
4. Tsuda I., Tahara T., and Iwanaga H. (1992) Chaotic
Pulsation in Human Capillary Vessels and its
Dependence on Mental and Physical Conditions,International Journal of Bifurcation and Chaos, Vol.2,No.2, pp.313-324, World Scientific Publishing Company.
5. Priesmeyer H. R., Kibok Baik (1989) Discovering thePatterns of Chaos, Planning Review, pp.14-21 andpp.46-47, November/December 1989.
6. Ito T. and Sakamoto M. (2007) A Consideration on Limit
Cycle Theory, The papers of Technical Meetings onInformation Systems, IS-07-10, pp. 19-23, The Instituteof Electrical Engineers of Japan (Japanese Edition).

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