Do Bitcoins Violate a Fundamental Economic Law?

Want to buy a bitcoin?

If you click over to Mt. Gox, the most famous bitcoin exchange, one unit of the crypto-currency will set you back $145. But at Bitstamp you would pay only $129. (At time of writing; prices can change quickly.)

Mt. Gox traders are thus paying a 12% premium for their bitcoins.

That spread seems to violate a fundamental economic law. When transaction costs are low, identical items should trade at nearly identical prices. Otherwise, arbitrageurs would step in to buy cheap and sell dear until the price gap narrows.

But that isn’t happening.

The “law of one price” used to hold. Last fall and winter bitcoin prices at the two big exchanges typically differed by less than 2 percent, a reasonable range given exchange fees and the cost of money transfers (click here if you don’t see the chart or want it bigger):

Bitcoin Spread

In April, however, the bitcoin market went haywire. After spiking to $266 on Mt. Gox, bitcoin prices cratered, falling as low as $54 just two days later. That volatility created large, but temporary spreads between prices on different exchanges (and made it difficult to measure spreads accurately).

When conditions calmed, spreads returned to normal. And then Mt. Gox’s troubles began.

On May 14 the U.S. government accused the exchange of operating an illegal money service business. The government seized $5 million that Mt. Gox held at Dwolla (an online payment processor) and Wells Fargo.

Fearing for their money, Mt. Gox customers converted their at-risk dollars into easy-to-withdraw bitcoins, and the Mt. Gox-Bitstamp spread spiked to 5%.

Spreads briefly normalized until Mt. Gox announced that it was suspending U.S. dollar withdrawals. Mt. Gox had become a Roach Motel (or, if you prefer, a Hotel California) for U.S. dollars. Traders could check their dollars in, but they couldn’t check them out.

Customers responded as you would expect. The spread spiked to 6%, as Mt. Gox traders again converted dollars into bitcoins. The spread briefly narrowed after Mt. Gox’s July 4 announcement of resumed dollar withdrawals. But spreads then spiked to record levels once Mt. Gox customers started reporting that withdrawals remained slow or nonexistent.

Mt. Gox prices are higher than on Bitstamp today because customers apparently can’t get their dollars out of Mt. Gox. So they pay extra for bitcoins. For those customers, a Mt. Gox bitcoin is different from one anywhere else. So the Mt. Gox price isn’t a clean measure of a bitcoin’s value. Instead, it measures the value of a bitcoin plus the desperation of Mt. Gox’s customers.

But that still leaves a puzzle. It makes sense that customers will pay a premium to get their money out. But who is willing to take the other side of the trade, selling bitcoins in return for “Mt. Gox dollars”?

As best as I can tell, those traders have stayed silent on the bitcoin chat boards. Perhaps they are newcomers who think they’ve found an arbitrage opportunity and don’t realize their dollars will be hard to withdraw. Or perhaps they believe that Mt. Gox will get its act together. (A more sinister take, raised on the boards, is that some preferred traders do have the ability to withdraw.) Whatever the case, they stand to make a tidy profit if they can get their dollars out, and sorely disappointed if they can’t.

Sources: For a quick explanation of bitcoin, try this introduction. For price data from numerous exchanges, visit bitcoin charts. My chart uses a 7-day moving average of spreads to smooth the volatility. The measured spread has at times been much higher, e.g., 40%+ on April 10, but that passed quickly.

Disclosure: I own 0.1 bitcoin.

The GM (er, Motors Liquidation) Anomaly

A few months ago, I wrote a series of posts about anomalies in the pricing of Citigroup common and preferred stock (see here for the final installment). At the time, Citi’s common stock traded at prices that appeared to be way too high relative to the preferred stock (which has since converted into common).

Limits on short-selling appeared to be the best explanation for that anomaly.

In today’s New York Times, Floyd Norris notes that the same thing is happening to shares of Motors Liquidation Company (symbol MTLQQ). Motors Liquidation is what remains of the bankrupt General Motors. It has no ownership in the new, post-bankruptcy GM and, a (see correction below). As far as I can tell, everyone believes that ML’s common stock is worthless. Yet, as Norris shows in an accompanying chart, the stock has persistently traded above $0.50 per share:

NYT - GM vs. Delta(One nit: I don’t think the top chart should be labeled “General Motors stock price …”; it should be “Motors Liquidation stock price …”)

Norris argues, correctly I think, that the difficulty of shorting ML common stock is why it trades at a positive price. Potential sellers have been unable to drive the price down where it belongs (close to zero) and, indeed, are occasionally forced to buy back shares to close their positions. Thus, the stock trades around $0.60 per share, and the number of shorted shares has been declining.

As a contrast, Norris points to Delta Airlines which went through bankruptcy back in 2006-7. In that case, short sellers increased their positions over time, and the stock price worked its way down to zero.

Correction (11/3/09): An astute reader points out that I was wrong to say that Motors Liquidation has no ownership position in the new GM. According to the investor FAQs for Motors Liquidation:

As part of the consideration for the acquisition of substantially all of the assets of the old General Motors Corporation, 10% equity in the new GM, as well as warrants for an additional 15%, will be provided to Motors Liquidation Company which is still in Chapter 11. Distribution of this equity to unsecured bondholders and other claim holders will be determined through the court process and will not occur until a plan of reorganization is submitted, accepted and implemented. It is too early to tell how long this may take.

If I am interpreting that correctly, it means that Motors Liquidation is, in essence, the conduit by which unsecured bondholders and other claim holders will eventually receive their equity stake in the new GM.

Another useful item on the Motors Liquidation web site is this warning to investors in common stock:

Management continues to remind investors of its strong belief that there will be no value for the common stockholders in the bankruptcy liquidation process, even under the most optimistic of scenarios. Stockholders of a company in chapter 11 generally receive value only if all claims of the company’s secured and unsecured creditors are fully satisfied. In this case, management strongly believes all such claims will not be fully satisfied, leading to its conclusion that the common stock will have no value.

Citigroup & Efficient Markets

The Citigroup pricing anomaly may be in its final days (earlier posts here and here).

Investors must submit their offers to exchange preferred shares for common shares by this Friday (which may require contacting your broker several days earlier). The common shares will then be delivered to investors on July 30.

The pricing gap between the common and preferred shares remains large (about 10% at the close on Monday), but has narrowed as the exchange date has drawn near.

It thus seems an appropriate time to reflect on what, if anything, the Citigroup anomaly illustrates about economics and finance more broadly. Happily, this week’s Economist carries a quote from Dick Thaler (previously quoted in my post about Catherine Zeta-Jones) that summarizes the lesson perfectly:

Mr Thaler concedes that in some ways the events of the past couple of years have strengthened the [Efficient Markets Hypothesis]. The hypothesis has two parts, he says: the “no-free-lunch part and the price-is-right part, and if anything the first part has been strengthened as we have learned that some investment strategies are riskier than they look and it really is difficult to beat the market.” The idea that the market price is the right price, however, has been badly dented.

To me, the Citigroup anomaly illustrates the strength of the “no-free-lunch” part of the EMH, and the limitations of the “price-is-right” part.  Continue reading “Citigroup & Efficient Markets”

The Citigroup Repo

As I’ve noted in a series of posts (here’s the most recent), there’s an anomaly in the pricing of Citigroup securities. Several issues of Citi’s preferred stock are scheduled to convert into common by the end of the month. Yet the common stock has been trading at a significant premium to the preferred in recent months. As I type this, for example, the common is trading at roughly a 14% premium to the preferred common, even though the conversion is just a few weeks away.

As best I can tell, the only explanation for this pricing anomaly is that Citigroup common stock is very difficult to sell short. So arbitrageurs can’t bid the spread down to levels that would be normal for such a deal.

This anomaly intrigues me for two reasons. First, it appears to be a blatant rejection of strong versions of the efficient markets hypothesis. However, as I will discuss in a later post, the market for Citigroup securities is actually ruthlessly efficient in many ways. As a result, it’s extremely difficult to profit from the anomaly. Sharp financial types have already bid other prices — most notably those for Citi options — to a level where obvious profit opportunities don’t exist.

Second, the anomaly is a big dangling carrot for big-money types to get creative. Markets always try to find ways around imperfections like the limits on short-selling. So I’ve been wondering what creativity would come out of the woodwork. Well, today I got an answer.

Continue reading “The Citigroup Repo”

Citigroup & Berkshire Anomalies

Summary: Both Citigroup and Berkshire Hathaway continue to violate the law of one price.


In previous posts (this is the most recent), I’ve pointed out that there are three ways you can purchase common shares of Citigroup:

Simple: Buy shares of common stock.

Preferred: Buy shares of preferred stock that will convert into common.

Synthetic: Use call and put options to replicate the financial returns of owning common stock.

In a perfect world, these three approaches would give nearly identical prices. That’s the law of one price.

Over the past few months, however, Citi securities have been breaking that law. Investors who have been buying common shares have been significantly overpaying relative to the values implied by the prices of the preferred stock and options.

Continue reading “Citigroup & Berkshire Anomalies”


Some good items elaborating on topics I’ve discussed in the past week:

The Citigroup Anomaly Lives

Summary: Citigroup securities are still violating the law of one price.

Later this week, Citigroup will finally launch its offer to convert some preferred stock into common stock.  That exchange has big implications for the government, which purchased preferred shares through the TARP program; after the exchange, the government will become Citi’s largest shareholder.

The exchange also has big implications for investors.

As I noted two weeks ago, there have been some anomalies in the pricing of Citigroup securities. Those anomalies have gotten smaller, but they are still with us. Citigroup is still violating the law of one price.

The crux of the pricing anomaly is that there are three different ways to invest in Citigroup’s common stock:

Continue reading “The Citigroup Anomaly Lives”

The Berkshire Anomaly

Readers seemed to enjoy my post about anomalies in the pricing of Citigroup securities, so I thought it would be fun to look at another anomaly, this time in the shares of Berkshire Hathaway, Warren Buffett’s famous company.

This pricing anomaly is small compared to the Citigroup one.  But it does raises some interesting questions about how well the markets are functioning (and, who knows, maybe someone can profit from it).

The root of the anomaly is that Berkshire Hathaway has two classes of shares: A and B.

Continue reading “The Berkshire Anomaly”

The Citigroup Anomaly

Something is amiss in the market for Citigroup securities: prices are out-of-whack with standard arbitrage relationships. This suggests that (a) recent financial turmoil — or, perhaps, the policy responses to it — have undermined market efficiency and (b) some investors are over-paying.

Summary: Something is amiss in the market for Citigroup securities: prices are out-of-whack with standard arbitrage relationships.  This suggests that (a) recent financial turmoil — or, perhaps, the policy responses to it — have undermined market efficiency and (b) some investors are over-paying.   

Recent weeks have witnessed yet another case of law-breaking in the financial sector: Citigroup is violating the law of one price.

When the market closed last Friday, there were at least three different ways you could invest in Citigroup’s common stock:

Simple: You could buy common shares of Citigroup, just as you would with any publicly-traded company.

Preferred: You could buy shares of preferred stock that will convert into common shares. Citi has announced, for example, that it intends to convert each share of Series F preferred into about 7.3 shares of common stock.

Synthetic: You could buy and sell options in a way that replicates the financial returns from owning Citi stock.  For example, you could buy a call option with a strike price of $4, sell a put option with the same strike price, and set aside $4 in a bank account.  Taken together, those investments will give you the same financial returns as owning a share of Citigroup common stock. (I am gliding over some small details here.)

In normal times, the law of one price would imply that you should pay nearly identical prices under any of these approaches.  Transaction costs might allow prices to stray a bit from one another, and the preferred might trade at a small discount if the conversion isn’t completely certain.  But any price differences should be small as arbitrageurs buy stock the inexpensive way and sell it the expensive way.

That isn’t the case today. Continue reading “The Citigroup Anomaly”