Apple’s Stock Split – Why Stock Splits do Matter!

With the news of Apple Inc. announcing a 7-for-1 stock split, the subject of stock splits have been in the financial news often. The consensus from journalists and academics alike seems to be that stock splits don’t matter – a simple division exercise.

What if stock splits do matter? What if the very act of splitting a company’s stock price, in this case Apple, from the low $600’s to $90 a share substantially increases our calculation of fair market value or model price?

What if I disclosed here that Apple’s “innocuous” (I will explain this quote later in the blog) 7-for-1 stock split increased the company’s fair market value by 22% or a cool $120 billion dollars.


Heresy, you say!


Let’s examine or parse a couple of financial articles – one article and one video – discussing Apple’s stock split that I found interesting over the last week.


The first article that caught my eye on the subject of stock splits was written by Mr. David Milstead of the Globe and Mail’s Report on Business. (Thursday, May 29th)


Mr. David Milstead writes.


Apple’s split is scheduled for June 9, benefiting all who own the shares as of June 2. In the strictest sense, the split will “do nothing,” [referencing Tim Cook’s comments on stock splits some time ago], as one Apple share trading at $700 is no more valuable than seven Apple shares trading at $100. That’s the basic economics of a stock split, and the reason why market professionals say splits have little meaning.


David continues,


Academic research has suggested stocks that split tend to outperform the shares of similarly sized companies in the near term…


Yes, this above noted phenomena has been reported in academia for quite sometime (over performance usually after the announcement of the stock split) and David continues his thought by offering what some academics are thinking as to why these gains are seen.


… in part because they’re an underappreciated signal of confidence: A management team that recommends a split to its board is confident the shares won’t drift lower.



The other article (video) of note on the subject of stock splits comes from the 67th CFA Institute Annual Conference held in Seattle this past May (2014) .  (OK, I can’t help myself poking fun at these guys!)

In this video (6:46 minutes) Mr. John Authers of the Financial Times interviews Mr. Aswath Damodaran, professor of finance at NYU Stern Business School about Apple.


In this interview, Mr. Damodaran correctly comments that in 2013 Apple announced a cash dividend (its first ever), corporate stock buybacks and significant borrowings (debt) and Apple’s stock did nothing to trend lower. He continues his observations by noting in April of this year Apple announces a dividend increase, more corporate buybacks, additional borrowings and an “innocuous” (7-for-1) stock split; further observing “seems to have triggered a move in the market [of the stock]”.


What’s going on here? Antidotal evidence seems to be piling up? Stock splits seem to have an unexplained positive impact on share values even though the simplistic theoretical textbook explanation seems to be wanting.


Enter Convexity


Model Price Theory (MPT) has many new concepts to offer the field of finance and investment management. Each of the new and original concepts – see Key Concepts tab – is grounded in a theoretical framework that is unique to MPT. Our convexity calculation variable is so important it’s one factor in our 3-factor algorithm that produces our model price value that you see on our model price charts.


Of course all public companies produce financial statements that include a balance sheet. All balance sheets have unique qualities that are specific to the company’s business, industry and choices made by the CEO and the Board of Directors on how they want to run the company. By analyzing each company’s balance sheet Model Price Theory (MPT) determines how the economic structure of the balance sheet is configured. More specifically a company’s economic structure can be viewed as a convex curve representing the specific nature of the balance sheet in question.


After a multitude of calculations we produce a convex curve that is unique to each company in our database. Some companies have very steep convex curves while others are relatively flat. The companies with steep convex curves may have little or relativity small amounts of recorded capital on their balance sheets’ for the simple reason they need little to no capital to run their businesses. Conversely companies that have very large balance sheets, relative to the size of the business, have convex curves that are relatively flat.


An example of a Convex Curve calculated from a public company's balance sheet

An example of a Convex Curve calculated from a public company’s balance sheet


So why should anybody care about the steepness of some calculated convex curve?


There are a lot of influences that are brought to bear on a public company’s stock price. One of the influences, according to Model Price Theory (MPT), is the feedback between the actual stock price dollar value and the calculated convex curve. As the stock price value (the actual number) moves up or down and depending on where the dollar value and the steepness of the convex curve intersect, feedback between these two variables will impact the fundamental value or fair market value of the company.


Assuming a company has a highly convex economic structure and a very low stock price (say penny stock), the feedback between the two can cause the stock price to be volatile. As the stock price increases in price value, say from $0.80 to $0.85 cents, the fundamental market value of the company increases substantially more than the change in price value because the steepness of the company’s convex economic structure curve. With the fundamental market value of the company increasing exponentially relative to the price movement may provide a further warranted price move, say $0.85 to $0.90 cents, recognizing the positive change in fundamentals. This feedback loop, between the company’s stock price and the convex economic structure of the company’s balance sheet, can go back and forth creating visible stock price momentum – oversized capital gains.

Unfortunately before you get too excited about this phenomenon the same feedback loop can happen on the downside as well.


Anecdotally this explains why lower priced stocks have more actual price volatility, especially penny stocks, than higher price stocks. Also this feedback loop is prominent in what is known as momentum stocks.


We Reduced Convexity to a Single Variable


We realized that looking at convex curves and their steepness was going to be a lot of work and interpretation. So we computed a variable that would combine the steepness of a company’s convex curve with the stock price dollar value of the company. So a company that has a convexity value of say 1.5 has a lot less convexity or share price feedback loop than a company with convexity of say 5.0.


Make sense.


With this background let’s start talking about Apple, Inc.


First let’s look at this table comparing the convexity values of the undernoted companies.

Companies Convexity Score
Microsoft Corp. 1.58
Oracle Corp. 1.54
Intl. Business Machines Corp. 1.14
Intel Corp. 1.65
Cisco Systems Inc. 1.89
S&P 500 Index 1.27
Apple 0.12



As one can see Apple’s convexity score (value) is very low compared with other large capitalized technology companies and the S&P 500.


If Apple’s management increased it’s convexity value the calculation of our model price or fundamental value would also increase.


So how do you increase Apple’s convexity?


There are two ways of increasing Apple’s convexity. The first is to focus on the balance sheet. Reducing the overall size of Apple’s balance sheet would make Apple’s convex curve steeper. This steepness would enhance the feedback loop between the positive stock movement and its fundamental value. Apple’s management starting in 2013 started this process by initiating a cash dividend and corporate stock purchases. Both of these actions in effect reduce the size of Apple’s balance sheet. Unfortunately the dollar size of these above noted corporate actions with Apple’s ample ongoing cash flow has had a negligible impact in doing anything to our convexity calculation. Laughingly with Apple’s bond deal (replacing Apple’s depleted cash) Apple’s convexity has gone from 0.14 back in January 2012 to 0.12 as of last week. You can see why Apple’s share price has languished for much 2013.


The second way of increasing convexity is to lower the stock dollar value of Apple’s share price. Yes, by doing a stock split. The lower the stock price dollar amount the higher convexity value computed. (Note: the act of splitting a company’s stock and lowering the monetary value of the stock price will not change the shape of the company’s convex economic structure curve but will change the intersection or the steepness where the Apple share price intersects on our computed curve)


Apple’s management shocked everybody, including myself, by announcing a 7-for-1-share split in April. So the question is what would happen to our calculation of convexity value with this corporate action. Not surprisingly our convexity value will increase from the present value of 0.12 to 0.84. This is probably one of the largest jumps in convexity I have ever seen – granted there are only a handful of companies with convexity value as low as Apple’s to begin with.


So what does this mean?


Below I have reproduced our model price chart of Apple, Inc. for Wednesday, May 28th from our Facebook application.


Apple's Model Price chart on Facebook captured on Wednesday night

Apple’s Model Price chart on Facebook captured on Wednesday, May 28, 2014


I have annotated on the chart where Tim Cook announced the stock split and the market’s positive reaction. This announcement helped close the gap between Apple’s share price and our calculation of fair market value. This is the fundamental view of how Apple looks at present and note that our calculated model price value is $628.99.


For fun, (yes, it’s fun) I split Apple’s stock in our database on the announced 7-for-1 basis and allowed our algorithms to recompute a new model price value allowing for the recalculated change in the value of our convexity score because of Apple’s lower stock price value producing the model price chart below.


Apple's new Model Price chart showing the impact of the 7 for 1 share split as of the same Wednesday May 28, 2014

Apple’s new Model Price chart showing the impact of the 7 for 1 share split as of the same Wednesday May 28, 2014



No other data inputs have been changed from the original Apple model price chart produced above. The only change I made was the share split announced by company’s management. With a lower share dollar value producing a higher convexity value (0.12 to 0.84) Apple’s new model price value would be $109.50 post split. Multiplying Apple’s new model price of $109.50 times 7 is $766.50.


Yes, just by changing the dollar value of Apple’s share price through a share split Apple increased their model price from $628.99 to $766.50! That’s a 22% increase or $120 billion increased in Apple’s market capitalization. Not bad!




Share splits do have an impact on fair market values of publicly traded companies both in terms of intrinsic fundamental value and over performance contrary to ‘experts’ in the field of finance and investment management. Model Price Theory (MPT) through our mathematical variable called convexity can help explain why share splits can have positive impacts on share price performance. By doing an “innocuous” share split Apple’s management will benefit all stakeholders, especially common shareholders, in making Apple more valuable. Hopefully through management’s other corporate actions we’ll see a steady increase in our convexity value further increasing the fair market value of Apple in the future.

One response to “Apple’s Stock Split – Why Stock Splits do Matter!

  1. LAURIE STAMP June 2, 2014 at 5:50 am

    Excellent article about stock splits, easy to read and understand.

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