Money Stuff: Apple Stock Will Get Cheaper

Money Stuff

Stock split

The way that Bitcoin works is that there will always be a maximum of 21 million Bitcoins, and if Bitcoin ever becomes the dominant store of value in the world then each of those Bitcoins will be worth an absolute ton of money. Like if you figure the global broad money supply is $90 trillion, then if Bitcoin becomes the new world currency then each Bitcoin might be worth $4 million or so. Anyone who owns a Bitcoin will be rich, but there won't be that many of them; certainly no more than 21 million people could own a Bitcoin.

This would be a big problem, for a proposed currency, if it were indivisible, if you could only own zero or one or two or some other integer number of Bitcoins. Even if it were a little bit divisible, like the dollar—if you could own 0.01 or 0.02 Bitcoins, etc.—it would not be very practical.

So the way it works is that Bitcoin is extremely divisible. The smallest unit is one one-hundred-millionth of a Bitcoin, which is called a "satoshi." Even in a world where each Bitcoin is worth $4 million—where, again, Bitcoin replaces all other currency in the world—a satoshi will be worth a few pennies, and there will be 2.1 quadrillion of them.

Of course none of this is true right now. Right now a Bitcoin is worth about $11,000, which means a satoshi is worth about 1/100th of a cent. Almost nothing in your daily life costs a Bitcoin, or a couple of Bitcoins; nothing at all costs a satoshi, or a couple of satoshis. If you don't have a lot of money and are looking to casually dabble in Bitcoin, you probably won't buy a Bitcoin, or even half a Bitcoin, but you might buy, say, a couple of million satoshis. 

Is that weird? Maybe a little? Not too weird. Nothing in the Bitcoin system is human-scale; you never deal in a normal number of things. But Bitcoins live on computers. Your computer is fine using a bunch of digits; it's fine putting the decimal point wherever it is supposed to go. Bitcoin is a currency system that was designed from the beginning for computers, and so it is freed from the constraints of being intuitively legible to humans. Freed, also, from the constraint of physical representation; there are no satoshi coins.

Also I am sorry to say it but Bitcoin has not replaced all other currencies, not at all, and so in fact if you are looking to casually dabble in Bitcoin you might find yourself buying, say, "$500 worth of Bitcoin." You will have an intuitive round integer number of dollars that you want to invest, you know what a dollar is, and the computer will do the weird work of translating it into, like, 4.5 million satoshis.

In the broad historical sweep this is all mildly uncanny. A 19th-century Englishman would be perfectly comfortable with having four farthings in a penny and 12 pence in a shilling and 20 shillings in a pound and 21 shillings in a guinea and two shillings sixpence in a half-crown, but would be freaked out by the idea of 100 million satoshis in a Bitcoin; how would you make change? But we lived in a computerized world now, we have gotten used to the idea that everything is just numbers on a screen, and the roundness of the numbers doesn't matter that much. Sure, hundred-millionths, whatever.

How many shares of stock should a company have? I feel like if you start from this hypermodern mindset, the right answer might be … one? Infinity? "Shares, what are shares, why would a 'share' be a thing," would actually be the answer. A company should be a thing, and people should be able to own a portion of its equity, and the portion that each person owned would be expressed as an arbitrarily precise percentage of the total. So I might own 5.3% and you might own 0.084535% and someone else might own 0.000529193432142%. The "stock price" would be what we now call the "market cap": The market would place a value of $X on the company as a whole, and if I wanted to buy another 0.01429% I would pay 0.01429% of $X.

And in fact some private companies work this way; they have a partnership agreement saying "I'll get one-third of the profits and you'll get half and our friend will get one-sixth," and nobody will bother to work out how many "shares" there are, it's all just fractions.

Public companies still have shares, and you buy and sell integer numbers of shares on the stock exchange, though that is eroding a bit. A lot of the big retail brokerages offer fractional shares: Instead of buying one or two or 100 shares of a particular stock, you can buy 0.1 or 2.1 or $500 worth of shares. In a sense this is not "real": You do not own fractional shares on the company's share ledger; instead, your brokerage owns a whole number of shares, and gives you an entitlement to a fraction of them. But that's how everyone owns stock anyway—you do not generally own shares on the share ledger but through your broker—and the fractional shares are real enough for most purposes.

On the other hand the stock market was not built from the ground up on computers and hypermodernism, like Bitcoin was. It was built on, you know, farthings and half-crowns. The traditional, 19th-century answer to how many shares a company should have was that stocks should have a normal price, they should cost like $40 to $100 or so, and if a company's stock price got much higher than $100 it should do a stock split, giving everyone two $60 shares for every $120 share, so that it could continue to have a normal price.

This was so standard that, when Charles Dow created a stock index in 1884, he just averaged the dollar stock prices of a bunch of stocks. He didn't think about market-cap weighting, he didn't say knowingly to himself "the division of a company into shares is arbitrary and what I actually want to average is the total economic value of these companies," and he certainly didn't have a computer. He just averaged some stock prices, because the stocks had normal prices.

Apple Inc. is a computer company but it is also pleasingly old-fashioned:

Apple on Thursday announced in its fiscal third-quarter earnings that the Board of Directors has approved a four-for-one stock split.

That means that, for each share of Apple stock that an investor owns, they'll receive three additional shares. It also makes single shares in Apple more affordable for investors to buy. It follows a similar move Apple made in 2014, when it offered a 7-to-1 stock split. At the time, Apple was trading above $600 per share. The split brought shares of Apple to about $92 a share.

Stock splits are cosmetic and do not fundamentally change anything about the company, other than possibly making the shares accessible to a larger number of investors because of their cheaper price.

Since Apple stock currently trades above $380, it means investors should expect to again have a chance to buy a share of Apple for around $100, depending on where the stock trades at the end of August.

You can try to tell smart stories about why Apple would do this in a world where people understand that the division of a company into shares is arbitrary, and can trade fractional shares. At the time of Apple's last split, in 2014, one popular explanation was that Apple was trying to get into the Dow Jones Industrial Average, which is still price-weighted and so still has an old-fashioned fondness for normal-priced stocks, but that worked and now it's in the Dow so that's no reason to split again.

There are market-structure advantages to normal-priced stocks. In the olden days "round lots" were a thing; if you wanted to buy stock, it was better to buy round lots of 100 shares than odd lots of 1 or 2 or 95 or 105 shares. Brokers often charged higher commissions for odd lots, and a company that wanted to be friendly to retail investors would split its stock to keep the price of 100 shares reasonable. Retail brokers don't charge commissions anymore so that's not such a problem. Still round lots continue to get some special treatment in market-structure regulation, as we discussed at the time of the last split. If you want to buy or sell stock, you are effectively guaranteed to get the best available price posted on an exchange for a round lot, whether or not you are buying a round lot. If you want to buy 25 shares, and there are 25 shares available for $380 and 100 shares available for $380.10, the "national best offer" is $380.10 and you might get filled at $380.10 even though enough shares were available at the lower price. The higher a company's stock price, the more likely it is that the best price available will be for an odd lot, and people will end up getting worse deals; splitting the stock to lower the price might fix that.

Or there is an argument that high-priced stocks reduce liquidity because traders have less incentive to post quotes. It is good for a stock to trade at a bid/ask spread of a couple of "ticks," the minimum price increment for trading. If a stock is worth $50 and trades at a bid/ask spread of $49.99/$50.01, a trader who posts a bid to buy at $49.99 will be able to buy from anyone who wants to sell immediately. If it's worth $500 and trades at $499.90/$500.10, a trader who posts a bid to buy at $499.90 might lose out to a trader who bids $499.91. You can't reliably earn a "normal" spread by trading the stock, so your incentive to provide liquidity is lower. Nasdaq published a paper arguing this point:

[Some] stocks trade at large multiples of the tick increment, leading to wider spreads, increased prevalence of odd-lots, flickering quotations, and non-displayed trading that doesn't support price discovery. When ticks are too narrow, time priority for resting orders diminishes in value: traders patiently awaiting passive executions are outbid by economically insignificant amounts. At the extreme, outbidding is so inexpensive that time priority becomes essentially non-existent, destroying the incentive to post passive liquidity and reducing quote competition. As quote competition declines, price discovery weakens and spreads widen; when spreads widen, quote competition and price discovery weakens further and so on. Investors and issuers suffer.

If you like market structure you might find all of this stuff interesting, but I find it hard to believe that Apple cares.

I guess there are other practical considerations. Apple grants stock and options to its employees, but not fractional shares, so if it wants to fine-tune compensation it helps to have cheaper stock. It's not that compelling.

There's the symbolism of making it cheaper. Here is Jim Cramer, citing Apple's Tim Cook:

"I think Apple is taking the right move. Tim told me last night, 'Hey, I want more people in the stock,'" Cramer said on "Squawk Box." … "The idea that he wants more people in his stock is refreshing," Cramer said of Apple's Cook. "He doesn't play to the hedge funds. He plays to the people who buy the product and have 99% satisfaction rating. That's who he plays to." 

Sure, I guess, whatever. Apple is the fifth-most-popular stock on Robinhood, with almost 600,000 holders. They can all buy fractional shares. Fractional shares aren't perfect—they're not "real," you can't easily transfer them between brokerages, etc.—but they're good enough for most purposes. The price is not an actual impediment to anyone buying Apple stock. It just kind of feels like one.

I like trying to think of smart explanations for stock splits, but I don't really believe them? I think Cook's and Cramer's explanation is probably right, even though it does not make strict sense. Apple is probably splitting its stock because it will feel better to normal people to have a normal stock price than to have a high stock price. Other companies take a more coldly logical approach; Inc. closed at $3,051.88 yesterday. That's fine too. If you've got a hundred bucks you can buy an Apple share or 0.032767 Amazon shares, either way, it's fine. Perhaps we are in a transitional stage: 20 years ago stocks cost normal amounts and you'd buy them in units of 100 shares, in 20 years you will buy stocks in arbitrary decimal fractions and the price of "a share" won't matter at all, but right now it could go either way.

Fairness opinions

In a merger or acquisition, one company will sell itself to another company at some price. The company that is selling itself, the target company, will get a "fairness opinion" from its investment bankers, reassuring it that the price is fair. (The buyer will also sometimes get a fairness opinion from its bankers, particularly in a stock-for-stock deal.) Why does it get this opinion? You might naively answer, well, the company doesn't know how much it is worth, so it asks the bankers, and they tell it "we think you are worth $70 and the buyer is offering $80 so this is a good deal," or whatever, but this is not quite right. It's not totally wrong—often bankers will do valuations to help the company's board and management figure out how much they're worth, so they can know what a good price is—but it's not the point of a fairness opinion.

The point of a fairness opinion is that once upon a time in the 1980s a company sold itself, and shareholders sued the directors claiming that they'd sold the company too cheap, and a Delaware court held the directors personally liable because they hadn't done enough to establish that the price was fair. "We do not imply that an outside valuation study is essential to support an informed business judgment," said the court, "nor do we state that fairness opinions by independent investment bankers are required as a matter of law," but it might as well have: After that case (called "Smith v. Van Gorkom" or "TransUnion"), no board of directors is going to sell a company without a certificate from an investment bank saying that the price is fair.

Which means that the point of a fairness opinion is to certify that the company can do the deal that it wants to do. And so in an M&A process you might have a sequence like this:

  1. Target is trading at $50 per share; Acquirer offers $60 to buy it.
  2. Target calls its bankers and says "we like this deal but how do we get more money."
  3. Bankers prepare a valuation showing that Target is worth $80 to $90.
  4. Target shows this valuation to Acquirer and says "see, we are worth $80 to $90, give us $80."
  5. Acquirer says "we'll give you $62."
  6. Intense negotiations ensue and Target talks Acquirer up to $65.
  7. Target calls its bankers and say "we are happy with this deal, please give us a fairness opinion."
  8. Bankers prepare a fairness opinion showing that Target is worth $60 to $70, so a $65 price is fair.

I mean, that is a pretty stylized version, and well-advised targets and bankers will be a bit more subtle. But in general a target company will want two sorts of valuations from its bankers, one arguing that it is worth a lot of money (to negotiate a higher price), and another arguing that it's not worth so much money (to justify the price it accepts), and there will be a certain amount of artistry and lawyering involved in fitting them together.

You can be extremely cynical about this, or you could just be the regular amount of cynical about this. Banks do try to get it right; they sign their names to their opinions, and have standards and approvals and committees to make sure that they are justifiable. At the same time the valuation of a company is always going to be subjective and uncertain, and you could use a wide range of projected future cash flows and discount rates to get, more or less, any number you want.

Here's a cool new empirical paper from Matthew Shaffer of the University of Southern California on fairness opinions, titled "Are Third-Party Fundamental Valuations Relevant in Public-Company Takeovers?" Some of his findings are mildly cynical. For instance, in many acquisitions both the buyer and the seller will get a fairness opinion, and mildly cynical logic would tell you that the buyer's opinion should have a higher value than the seller's. (If Acquirer is paying $65 for Target, Acquirer's bankers will tend to say "this deal is fair to Acquirer because Target is worth $70," and Target's bankers will tend to say "this deal is fair to Target because Target is worth $60," though really they'll both give ranges and can overlap.) And in fact:

Cain and Denis (2013) note that target-side fairness-opinion providers are alleged to be biased to produce lower valuations of the target, to make the negotiated deal price appear more attractive by comparison to target shareholders, relative to acquirer-side providers, to facilitate deal completion. Consistent with this, I find that target-side advisers produce systematically lower DCF [discounted cash flow] valuations relative to acquirer-side advisers when valuing the target in the same transaction, including when subsetting down to standalone (i.e., synergy-exclusive) valuations (Table 9). However, this difference could represent disagreement between the target's and acquirer's advisers, which would also explain why they would engage in the transaction. (E.g., the acquirer could anticipate faster profitability and free-cash-flow growth for the target than the target's management does.) So, I examine how the discount-rate (WACC) assumptions vary between target vs. acquirer-side advisers' valuation models. This provides an especially credible opportunity to test for bias in valuations because economic and financial theory, as well as established industry practices, provide rich guidance on the normative determinants of discount rates. I find that target-side providers assign systematically higher WACCs in their DCF valuations of targets, relative to acquirer-side providers in the same transaction, and relative to an estimated normative benchmark. This is consistent with opinion providers toggling their valuation models to fit the desired result ex post, as alleged, rather than producing a fully independent valuation audit.

Again, my view is that the point of a fairness opinion is to justify a negotiated price, not to provide a fully independent valuation audit, so I buy that.

But Shaffer also finds that fairness opinions are surprisingly good at valuation, at least in some cases. For instance a question you might ask, in my stylized example above, is: If Target's stock was trading at $50, and Target's bankers prepare a fairness opinion saying it's worth $60 to $70, who was right? Did the stock market undervalue the company, or did the bankers overvalue it? It is generally hard to answer this question because, ordinarily, Target goes away after the merger, but sometimes not[1]:

I identify a subsample of transactions in which targets had their offers unexpectedly terminated (almost always due to regulatory scrutiny) at a late stage in the deal process, after receiving and disclosing their fairness valuations, and, thus, continued to trade as independent firms. For this subsample, I can implement a test akin to the classic equity analyst test above. I first translate the DCF fairness valuation of each target into an implied predicted return. I find that this can forecast the targets' subsequent abnormal returns after termination of the deal, over the medium to long-term horizon. This difference persists after additionally conditioning on the target's foregone market premium. That is, the fairness valuations can forecast the former target's medium-to-long-term price performance, and this difference is not subsumed by the target's pre-deal market price. I interpret this as evidence in favor of the claim that these fundamental valuations can provide a signal about the targets' relative ex ante fundamental mispricing.

So there is some evidence that, when a company's investment bankers and its stock price disagree about its value, the bankers might be right. 

Even better, when the investment bankers and the buyer disagree, the bankers might be right. Typically a target's fairness opinion will provide some range of values, and the deal price will be in that range or above it. If the deal price is $65, Target's bankers might say Target is worth $60 to $70, or $55 to $65, or $65 to $75, or $50 to $60. If the deal price is above the range then Target's bankers are essentially saying that Acquirer is overpaying. If the deal price is in the middle of the range then, you know, good job everyone. If the deal price is at the bottom of the range—if the fairness opinion values target at $65 to $75, for a $65 deal price—then the implication is that Target didn't have much negotiating power and its bankers needed to work hard to massage the numbers to get the fairness opinion to work.[2]

Does this matter? Is it all for show, all fake numbers, or do the bankers' numbers imply how good a deal the buyer is getting? If the deal price is at the top of, or above, the fairness-opinion range, is the acquirer actually overpaying?

I use a toy model of an acquisition to calculate what the impact of the transaction on the acquirer would be if the fairness valuation of the target correctly measured its value to the acquirer. I call this quantity the FOPRa (for "Fairness Opinion Predicted Return for the Acquirer"). For example, suppose that the acquirer has a market cap of $100, and it buys a target for $10, but the average fairness valuation indicates that the target is worth $9. If the fairness opinion valuation correctly measured the value of the target to its acquirer, the NPV to the acquirer from the transaction would be −$1, yielding a FOPRa of −1%. This allows me to validate the fairness opinion valuation of the target using the ex post outcomes for the acquirer.

I find that the FOPRa can forecast the announcement-date abnormal returns for the acquirer (Figure 2 and Table 7). This holds after controlling for the the TSPRa—the "Target Pre-Deal Stock Price Predicted Return for the Acquirer," which is constructed equivalently, with the target's pre-deal stock price in lieu of the fairness valuation. In other words, the fairness valuation of the target can forecast acquirer performance incremental to the target's pre-deal stock price.

When the bankers and the acquirer disagree, it is not just because the bankers put some arbitrary numbers in a spreadsheet to make the target feel better. Those arbitrary numbers are sometimes more correct than the actual negotiated price.

Reps and warranties

The Wall Street Journal  has a fascinating story about the weird investment that SoftBank Group Corp. sort of made in Wirecard AG last year, not long before Wirecard's collapse in a fake-revenue scandal. (SoftBank didn't technically make the investment—an affiliated fund owned largely by SoftBank executives did—and the fund immediately sold all of the risk to third parties, making this actually a good deal for SoftBank, other than as a reputational matter.) There is a lot going on but this is the part I found most interesting:

SoftBank set strict conditions, according to some of the people familiar with the deal. Wirecard had to address specific allegations about its accounting in deal documents with SoftBank. This included Wirecard promising that an internal spreadsheet described in Financial Times articles as evidence of accounting irregularities didn't exist. 

As it happens, oops:

In mid-October, the Financial Times published excerpts of the spreadsheet Mr. Braun had told SoftBank didn't exist, reviving concerns about the company's accounting.

But there is a deeper conceptual mistake here. The point of "representations and warranties"—the factual promises that a company makes in deal documents—is, largely, to force disclosure. The way it works is that the buyer sends an investment agreement to the seller, and the agreement says "Seller promises it has no legal violations," and the seller says, well, actually, we have a few parking tickets, and it discloses those violations to the buyer, and the final agreement says something like "except as disclosed on Schedule X, Seller has no legal violations." The buyer asks the seller to make the representation not because it expects the seller to be totally clean—not because it expects the representation to be completely true—but because the representation will focus the seller's mind and force it to disclose anything that might be trouble.

For this to work you need some baseline level of trust; it works in normal situations, but not so much in frauds. The seller will always represent something like "our public financial statements accurately represent our financial condition"; perhaps it will qualify that by telling the buyer about open questions that its auditors have raised about a few debatable matters of accounting policy. But it will never get that draft representation and reply "oh actually funny story all of our financial statements are fake." Faking the financial statements is the hard part! Once you've done that, signing a representation to a potential investor saying "our financial statements are not fake" is just routine.

If someone reputable—like, say, the FT—tells you that a company is cooking its books, and you are considering a big investment in that company, you can't go to the company and be like "we'll give you a billion dollars if you promise that you're not cooking the books." Once you are asking about specific allegations of fraud, you can't just take the company's word for it! You've got to satisfy yourself that the spreadsheet doesn't exist!

People are worried about bond market liquidity

The Financial Times has a deep dive on "US Treasuries: the lessons from March's market meltdown." One way to tell this story is that in olden times Treasuries were mostly traded through banks, which bought and sold them and kept large inventories and could be relied on to stabilize prices a bit, but in modern times Treasuries are mostly traded through electronic market makers, who do not hold long-term positions, and are largely held by relative-value hedge funds, who hold very leveraged positions:

Compounding the volatility was an under-appreciated evolution in the Treasury market ecosystem. Over the past decade, high-speed algorithmic trading firms have become increasingly integral in matching buyers and sellers in the Treasury market, with many "primary dealers" — the club of big banks that arrange government debt sales — copying their tactics. …

In normal times, algorithmic market-making helps to keep trading conditions smooth and ensures tiny gaps between bids and offers for even big chunks of Treasury bonds. But when volatility spikes, market-makers automatically ratchet back the size of trades they are willing to do, and pricing quotes on purchases and sales are widened to compensate for the additional risks.


The dysfunction was instead exacerbated by the unwinding of what is known as the "basis trade". It involves highly-leveraged market participants arbitraging the difference between Treasury futures and Treasury bonds, which are slightly cheaper than futures due to different regulatory treatment. A favoured trading strategy has been to buy cash Treasuries and sell the corresponding futures contract.

The price differential is often small, but hedge funds can juice returns by using huge amounts of leverage. The main way to do so is by swapping Treasuries for more cash in the "repo" market, one of the world's largest hubs for short-term, collateralised loans. The extra cash can then be recycled into even bigger positions, repeating the process to further augment returns.

These trades have exploded in popularity since the financial crisis, as hedge funds — such as Capula Investment Management, Millennium Management, ExodusPoint Capital Management and Citadel — jumped into the void left by hamstrung bank trading desks. …

As is so often the case in financial markets, the tradeoff here is that these new mechanisms are more efficient than the old ones, most of the time: Electronic market makers offer faster trades at tighter spreads than banks used to, and highly levered relative-value hedge funds will pay a bit more for Treasuries than real-money investors will. But they are also more fragile: The market makers will withdraw and the hedge funds will blow up in a crisis.

"One can argue that the [activity] helps to lower interest costs for taxpayers during periods where there is no volatility, but are we comfortable with central banks having to step up in this magnitude and become liquidity providers of last resort when this levered trade blows up going forward?" asks Matthew Scott, head of the global rates, securitised assets and currency trading teams at AllianceBernstein.

But one specific lesson of March might be … yeah, that's fine? I mean, for Treasuries, at least? It is weird and complicated for the Fed to bail out, say, high-yield bond markets, but the Fed is actually pretty good at buying and selling and repoing Treasuries, it does that as part of its ordinary operations, so stepping in to do a ton of it during a crisis is relatively fast and straightforward and low-risk. It's possible that replacing a system of "the banks buy and sell the Treasuries, and are kind of slow and expensive and sometimes blow up" with a system of "hedge funds and electronic traders buy and sell the Treasuries, and are good and fast and cheap, but occasionally they stop working and then the Fed has to do it instead" is strictly an improvement?

Things happen

Inside Goldman's Five-Day Race to Seal a 1MDB Deal With Malaysia. (Earlier.) Private equity gags on its own medicine in contentious debt battles. Antique Chinese bonds are now in play. Gold Traders Issue Largest Delivery Notice on Record at Comex. Affirm Prepares IPO That Could Value Fintech Firm at Up to $10 Billion. People are worried about stock buybacks. Germany Asks Russia to Help Find Former Wirecard Executive. Twitter Links Hack to Phone-Based Phishing AttackLinkedIn spy scandal shines spotlight on China's online espionage.

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[1] Some parentheticals and citations omitted.

[2] If the deal price is *below* the range, then the price is "unfair" and the target won't get a fairness opinion. You won't see those, though: If Target's bankers won't give it a fairness opinion, then either (1) the deal won't happen, (2) the price will get negotiated up, (3) the bankers will be told to try harder and will revise their range down, or (4) Target will hire new bankers who will do it.


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