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Eight Growth Strategies for Small Business Owners

Figuring out how to grow your company sustainably can be tricky. Christina Morillo/Pexels

1 April 2023 – The following is a guest post by Julia Mitchell, lifestyle consultant with Outspiration Network.

As a small business owner, figuring out how to grow your company sustainably can be tricky. You already wear so many hats that experimenting with new initiatives might leave you feeling overwhelmed, but at the same time you’re eager to see what you can achieve. Start by brainstorming workable ideas for growth. To get started, here are some growth tactics that you may be able to implement at your company, from engaging in business process management to focusing on content marketing.

Utilize Business Process Management

If you’re running your business based on inefficient processes, your company will not be able to grow to its full potential. With business process management (BPM), you can leverage automation to free your time from burdensome processes, and you can also gain a clear perspective of the ways in which systems, people, and data interact within your company. BPM will help you work out the kinks in your processes to make your business operate more easily.

After you create a BPM framework, you’ll need to assess its effectiveness from time to time to ensure that you’re getting the results you want. If you notice any issues, you’ll be able to adjust your framework accordingly to get the best results.

Invest in Content Marketing

Today, lots of companies invest in content marketing to promote their products and services. The term “content marketing” can encompass any written marketing materials across digital platforms. This could mean blog posts on your company’s websites, promotional e-books, social media captions, and more! Through content marketing, you can deepen your relationship with your audience and establish your digital platforms as credible sources of information. By creating evergreen content, you’ll have digital marketing assets that you can utilize over and over again for years to come. This will save time as you create new campaigns in the future!

Perhaps you haven’t thought much about content marketing before, and you’re not sure how to build up a robust content marketing strategy. Utilize online marketing resources to get your strategy off the ground. In time, you’ll likely notice a boost in sales as a result of content marketing!

Network Online and in Person

Perhaps you became an entrepreneur because you preferred working solo to working with other people. But, even if you’re an introvert, there’s simply no escaping the importance of networking when you run a business! To get comfortable with networking as an introvert, Creo Incubator recommends opting for one-on-one meetings with your industry contacts, setting goals for the number of people you want to talk to at events, and letting go of the idea that you have to become an extrovert to succeed in business. If you get comfortable with being yourself, other people in your industry will naturally gravitate towards you.

Launch New Products and Services

As you connect with a broader customer base, you’ll need to tune into their consumer demands so that you can match your offerings with their needs. If you’re thinking about developing and launching new products and services, you’ll have to make a plan! Marcus Lemonis recommends conducting extensive market research before building your new product, surveying your competition for ideas, estimating how much revenue you could earn from specific offerings, pitching the idea to any necessary stakeholders, and building buzz before the official launch date.

Expand Your Team

If you’re planning to grow your business, you can’t do it all by yourself! This is the time to start expanding your team so that you’ll have enough staff to handle all of your new projects. Create job listings for several online platforms, let your friends, relatives, and professional network know that you’re hiring, and prepare your interview questions ahead of time so that you can determine if a candidate will be a good fit.

Cultivate Partnerships

It’s easy to view other businesses solely as competition, but by partnering up with other companies that are not your direct competitors, you can reap lots of benefits! If you’re curious about partnering with another business for a marketing initiative, you’ll want to look to businesses that provide offerings your customers would also be interested in. However, you don’t want to pitch a partnership to a business that sells the same products! For example, if you run a company selling baking tools or kitchenware, you could launch a partnership with a business that sells artisan ingredients. Make sure that your offerings complement each other.

Seek Additional Funding

What if you have an idea in mind for a new product, service, or other initiative, but you simply don’t have the funds to make it a reality? You don’t necessarily have to wait until your revenue is higher. Instead, you can seek outside funding. If taking out a loan feels too risky, it’s time to start looking into small business grants.

Lots of organizations offer small business grants – you can find grants funded by both public and private institutions. It also helps to look up grants that are specifically targeted towards your industry. As you prepare your applications, go over the eligibility criteria closely! While pulling your pitch together, be very clear about what you plan to use the money for.

Host Events and Workshops

Facilitating events and workshops either online or at your company’s physical location is a fantastic way to “give back” to your audience. You can also film events and workshops and put the footage up on your website—this will allow people who missed the event to go back and watch it! You’ll be able to bring your audience together and foster valuable connections.

Growing your business takes time – and you’ll need to get comfortable with testing out strategies that don’t necessarily work. But, as you experiment, you’ll figure out how to draw in more customers, increase your sales, and deliver new offerings that your audience really wants. With these tips, you’ll be ready to explore the potential of business process management, content marketing, networking, and other growth tools.

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How to create a thriving business from your home base

Building a thriving business from home is a dream of many. Huseyn Kamaladdin/ Pexels.

2 November 2022 – The following is a guest post by Julia Mitchell, lifestyle consultant with Outspiration Network.

Building a thriving business from home is a dream of many. After all, what could be more satisfying, not to mention rewarding, than working from home and doing what you love? So if that’s you, and you always envisioned being an entrepreneur from your home base, here are some helpful tips on how to accomplish this.

Think of a unique business idea

Certainly, thinking of a unique business idea is the first step in creating a successful business, provided that there is a demand for your offering and you can make a profit at the end of the day. Establishing whether your business idea is feasible or not is going to be a task in itself because you’ll have to do extensive market research to figure this out. A simple solution to this dilemma would be to ask yourself if there is a problem that people are seeking a solution to and then find out how you could provide an answer for it. Then it’s about thinking creatively about how you could go about this; creative brainstorming sessions are usually a necessary part of this process.

Formulating a business plan

Suppose you’ve decided on a niche business idea that you believe would take your target market by storm, then the next thing to do is to develop a business plan to set the wheels in motion, so to speak. A business plan will be invaluable in helping you establish your next steps while keeping your focus on your end goals simultaneously.

Getting funding

In order to access the capital you need, one of the first things that you will need to do is to check your credit report. This will give you an overview of your financial situation and allow you to identify any potential issues that might affect your chances of getting funding. This is particularly important if you’re attempting to take out a loan. Other ways you could obtain funding include finding investors or applying for grants.

Upskilling yourself in the meantime

Before launching your business, you will need to have all your ducks in a row as well as the confidence to launch your business without hesitation. But, suppose you do have some reservations about going ahead with your business plan because you feel like your skill set could use some improvement. Then you could opt to study online even in the beginning stages of building your business to boost your skill set in the requisite areas of business management, leadership, and marketing.

Registering your business

The next step in setting up your business is registering it so that it has a legal identity. This will also help boost your business’s credibility when approaching vendors, suppliers, and potential customers when you are ready to create a pitch to win them over. Registering as an LLC is a good idea if you desire a business structure that is easy to manage in the beginning stages.

Moreover, an LLC is often the preferred option for novice entrepreneurs as a result of its many benefits that include greater flexibility in regard to the structure of your business. It has less paperwork to complete, limited liability, and tax advantages. Learn more about how to form an LLC—the process typically requires five distinct steps, depending on which state you reside in. For more information, contact your local corporations commission.

Setting up your home office

This is perhaps the most exciting part of getting going because you can pretty much design your home office space to be a true reflection not only of your brand but your authentic self, too. Just remember to keep it professional. But again, don’t be afraid to have fun with your vision by taking a chance with your decor, as this should be one of the less risky business decisions you can make.

Applying for an Employer Identification Number

Applying for an Employer Identification Number (EIN) is a necessary next step if you plan to hire employees. Furthermore, an EIN can help you to obtain a loan if necessary, open a separate business bank account, and it’s also often required by the IRS for tax purposes. Keeping financial records for your business separated from your personal accounts not only saves headaches, it is also the best way to avoid tax audits later on!

Getting ready for the first sale

Once you’ve established all of the above, then all you need to do is get ready for your first sale. Furthermore, you will probably have to start off small in the beginning to see what sales and marketing strategy works best for you, then scale up from where your sales start to skyrocket.

These steps should help you with creating a business that’ll help you realize your dreams in an environment where you feel the most comfortable.

About the Author

Julia Mitchell knew from a young age she wanted to have a career that made her excited to wake up every day. Now in a top-level position with Outspiration, a financial services firm, she’s got her dream job alongside multiple side-income entrepreneurial ventures. She is incredibly passionate about the activities that fill her days, she wants to share her adoration for her favorite lifestyle topics with the world and encourage others to turn their INspiration into OUTspiration.

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The Immigrant

There was a creature standing lonely in the corner of the room. Image by Kanyanat Wimonkanjana/Shutterstock

24 March 2121 – I had a dream the other night. We had just moved into our new house in a deep, dark forest. It wasn’t a new house, but it was new to us, and we felt warm and safe because we had power to control what went on inside our house, even though outside was a deep, dark forest full of dangers. They could not get to us in our warm, safe house.

Something woke us up, however, in the middle of the night. Looking around, I realized that there was a creature a little less than three feet tall standing lonely in the corner of the room. It was most definitely not like us.

It was not frightening or aggressive. It did not seem dangerous or powerful. It was shyly quiet and passive. I reached out to touch it, patting its head between large, round ears. It was warm and fuzzy like large a grey teddy bear, but alive with large, expressive eyes.

It was not threatening. It made no demands, not even a request. It just was just hoping for a place in which to stand quietly, safe from the dangers lurking in the deep, dark forest outside. We thought, what kind of monsters we would be to chase it back out into the deep, dark forest among dangers it would almost certainly not survive. So, we decided to leave it alone for now.

The next morning, we talked about the creature that came to us in the night with no demands, just hoping to find a safe place to stand. We’d encountered similar creatures in the past. Most of the time, we’d accepted them into our family when we could. Most had brought some troubles, and took a while to fit into our home, but in the end they did. The life they added was worth the small troubles they brought. Some proved spectacularly successful. Others less so. All just wanted a safe place to stand.

The next night, we found the creature standing timidly in the corner again, just hoping for a safe place to stand. It eyed us carefully, not knowing if we were the kind of monsters who would drive it out into the deep, dark forest full of dangers that it surely would not survive. We called it over and patted it on its head between its large round ears to show that we would not drive it away. It lay its warm, fuzzy head on the edge of the bed with a grateful smile. It was grateful just to have a safe place to stand.

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Systems Organization of Modern Enterprises

Wild dog pack walking in the forest, Okavango delta, Botswana, Africa. Note that while the pack leader (center) is fixated on the pack’s prey, the followers fixate on the leader, watching for clues as to what he wants them to do. Photo by Ondrej Prosicky/Shutterstock.

20 January 2021 – The following text is a lightly edited version of a posting I made on 13 January 2021 to the discussion forum for a class in my Doctor of Business Administration program at Keiser University.

Systems Theory as Emergent Organizational Design

At the turn of the 20th century, management theorists, Frederick Taylor in particular, proposed a horrid theory known as “scientific management,” which was based on the then nearly universal assumption of hierarchical business organization (Kiechel, 2012). Whenever someone promotes some idea as “scientific,” it sends up a red flag that the promoter has no understanding of either science or whatever reality the promoted idea is intended to explain. So-called “scientific” management was the poster child for sending up such a red flag.

Taylor’s assumption of hierarchical organization, however, was not surprising. Human beings, after all, evolved as pack hunters, and the hunting-pack model has clear evolutionary advantages for pack-hunting animals (Bailey, et al, 2013). Ethologists understand the impulse to form hierarchical organizations as a step up from the dominance system of pack hunters, which has one dominant individual leading an otherwise egalitarian team to accomplish some common goal (Wilson, 1975). One can visualize the hierarchical organization as consisting of packs within packs. Thus, natural selection has imprinted the tendency to favor this kind of dominance system into our DNA.

By the mid-20th century, management theorists, such as Peter Drucker, began to question the hierarchical organization model (Kiechel, 2012). James Miller (1955) provided a new model by applying systems theory to topics in the life sciences. Eventually, Henry Mintzberg introduced the idea that systems organizations – teams of teams, or adhocracy – arise naturally within modern complex organizations (Mintzberg & McHugh, 1985). Following this line of reasoning, and observing how large organizations have actually operated as far back as when ancient Egyptians were building pyramids, indicates that the hierarchical model was never valid (Procter & Kozak-Holland, 2019). Large organizations have always had a de facto systems, or adhocracy, organization, just as Mintzberg discovered arising naturally within modern organizations (Mintzberg & McHugh, 1985).

Mintzberg’s systems model is the natural way that pack animals collaborate to reach a common goal (Bailey, et al, 2013). Moving another step up the organization-model ladder, moves from the pack to the team. The difference between a pack and a team is that in a hunting pack subordinate individuals work together by playing similar roles in the hunting activity. More evolved groups go further by collaborating. Individuals in collaborating teams play different roles in the process, each according to their particular skills and talents.

As Adam Smith (1776) famously pointed out, it is more efficient for individual team members to specialize in performing different tasks than for them to all divelop and use similar skill sets. In the context of productivity of collections of nation states, David Ricardo showed how doing what one does best, and leaving it to others to do the rest, maximizes group productivity (Costinot & Donaldson, 2012; Felipe & Vernengo, 2002). Ricardo’s comparative advantage theory, when translated to team collaboration, indicates that the most effective teams are those made up of members with the appropriate complementary set of diverse skills needed to complete the task (Bailey, et al, 2013).

In the end, humans seem to have finally found the most effective organizational model for reaching any common goal (Project Management Institute, 2004). It consists of ad hoc collaborating teams working together toward a common goal. Each team has their own task to help reach the goal. Each individual team member has the skills needed to complete their particular part of the team’s task.

The following text is a lightly edited version of a comment I made on 15 January 2021 to another student’s posting to the same forum. It illustrates how the systems theory organizational model is supposed to work. The included figure projects the planned structure of the organization.

Response to BE post

Yes, BE, the system model for business organization lends itself to strategic development, human resources development, and most other activities organizations engage in (Aubry & Lavoie-Tremblay, 2018). I’d like to use a film project I’m executive producer on to illustrate how systems concepts lead to superior organization performance. The project goal is to develop, produce, and distribute a motion picture (provisionally entitled False Gods) from concept to screening.

Figure 1 shows the enterprise’s corporate structure (Hoover, 2013). It forms a star network centered on the False Gods LLC holding company, which retains the intellectual property and other assets (e.g., investor funds). There are four subsystems within the network: business, production, marketing, and legal. Each subsystem consists of at least two components, each of which has its own corporate identity. For example, the business subsystem includes C.G. Masi LLC, which provides project management services, and Mercury Bank, which provides financial services (e.g., checking and savings). One of the subunits of the Production subsystem is Sound (Hoover, 2013). This subunit includes a number of subcontractors, such as a recording studio, a number of voice actors, and a Foley artist (to provide sound effects). The Music subunit is located in Spain, and is contracted to provide an original musical score, musicians to play the score, and recording facilities. These form another layer of subsystems within the Music subsystem.

Illustration of systems-theory model for organizational structure using False Gods project team design.

The systems model views each of these components as a separate system with its own inputs, process, and outputs (Miller, 1955). For example, the Animation subunit is a complete studio, with its own artists, equipment, and management. It has as inputs the existing script and instructions from the Director. The process consists of breaking the script down into individual shots and creating video clips for each shot. The output is a large number of digital-video files (estimated to number approximately 1,500 for False Gods), one for each clip, which the animation studio transmits electronically to the Film Editor.

Finally, the film editor combines those digital files with digital files from the Music, Foley and Sound subunits to fashion the complete film as one large digital-video file (Hoover, 2013). Each of these systems and subsystems has its own expertise, which it lends to the overall project. A voice actor, for example, in the Sound subunit has expertise in expressing emotion in spoken utterances that fit the requirements of the script and the timing of the animated images. All of these components combine like a giant multi-dimensional jigsaw puzzle to tell the story of the motion picture.

References

Aubry, M., & Lavoie-Tremblay, M. (2018). Rethinking organizational design for managing multiple projects. International Journal of Project Management, 36(1), 12-26.

Bailey, I., Myatt, J. P., & Wilson, A. M. (2013). Group hunting within the carnivora: Physiological, cognitive and environmental influences on strategy and cooperation. Behavioral Ecology and Sociobiology, 67(1), 1-17.

Costinot, A., & Donaldson, D. (2012). Ricardo’s theory of comparative advantage: Old idea, new evidence. American Economic Review, 102(3), 453–458.

Felipe, J., & Vernengo, M. (2002). Demystifying the principles of comparative advantage. International Journal of Political Economy, 32(4), 49–75.

Hoover, S. (2013). Film production: Theory and practice. Stephen Hoover.

Kiechel, W. (2012) The Management Century. Harvard Business Review., 90(11), 62-75.

Miller, J. G. (1955). Toward a General Theory for the Behavioral Sciences. American Psychologist, 10(9), 513-531.

Mintzberg, H., & McHugh, A. (1985). Strategy formation in an adhocracy. Administrative Science Quarterly, 30(2), 160–197.

Procter, C., & Kozak-Holland, M. (2019). The Giza pyramid: Learning from this megaproject. Journal of Management History, 25(3), 364-383.

Project Management Institute. (2004). A Guide to the Project Management Body of Knowledge (PMBOK Guide). Newtown Square, PA: Project Management Institute.

Smith, A. (1776). An inquiry into the nature and causes of the wealth of nations. Edinborough: W. Strahan.

Wilson, E. O. (2012). Sociobiology: The new synthesis. Harvard University Press.

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Independent and Dependent Variables

Figure 1: Causation leads to correlation.

11 December 2020 — The following essay is taken verbatim from a posting I made to the discussion forum for a class in my Doctor of Business Administration program at Keiser University.

Sometimes, but not always, variables of interest in survey studies depend on each other (Alreck, 2019). As Figure 1a shows, this sets up two kinds of relationship: causality and correlation. Causality is the stronger of the two. It means that variable A, called the independent variable, has whatever value it happens to have because of extraneous factors, but variable B gets its value because of variable A’s value. Mathematically, we symbolize this relationship as A → B, which means “A implies B.” If extraneous things change A’s value, variable B’s value will change as a result.

Correlation, however, is weaker. It just means that both A and B generally change similarly. Figure 1b shows one possible way this can happen. In this instance, not only there is a causal relationship between A and B, there is also a causal relationship between A and C. In such a case, there will also be a correlation between B and C, but no causal relationship between them. If researchers include questions about only B and C, but fail to ask about A, they will miss the most important part of the relationship.

Figure 1b: Variations in multiple dependent variables may be caused by the same independent variable.

Simple statistical analysis can thus show correlation, but cannot show causation (Alreck, 2019). For example simple scatter plots can show cross-correlations between variables, and even show degrees of correlation (Weiss, 2012). They cannot, however, prove that there is a causal relationship between them (Alreck, 2019). That requires some outside information (Bekiros & Sweeney, 2018). Essentially, an understanding of the system under study must be available to ensure that all relavant variables have been observed (Coetzee & Erasmus, 2017).

Figure 2: A more complicated web of dependencies.

Figure 2 shows a more complicated web of interrelationships between variables. A second independent variable D appears that also affects the value of variable C, but not that of B. In this case, B is still closely correlated with A, but A’s correlation with C is less close because D variations also affect C. To find causation in such situations, use factorial ANOVA (Steinberg, 2008).

References

Alreck, P. L. (2019). Survey research handbook (3rd ed.). McGraw-Hill Education.

Bekiros, S., Sjö, B., & Sweeney, R. J. (2018). Pitfalls in cross‐section studies with integrated regressors: A survey and new developments. Journal of Economic Surveys, 32(4), 1045–1073.

Coetzee, P., & Erasmus, L. J. (2017). What drives and measures public sector internal audit effectiveness? Dependent and independent variables. International Journal of Auditing, 21(3), 237–248.

Steinberg, W. J. (2008). Statistics Alive! Sage Publications.

Weiss, N.A. (2012). Elementary Statistics (8th ed.) Addison Wesley.

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Protest Demonstrations and the American Revolution

Tea Party Stamp
Stamp printed in USA to commemorate the Boston Tea Party as part of the Bicentennial celebration in the United States, circa 1976. Image by neftali/Shutterstock

30 July 2020 – Over the last few days, I’ve engaged in a social-media exchange about events in Portland, OR involving protest demonstrations there, and camo-clad so-called “Federal agents.” So, it seems timely to point out why we have a First Amendment to our Constitution, and remind readers that the American Revolution started with a protest demonstration—the Boston Tea Party. Lest we forget, the Portland demonstrations were organized (if that word applies) by the Black Lives Matter movement to protest police brutality, especially the alleged murder of George Floyd by Minneapolis, MN police officer Derek Chauvin.

The social-media exchange I mentioned above devolved into a dispute about where protest demonstrations fit into the workings of a democracy. My position, which I get to explain in this essay because I pay for this space in the World Wide Web to post whatever I darn well please, is that protest demonstrations are a necessary part of a properly functioning democratic society. My opponent (who will remain unnamed, as will the social-media platform that carried the exchange) took the position that such demonstrations were not. Effective or not, he (There, I’ve narrowed his identity down to 49.1% of the U.S. population!) claimed that protest demonstrations were not part of the formal functioning of government, and were, thus, illegitimate. In rebuttal, I pointed him to the First Amendment, which guarantees “the right of the people peaceably to assemble, and to petition the Government for a redress of grievances,” and to the history of the Boston Tea Party that effectively began the American Revolution.

In this essay, I’m not going to recite the history of the Boston Tea Party, which you can read for yourself by following the link above. It’s a pretty good account that agrees with the mass of American History texts I’ve read over the years. (It’s important to point that out these days, as an example of how we verify that something is not fake news.) Instead, I hope to point out parallels between Boston Tea Party events and public protest demonstrations in the 21st century.

The Revolutionary War in America is generally acknowledged to have started with what Ralph Waldo Emerson called “Shot Heard Round The World,” in Lexington, MA in 1775. The actual American Revolution, as an historical movement, began years earlier, however. A protest organization named “The Sons of Liberty,” which had by then been active for over a decade, was responsible for mounting a force of 100 protesters, who boarded the ships Dartmouth, Beaver, and Eleanor docked at Griffin’s Wharf in Boston, MA disguised as Native Americans. The Sons of Liberty, of course, are an exact parallel to today’s Black Lives Matter movement.

Once aboard the ships, the protesters dumped the ships’ cargoes of tea, belonging to the East India Trading Company and valued at $1 million today, into Boston Harbor. After dumping the tea, the protesters cleaned up the decks of the American-owned ships! This represents, of course, an ideal example of how a peaceful protest as envisioned by the First Amendment should be carried out

Protests this Summer in the streets of Portland, Minneapolis, and other cities have been far larger, involving hundreds of thousands of protesters. They have also sometimes devolved into violence. However, it should be noted that the 2020 demonstrations were in response to government actions (i.e., police brutality) that ended with loss of life, rather than just a tax on tea. It is reasonable to expect folks to get a bit more worked up after suffering homicidal attacks perpetrated by government agents (which policemen are)!

That said, the modern protest demonstrations have been predominantly peaceful. Most violence has occurred in situations where demonstrators have been met with armed resistance. The same thing happened in the American Revolution. Five years before the Boston Tea Party, British soldiers shot at demonstrators protesting the presence of armed troops in city streets, injuring six protesters and killing five. Called “The Boston Massacre, the moral of that story is that the surest way to make a demonstration turn violent is to send in armed troops.

To summarize my position on protest demonstrations’ place in a democracy, when government in a democratic society fails to function properly for any reason, the people have the duty to take to the streets in protest. It is every bit as important as having a free press, which is generally acknowledged as a requirement for proper functioning of a democracy. Far from being some kind of extra-legal activity, both are specifically written into the U.S. Constitution by the First Amendment. You can’t get more legal than that!

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The Dead-Cat Bounce

Dead Cat Bounce
Chaotic market theory and basic control theory combine to explain equities markets’ dead-cat bounce phenomenon.

10 June 2020 – The title of this essay sounds like a new Argentinian dance craze, but it’s not. It’s a pattern of stock-price fluctuations that has been repeated over, and over, since folks have been tracking stock prices. It doesn’t get the attention it deserves because people who pretend that they have power (i.e., the People In Charge – PIC), and can wisely dispense it, don’t like things that show how little power they actually have. So, they ignore the heck out of them, thereby proving themselves dumb, as well as powerless.

There’s been a lot of blather in the news media recently about some hypothetical “V-shaped recovery,” which a lot of pundits, especially those of the Republican-Party persuasion (notably led by that master of misinformation, Donald Trump), want you to believe the U.S. economy is experiencing. In an attempt to prove their case, they point to the performance over approximately the past three months of all three major equity-market indices, those being the Dow-Jones Industrial Average (DJIA), the Standard and Poor’s 500-Stock Composite Index (S&P), and the National Association of Securities Dealers Automated Quotations index (NASDAQ),. Those three indices do tell a consistent story, but it’s not the one the V-shaped-recovery fans want you to believe. The story is actually much more complicated. It’s what’s called the dead-cat bounce.

To understand the dead-cat bounce that has been going on since the U.S. equities market crashed in March, you have to understand what I was driving at in this space on 18 March 2020. That was about the time the market bloodbath hit bottom. By the way, I’d been mostly out of the market, and into cash, for several months at that point. I could see that something evil was bound to happen in the near future. I just didn’t know what it would be. It turned out to be a pandemic coming out of the blue.

In that 18 March essay, I spent a whole lot of space developing the chaotic-market theory, which visualizes markets as having an equilibrium value based on classical efficient-market theory, with a free-roaming chaotic component riding on it. The chaotic component arises as millions of investors jostle to control prices of thousands of equity instruments (stocks). One of the first things those of us who have been responsible for designing and building feedback control systems run into is a little phenomenon called pilot-involved oscillation (PIO), named after an instability all pilots have to deal with when learning to land an airplane. PIO arises from the inescapable fact that feedback response comes some time after the system moves off equilibrium. Obviously, the response can’t come before the movement, it has to come after. That’s why they call it a “response!” That time lag is what causes the PIO.

A feedback-controlled system’s behavior follows what’s called a inhomogeneous time-dependent linear differential equation. Let me break that name down a bit. The “inhomogeneous” part just means there is something driving the system. In the case of equities markets, that’s the underlying economy setting the equilibrium in accordance with Adam Smith’s supply and demand. The “time-dependent” part just means that things change over time. As Jim Morrison said: “The future’s uncertain and the end is always near.” A “linear differential equation” means that what happens next depends on what happened before, and the rate at which things are changing, now. Without going into the applied mathematics of finding a solution, I’ll just skip to the end, and tell you that there’s only one solution: the dratted things oscillate. That is, they go up and down, always overshooting and undershooting the equilibrium point.

Do you see the connection, now?

That solution is called a damped harmonic oscillator, which simply means that the thing’s overshooting and undershooting follows a regular sinusoidal (you’ll have to look that one up, yourself) pattern, but it dies out over time. The rate at which the oscillation dies out is controlled by something called the damping ratio, which can take on any value from zero to infinity. Zero damping means the oscillation doesn’t die out. A damping ratio exactly equal to one means the system over- or undershoots once, then comes back to its equilibrium value. A damping ratio much over one makes the system respond sluggishly, and not oscillate at all.

Now, with that explanation in mind, look at the market behavior depicted in the graph above. The graph starts at the beginning of March 2020. Investors started to realize that the pandemic was going to trash the U.S. economy around mid-February, so you see that I’ve cut off some of the start of the crash that happened before 1 March. By 1 March, stock prices were falling like a stone until 23 March. That’s when the dead cat hit the pavement, and bounced. It bounced too high and, around 27 March, it started falling back down, only to undershoot again. Around 2 April, it bottomed and started back up, again. Looking at these movements quantitatively, we can see the clear pattern of a damped oscillation with a period of about 12 days, and a damping ratio of between 0.2 and 0.4.

To bring out the underlying pattern, I’ve filtered the data by averaging over three days for each point in the data set to get the smoother red line. The three-day filter (called a Butterworth filter, by the way) does little to suppress the slower 12-day oscillations, or the even slower smack from the pandemic’s economic hit. I does, however, pretty well filter out the daily noise from the fast-moving day-trading fluctuations.

Clearly, we are in a recovery. There’s no doubt about that! The economy is coming back to life after being practically shut down for a short period of time. The initial shock from the pandemic is largely over. Look for a gradual return to the three-to-five-percent-per-year long-term growth rate we’ve seen over the century-and-a-quarter history of the DJIA.

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Analysis of an Investment Opportunity

InvestmentImage
Take time to analyze an investment opportunity before pulling the trigger. Image by Peshkova/Shutterstock

13 May 2020 – This essay is based on a paper I wrote recently as part of my studies for a Doctor of Business Administration (DBA) at Keiser University. I thought readers might like seeing how to properly analyze investment opportunities before making a final decision, so I’ve revised the paper for presentation here.

In a surprising coincidence, bright and early Monday (3/23/2020) morning I received a call from Saira Morgan of Rustik Haws (RH) publishers wanting to republish a novel (entitled Red) that I launched in 2010 with another publisher (iUniverse), which had a disappointing sales history. It seems RH’s editors had reviewed the book, and felt that the problem was not the book’s content, but that it had been badly mispriced at $29.95 in paperback, or $39.95 in hardcover. RH wanted to re-launch a new edition of the book priced more reasonably at $12.99 in paperback. The original publisher had based their price on the book’s large page count (588 pages), and I had uncritically accepted their suggestion. The contract I have with iUniverse stipulates that I own the copyright, and am free to republish the work at will.

SM’s call was a surprising coincidence because that week’s topic for the Financial Theory & Policy course I was taking at the time was the question: “How can you use [mean variance optimization] to ensure that the business organization you are leading will succeed without losing money in some investment activities?” The RH proposal thus presented an opportunity to use the capital asset pricing model (CAPM) to evaluate their offer (Fama, & French, 2004), and write about it on the class forum.

My initial reaction to SM’s call was positive because feedback I’ve received from booksellers was that the price impediment was enough to prevent booksellers from carrying the book at all, thus preventing potential readers from ever sampling its content. Before even starting to evaluate RH’s proposal, however, I wanted to find out who the company was, and whether I wanted to take their offer seriously. I have received offers from other vanity-press publishers that were not at all professional.

Thus, I started evaluating the opportunity by visiting the Rustik Haws website. A cursory inspection showed that it looked quite professional and offered a full suite of the services one would expect from a modern self-publishing house. The biggest concern was that they only started the company in 2014, which is recent in a business where many firms have been around for a century or more.

A visit to the Better Business Bureau (BBB) website showed them to have an A- rating, and the only derogatory comment was about RH’s time in business (Better Business Bureau, 2020). BBB counted as time-in-service only the one year from RH’s move to Tampa, FL in May of 2019. The company did get two derogatory customer reviews, but both were by individuals who never actually worked with them. They’d been put off by RH’s tactic of cold-calling potential customers. I discounted those because how else are you going to drum up business? There were no complaints from actual customers. Altogether, I judged that it was worthwhile to at least evaluate RH’s offer.

The appropriate tool for evaluating a potential investment like this one is the corporate asset pricing model (CAPM). Copeland, Weston, and Shastri (2005) show the inputs for the CAPM to be the risk-free rate of return, the expectation value of the market rate of return, the market variance, and the asset-return’s covariance with the market return, which is called its beta. The first four should be available from online sources or my stock broker.

The asset’s expected returns and its beta are another matter, however. I would have to estimate the potential returns based on the deal RH is offering and sales history of other books I’ve written. Luckily, I have quarterly sales history for a how-to book (entitled How to Set Up Your Motorcycle Workshop) that I launched in 1995 with another publisher (Whitehorse Press), and which is still selling well in its third edition. I would be able to calculate beta by matching sales figures with contemporary market gyrations. So, I judged that I had identified adequate sources for the information needed to evaluate the RH offer using mean variance optimization (specifically CAPM), and compare it to the RH buy-in price.

Estimating Beta from Historical Data

It happens that not only did I have the quarterly reports from WP available, I also had complete daily closing prices for the Dow Jones Industrial Average (DJIA) going back to the beginning of the index. I selected from all this information data to form a picture of the first 10 quarters (two-and-a-half years) of the WP-book’s performance using an Excel spreadsheet (summarized as Table 1 below). The first two columns of the spreadsheet include an index (I always include an index as a best practice when composing a spreadsheet), and dates of the closing day of each quarter. The index runs from zero to ten to provide a pre-date-range value to allow taking differences between entries. Note that the first period was dated two weeks before the close of the first quarter because that is when WP closed its books and issued the report for the first-quarter’s performance. It does report a full quarter’s results, though. I chose to start with the initial post-book-launch data as that most likely paints a representative picture of sales for a new-book launch.

The third through fifth columns list DJIA’s closing prices, changes from the previous quarter’s value, and those changes relative to the previous quarter’s closing value (thus, the DJIA rate of change per quarter). Beneath those columns I’ve collected the mean, standard deviation, and variance computed using Excel’s statistical functions. Similarly, I’ve listed the WP data and calculations in columns seven through nine. Column seven lists the WP book’s unit sales. Column eight lists quarterly royalties paid. Column nine converts those royalties into quarterly returns on a hypothetical $1,000 initial investment by WP. I do not have information about what WP’s initial investment actually was, but the amount matches what Rustik Haws was asking, and is fairly typical for the industry. Below the WP performance data is the mean, standard deviation, and variance for the return on investment (ROI) computed by Excel’s statistical functions.

I was unhappy with the results returned by Excel’s covariance function, so I added column six that manually computes the covariance between the DJIA fluctuations and those of the ROI. The columnar portion computes the product of quarterly changes in the DJIA and those of the ROI. Cells below the column sum the quarterly contributions from column nine, then divides that sum by a count of the values in the sum to average the covariance values. Finally, I added a cell below that computes the investment’s beta by dividing by the variance Excel computed for the DJIA fluctuations.

The estimated beta has a magnitude of slightly over 0.6 and moves opposite the market fluctuations (shown by its having a negative sign). These data will inform the CAPM calculation of an expected return on the contract proposed by Rustik Haws (Ross, 1976).

Expected Value of Rustik Haws Proposal

To be an attractive proposition, the Rustik Haws proposal would have to provide an expected quarterly return greater than that projected by the CAPM (Fama, & French, 2004), which reads:

Ei = Rf + β(Em – Rf),

where Ei is the expected return required for the investment, Rf is the return on a risk-free asset (e.g., a three-month Treasury Bill), β is the covariance of royalties from the sale of the WP book with the market chosen for comparison (the DJIA), Em is the expected market return.

The quarterly returns from the DJIA give Em = 0.0489 ≈ 0.05 (the average relative return per quarter), and β = -0.06172 ≈ -0.06. I’ll take the risk-free rate to be the Federal Reserve’s target rate. Right now, the Fed has decided to set its target interest rate anomalously low (approximately zero) in response to stress on the economy from the COVID-19 pandemic, but it is reasonable to expect that to rise back to the pre-pandemic rate of 2% per annum (0.02/4 = 0.005 per quarter), which can be used for the risk-free rate, Rf. Plugging these values into the CAPM equation gives a required quarterly return of 0.0473, or 4.7%. That return on a $1,000 investment means the quarterly royalty projection should be >$47.30.

Not surprisingly, Rustik Haws has not projected quarterly sales for the re-launched book, but the assumption for this analysis is that unit sales might be similar to those of the WP book, which appear in Table 1. Rustik Haws’ per-copy cost structure provides $12.99 (retail price) – $3.89 (bookseller’s commission) – $5.83 (printing cost) = $3.27. The average quarterly sales for the WP book was 211 during that first 10 quarters. That makes the expectation value of royalties equal to $3.27 x 211 = $689.97. This is over 14 times the $47.30 required by CAPM, and argues strongly in favor of accepting the offer.

Best Competing Use of Funds

Completing the analysis requires using the CAPM to compare the RH opportunity to the best alternative use of the funds. That happens to be expanding my portfolio of stocks. To do that, requires estimating the expected return on the stock market going forward, and the beta of the portfolio.

The stock market is currently in the recovery phase after a serious disruption by the COVID-19 pandemic. So far, the recovery appears to be more-or-less L-shaped. That is, after a 34% initial drop (23 March), there was an immediate recovery to somewhere around 17% down, followed by a movement around that 17% down value with no clear direction. I interpret the 34% initial drop to be an overcorrection that was reversed by the rise back to 17% down. That I consider the true level based on the market’s expectation of future returns. The flatness of the current movement of both the DJIA and S&P 500 indices signals uncertainty as to whether there will be a second peak in COVID-19 cases.

Historically, after a financial crisis markets recover to their previous-high level after about a year (which would be near the end of 1Q 2021). So, guesstimating a typical recovery scenario without a double-dip, we can expect a 17% recovery from the current level in very roughly one year, which gives a compound quarterly growth rate of 4.9% on the $1,000 investment, or only $49.26. This still argues in favor of taking the RH opportunity.

In actual fact, experience shows that it takes roughly a year to bring a new edition of a book to launch. Thus, the returns for both the relaunched book and recovering stock market should commence more-or-less at the same time. At that point, experience indicates the market should have settled on the long-term compound annual growth rate, which is 7% (corrected for inflation) for the S&P 500 (Moneychimp, 2020). This translates into $70.00 for the projected $1,000 investment, which is still only one tenth of the expected $689.97 quarterly return on the RH investment. Thus, working with RH to relaunch Red appears to be by far the best use of funds.

References

Better Business Bureau (2020) Rustik Haws LLC. [Web site] Clearwater, FL: Better Business Bureau. Retrieved from https://www.bbb.org/us/fl/tampa/profile/digital-marketing/rustik-haws-llc-0653-90353994

Copeland, T. E., Weston, J. F., & Shastri, K. (2005). Financial Theory and Corporate Policy. Boston, MA: Pearson.

Fama, E. F., & French, K. R. (2004). The Capital Asset Pricing Model: Theory and Evidence. Journal of Economic Perspectives, 18(3), 25–46.

Moneychimp. (2020). Compound annual growth rate (annualized return). http://www.moneychimp.com/features/market_cagr.htm

Ross, S. A. (1976). The arbitrage theory of capital asset pricing. Journal of Economic Theory, 13, 341-360.

 

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The Old New Business Model

Supply networks
Next-generation, self-healing supply networks will feature robustness against supply interruptions. Image by urbans/Shutterstock

15 April 2020 – Business organizations have always been about supply networks, even before business leaders consciously thought in those terms. During the first half of the 20th century, the largest firms were organized hierarchically, like the monarchies that ruled the largest nations. Those firms, some of which had already been international in scope, like the East India Trading Company of previous centuries, thought in monopolistic terms. Even as late as the early 1960s, when I was in high school, management theory ran to vertical and horizontal monopolies. As globalization grew, the vertical monopoly model transformed into multinational enterprises (MNEs) consisted of supply chains of smaller companies supplying subassemblies to larger companies that ultimately distributed branded products (such as the ubiquitous Apple iPhone) to consumers worldwide.

The current pandemic of COVID-19 disease, has shattered that model. Supply chains, just as any other chains, proved only as strong as their weakest link. Requirements for social distancing to control the contagion made it impossible to continue the intense assembly-line-production operations that powered industrialization in the early 20th century. To go forward with reopening the world economy, we need a new model.

Luckily, although luck had far less to do with it than innovative thinking, that model came together in the 1960s and 1970s, and is already present in the systems thinking behind the supply-chain model. The monolithic, hierarchically organized companies that dominated global MNEs in the first half of the 20th century have already morphed into a patchwork of interconnected firms that powered the global economies of the first quarter of the 21st century. That is, up until the end of calendar-year 2019, when the COVID-19 pandemic trashed them. That model is the systems organization model.

The systems-organization model consists of separate functional teams, which in the large-company business world are independent firms, cooperating to produce consumer-ready products. Each firm has its own special expertise in conducting some part of the process, which it does as well or better than its competitors. This is the comparative-advantage concept outlined by David Ricardo over 200 years ago that was, itself, based on ideas that had been vaguely floating around since the ancient Greek thinker Hesiod wrote what has been called the first book about economics, Works and Days, somewhere in the middle of the first millennium BCE.

Each of those independent firms does its little part of the process on stuff they get from other firms upstream in the production flow, and passes their output on downstream to the next firm in the flow. The idea of a supply chain arises from thinking about what happens to an individual product. A given TV set, for example, starts with raw materials that are processed in piecemeal fashion by different firms as it journeys along its own particular path to become, say, a Sony TV shipped, ultimately, to an individual consumer. Along the way, the thinking goes, each step in the process ideally is done by the firm with the best comparative advantage for performing that operation. Hence, the systems model for an MNE that produces TVs is a chain of firms that each do their bit of the process better than anyone else. Of course, that leaves the entire MNE at risk from any exogenous force, from an earthquake to a pandemic, which distrupts operations at any of the firms in the chain. What was originally the firm with the Ricardoan comparative advantage for doing their part, suddenly becomes a hole that breaks the entire chain.

Systems theory, however, provides an answer: the supply network. The difference between a chain and a network is its interconnectedness. In network parlance, the firms that conduct steps in the process are called nodes, and the interconnections between nodes are called links. In a supply chain, nodes have only one input link from an upstream firm, and only one output link to the next firm in the chain. In a wider network, each node has multiple links into the node, and multiple links out of the node. With that kind of structure, if one node fails, the flow of products can bypass that node and keep feeding the next node(s) downstream. This is the essence of a self-healing network. Whereas a supply chain is brittle in that any failure anywhere breaks the whole system down, a self-healing network is robust in that it single-point failures do not take down the entire system, but cause flow paths to adjust to keep the entire system operating.

The idea of providing alternative pathways via multiple linkages flies in the face of Ricardo’s comparative-advantage concept. Ricardo’s idea was that in a collection of competitors producing the same or similar goods, the one firm that produces the best product at the lowest cost drives all the others out of business. Requiring simultaneous use of multiple suppliers means not allowing the firm with the best comparative advantage to drive the others out of business. By accepting slightly inferior value from alternative suppliers into the supply mix, the network accepts slightly inferior value in the final product while ensuring that, when the best supplier fails for any reason, the second-best supplier is there, on line, ready to go, to take up the slack. It deliberately sacrifices its ultimate comparative advantage as the pinnacle of potential suppliers in order to lower the risk of having its supply chain disrupted in the future.

This, itself, is a risky strategy. This kind of network cannot survive as a subnet in a larger, brittle supply chain. If its suppliers and, especially, customers embrace the Ricardo model, it could be in big trouble. First of all, a highly interconnected subnet embedded in a long supply chain is still subject to disruptions anywhere else in the rest of the chain. Second, if suppliers and customers have an alternative path through a firm with better comparative advantage than the subnet, Ricardo’s theory suggests that the subnet is what will be driven out of business. For this alternative strategy to work, the entire industry, from suppliers to customers, has to embrace it. This proviso, of course, is why we’ve been left with brittle supply chains decimated by disruptions due to the COVID-19 pandemic. The alternative is adopting a different, more robust paradigm for global supply networks en masse.

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Efficient Markets and Chaos

DJIA1900-2020
Semi-logarithmic plot of historic record of Dow Jones Industrial Average closing values from 1900-2020 plotted against an increasing exponential function to show chaotic oscillations.

18 March 2020 –Equities markets are not a zero-sum game (Fama, 1970). They are specifically designed to provide investors with a means of participating in companies’ business performance either directly through regular cash dividends, or indirectly through a secular increase in the market prices of the companies’ stock. The efficient market hypothesis (EMH), which postulates that stock prices reflect all available information, specifically addresses the stock-price-appreciation channel. EMH has three forms (Klock, & Bacon, 2014):

  • Weak-form EMH refers specifically to predictions based on past-price information;
  • Semi-strong form EMH includes use of all publicly available information;
  • Strong-form EMH includes all information, including private, company-confidential information.

This essay examines equities-market efficiency from the point of view of a model based on chaos theory (Gleick, 2008). The model envisions market-price movements as chaotic fluctuations around an equilibrium value determined by strong-form market efficiency (Chauhan, Chaturvedula, & Iyer, 2014). The next section shows how equities markets work as dynamical systems, and presents evidence that they are also chaotic. The third section describes how dynamical systems work in general. The fourth section shows how dynamical systems become chaotic. The conclusion ties up the argument’s various threads.

Stock-Market Dynamism

Once a stock is sold to the public, it can be traded between various investors at a strike price that is agreed upon ad hoc between buyers and sellers in a secondary market (Hayek, 1945). When one investor decides to sell stock in a given company, it increases the supply of that stock, exerting downward pressure on the strike price. Conversely, when another investor decides to buy that stock, it increases the demand, driving the strike price up. Interestingly, consummating the transaction decreases both supply and demand, and thus has no effect on the strike price. It is the intention to buy or sell the stock that affects the price. The market price is the strike price of the last transaction completed.

Successful firms grow in value over time, which is reflected in secular growth of the market price of their stocks. So, there exists an arbitrage strategy that has a high probability of a significant return: buy and hold. That is, buy equity in a well-run company, and hold it for a significant period of time, then sell. That, of course, is not what is meant by market efficiency (Chauhan, et al, 2014). Efficient market theory specifically concerns itself with returns in excess of such market returns (Fama, 1970).

Of course, if all investors were assured the market price would rise, no owners would be willing to sell, no transactions could occur, and the market would collapse. Similarly, if all investors were assured that the stock’s market price would fall, owners would be anxious to sell, but nobody would be willing to buy. Again, no transactions could occur, and the market would, again, collapse. Markets therefore actually work because of the dynamic tension created by uncertainty as to whether any given stock’s market price will rise or fall in the near future, making equities markets dynamical systems that move constantly (Hayek, 1945).

Fama (1970) concluded that on time scales longer than a day, the EMH appears to work. He found, however, evidence that on shorter time scales it was possible to use past-price information to obtain returns in excess of market returns, violating even weak-form efficiency. He concluded, however, that returns available on such short time scales were insufficient to cover transaction costs, upholding weak-form EMH. Technological improvements since 1970 have, however, drastically reduced costs for high volumes of very-short-timescale transactions, making high-frequency trading profitable (Baron, Brogaard, Hagströmer, & Kirilenko, 2019). Such short-time predictability and long-time unpredictability is a case of sensitive dependence on initial conditions, which Edward Lorentz discovered in 1961 to be one of the hallmarks of chaos (Gleick, 2008). Since 1970, considerable work has been published applying the science of chaotic systems to markets, especially the forex market (Bhattacharya, Bhattacharya, & Roychoudhury, 2017), which operates nearly identically to equities markets.

Dynamic Attraction

Chaos is a property of dynamical systems. Dynamical-systems theory generally concerns itself with the behavior of some quantitative variable representing the motion of a system in a phase space. In the case of a one-dimensional variable, such as the market price of a stock, the phase space is two dimensional, with the variable’s instantaneous value plotted along one axis, and its rate of change plotted along the other (Strogatz, 2015). At any given time, the variable’s value and rate of change determine the location in phase space of a phase point representing the system’s instantaneous state of motion. Over time, the phase point traces out a path, or trajectory, through phase space.

As a simple example illustrating dynamical-system features, take an unbalanced bicycle wheel rotating in a vertical plane (Strogatz, 2015). This system has only one moving part, the wheel. The stable equilibrium position for that system is to have the unbalanced weight hanging down directly below the axle. If the wheel is set rotating, the wheel’s speed increases as the weight approaches its equilibrium position, and decreases as it moves away. If the energy of motion is not too large, the wheel’s speed decreases until it stops, then starts rotating back toward the fixed equilibrium point, then slows again, stops, then rotates back. In the absence of friction, this oscillating motion continues ad infinitum. In phase space, the phase point’s trajectory is an elliptical orbit centered on an attractor located at the unbalanced weight’s equilibrium position and zero velocity. The ellipse’s size (semi-major axis) depends on the amount of energy in the motion. The more energy, the larger the orbit.

If, on the other hand, the wheel’s motion has too much energy, it carries the unbalanced weight over the top (Strogatz, 2015). The wheel then continues rotating in one direction, and the oscillation stops. In phase space, the phase point appears outside some elliptical boundary defined by how much energy it takes to drive the unbalanced weight over the top. That elliptical boundary defines the attractor’s basin of attraction.

Chaotic Attractors

To illustrate how a dynamic system can become chaotic requires a slightly more complicated example. The pitch-control system in an aircraft is particularly apropos equities markets. This system is a feedback control system with two moving parts: the pilot and aircraft (Efremov, Rodchenko, & Boris, 1996). In that system, the oscillation arises from a difference in the speed at which the aircraft reacts to control inputs, and the speed at which the pilot reacts in an effort to correct unintended aircraft movements. The pilot’s response typically lags the aircraft’s movement by a more-or-less fixed time. In such a case, there is always an oscillation frequency at which that time lag equals one oscillation period (i.e., time to complete one cycle). The aircraft’s nose then bobs up and down at that frequency, giving the aircraft a porpoising motion. Should the pilot try to control the porpoising, the oscillation only grows larger because the response still lags the motion by the same amount. This is called pilot induced oscillation (PIO), and it is a major nuisance for all feedback control systems.

PIO relates to stock-market behavior because there is always a lag between market-price movement and any given investor’s reaction to set a price based on it (Baron, Brogaard, Hagströmer, & Kirilenko, 2019). The time lag between intention and consummation of a trade will necessarily represent the period of some PIO-like oscillation. The fact that at any given time there are multiple investors (up to many thousands) driving market-price fluctuations at their own individual oscillation frequencies, determined by their individual reaction-time lags, makes the overall market a chaotic system with many closely spaced oscillation frequencies superposed on each other (Gleick, 2008).

This creates the possibility that a sophisticated arbitrageur may analyze the frequency spectrum of market fluctuations to find an oscillation pattern large enough (because it represents a large enough group of investors) and persistent enough to provide an opportunity for above-market returns using a contrarian strategy (Klock, & Bacon, 2014). Of course, applying the contrarian strategy damps the oscillation. If enough investors apply it, the oscillation disappears, restoring weak-form efficiency.

Conclusion

Basic market theory based on Hayek’s (1945) description assumes there is an equilibrium market price for any given product, which in the equity-market case is a company’s stock (Fama, 1970). Fundamental (i.e., strong-form efficient) considerations determine this equilibrium market price (Chauhan, et al, 2014). The equilibrium price identifies with the attractor of a chaotic system (Gleick, 2008; Strogatz, 2015). Multiple sources showing market fluctuations’ sensitive dependence on initial conditions serve to bolster this identification (Fama, 1970; Baron, Brogaard, et al, 2019; Bhattacharya, et al, 2017). PIO-like oscillations among a large group of investors provide a source for such market fluctuations (Efremov, et al, 1996).

References

Baron, M., Brogaard, J., Hagströmer, B., & Kirilenko, A. (2019). Risk and return in high-frequency trading. Journal of Financial & Quantitative Analysis, 54(3), 993–1024.

Bhattacharya, S. N., Bhattacharya, M., & Roychoudhury, B. (2017). Behavior of the foreign exchange rates of BRICs: Is it chaotic? Journal of Prediction Markets, 11(2), 1–18.

Chauhan, Y., Chaturvedula, C., & Iyer, V. (2014). Insider trading, market efficiency, and regulation. A literature review. Review of Finance & Banking, 6(1), 7–14.

Efremov, A. V., Rodchenko, V. V., & Boris, S. (1996). Investigation of Pilot Induced Oscillation Tendency and Prediction Criteria Development (No. SPC-94-4028). Moscow Inst of Aviation Technology (USSR).

Fama, E. (1970). Efficient capital markets: A review of theory and empirical work. The Journal of Finance, 25(2), 383-417.

Farazmand, A. (2003). Chaos and transformation theories: A theoretical analysis with implications for organization theory and public management. Public Organization Review, 3(4), 339-372.

Gleick, J. (2008). Chaos: Making a new science. New York, NY; Penguin Group.

Hayek, F. A. (1945). The use of knowledge in society. American Economic Review, 35(4), 519–530.

Klock, S. A., & Bacon, F. W. (2014). The January effect: A test of market efficiency. Journal of Business & Behavioral Sciences, 26(3), 32–42.

Strogatz, S. H. (2018). Nonlinear dynamics and chaos. Boca Raton, FL: CRC Press.