One Company, Two Prices: The Royal Dutch and Shell Puzzle

The law of one price is about as fundamental as finance gets. Two claims to the same cash flows must trade at the same price. If they do not, buy the cheap one, sell the expensive one, and you have free money. Because free money cannot exist, the prices must be equal.

Froot and Dabora found a case where the law of one price was violated for decades, in enormous, heavily traded, world-famous stocks, and where the deviation was predictable from something that should be utterly irrelevant: which country the stock happened to be listed in.

The problem: the same company, in two flavours

The star of this paper is Royal Dutch Petroleum and Shell Transport and Trading, one of the strangest corporate structures ever devised, and a gift to financial economists.

In 1907, two oil companies, one Dutch and one British, decided to merge their operations but not their share listings. They created a single combined business, and agreed by contract that all the cash flows would be split in a fixed ratio: 60 percent to Royal Dutch, 40 percent to Shell Transport. Forever. Written into the founding agreement.

Royal Dutch shares traded mainly in Amsterdam and New York. Shell shares traded mainly in London.

Now, the two stocks are claims on the same underlying pot of oil money, in a fixed, contractually specified proportion. So the market value of Royal Dutch should be exactly 60 over 40, or 1.5 times, the market value of Shell. Always. This is not an estimate. It is not a valuation opinion. It is contractual arithmetic. Whatever the oil business is worth, the split of it is fixed.

Froot and Dabora simply checked whether the ratio held.

It did not. The two stocks deviated from their contractual ratio by large amounts, sometimes by tens of percent, for long stretches of time, over many years. One twin would be persistently expensive and the other persistently cheap, and the gap would sit there, visible to everyone, refusing to close.

These are not obscure micro-caps. This is one of the largest companies in the world, followed by every analyst on earth, traded in the deepest markets on the planet.

The key idea via analogy: two tickets to the same concert

Imagine a concert where two ticket booths sell tickets to the same show, the same seats, the same night. One booth is in Paris and one in Berlin. The tickets are literally interchangeable.

You would expect identical prices, because anyone could buy in the cheap city and sell in the expensive one.

Instead, you find that when the French stock market is having a good week, the Paris ticket gets more expensive. When the German market rallies, the Berlin ticket does. The tickets drift with the mood of the city they are sold in, not with anything about the concert.

That is precisely what Froot and Dabora found, and it is the paper's central result.

The relative price of the twins moved with the markets where they traded. When the UK market rose, Shell (traded in London) got relatively more expensive. When the US and Dutch markets rose, Royal Dutch got relatively more expensive.

Sit with the strangeness of this. The location of trading affected the price of a claim on a fixed pot of cash. The oil in the ground does not know where the shares are listed. The 60/40 split does not change when the FTSE rallies. The only thing connecting Shell's price to the British stock market is that British investors, in a British mood, happen to be the ones trading it.

Froot and Dabora went hunting for boring, rational explanations, and they went through them carefully, because if any of them worked the paper would be dead:

• Currency movements? Checked. Cannot explain it.
• Different dividend policies or the timing of ex-dividend dates? Checked. Not enough.
• Differences in voting rights or control? Checked. Not enough.
• Different corporate expenditures at the parent level? Checked. Not enough.
• Taxes and investor heterogeneity? This is the one that gets closest. Different investors in different countries face different tax treatment of dividends, which gives them genuinely different preferences over the twins. Froot and Dabora find that tax-induced clienteles can explain some of the pattern. But not all of it, and not the co-movement with local markets.

So after eliminating the rational explanations, what is left is a clientele and sentiment story: each twin is held disproportionately by investors in its own country, and those investors' moods and flows move the local market as a whole. When British investors buy stocks, they buy Shell, and Shell goes up relative to Royal Dutch, for no reason connected to oil.

And then the obvious question: why didn't arbitrageurs fix it? The trade is nearly perfect. Buy the cheap twin, short the expensive one, wait for convergence. The cash flows are contractually locked, so this is about as close to riskless as arbitrage gets.

The answer is the familiar one, and it is why this paper is a pillar of the limits-of-arbitrage literature. The gap can widen before it closes. An arbitrageur who put the trade on when the twins were 10 percent apart could watch them go to 20 percent apart, face margin calls, and be forced out at the worst possible moment. There is no date at which convergence is guaranteed. This is textbook noise trader risk, and it is exactly the trade that helped destroy Long-Term Capital Management, who reportedly held the Royal Dutch and Shell spread and were forced to liquidate it at a loss during the 1998 crisis, before it eventually converged.

Why it mattered

• It is one of the cleanest violations of the law of one price ever documented. No risk model needed. No valuation assumptions. The 60/40 split is written in a contract. Either the ratio holds or it does not, and it did not.
• It shows that mispricing lives in the biggest, most liquid stocks too. The comfortable assumption is that anomalies hide in small, obscure, illiquid corners. Royal Dutch and Shell were among the largest, most scrutinized securities on earth. If the law of one price fails there, the idea that markets are precisely efficient anywhere becomes hard to sustain.
• It proves that "who is trading" affects prices. In a frictionless world, the identity and location of the marginal buyer is irrelevant. Froot and Dabora show it is not. Investor clienteles and their local sentiment leave a footprint on prices, which is a foundational fact for anyone thinking about flows, index inclusion, or market segmentation.
• It is the empirical proof that arbitrage can be right and still lose. The convergence trade here was as certain as they come, and it still could not be safely held. That is Shleifer and Vishny's theory, demonstrated in the wild, at the scale of billions of dollars.

The honest limitations

• The taxes-and-clienteles story is not fully dismissed. Froot and Dabora themselves find that tax-driven investor heterogeneity explains part of the puzzle. A determined rationalist can argue that with enough institutional detail (tax treaties, withholding rules, index membership, pension fund mandates) most of the gap could be rationalized. They would be arguing uphill, but the hill is not vertical.
• The convergence has a happy ending that undercuts the drama slightly. Royal Dutch and Shell eventually unified into a single company in 2005, and the gap closed. So the mispricing was real and it did eventually pay. It just took a very long time, which is precisely the paper's point but also means the market did, sluggishly, get there.
• Two firms is a small sample. The paper looks at Royal Dutch and Shell and a couple of other dual-listed twins (Unilever, and a few others). The mechanism is compelling but the statistical base is a handful of cases.
• It does not tell you how to size the trade. The lesson is that the gap can widen. It does not tell you how far, which is the only thing that would have saved you.

The one-line takeaway

Froot and Dabora showed that two stocks with a contractually fixed claim on the same cash flows traded at persistently different prices for decades, and that each one drifted with the stock market of the country it happened to be listed in, which means the location of trading, a thing that should be completely irrelevant, is quietly sitting inside the price.