Donald Marron's  Instablog

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.

When the markets closed last Friday, the cost of buying 1,000 shares of Citigroup in these three ways were (using price quotes from Yahoo and ignoring transaction costs):

Method                 Cost

Simple                   $3,670

Preferred               $3,052

Synthetic               $3,160

Note: The preferred calculation is based on the Series F; other preferreds give slightly different values.  The synthetic is based on options that mature in September 2009 with a strike price of $4.

What’s going on here?  Why does it appear that investors in the common stock are overpaying by as much as 20%?

A natural hypothesis for the difference between the simple approach (buying common) and the preferred approach (buying preferred) is that Citigroup might change the terms of the announced conversion.  Citi has, however,&... the terms on several occasions, most recently with the filing of a draft registration statement with the SEC.  Still, there’s always some risk that the terms may become less favorable.  (There appears to be little reason to worry that Citigroup will cancel the conversion; Citi desperately needs to increase common equity to meet the requirements of the stress test and to limit the Federal government’s ownership stake.)

A competing hypothesis is that the spread persists because arbitrageurs are finding it difficult or expensive to exploit the pricing differences.  Indeed, some reports indicate that they are finding it hard to find common shares to short.  As we learned during the technology bubble, when shorting becomes difficult, stock prices can get persistently overvalued.  As a result, it may well be that the price of Citigroup common stock is too high, not that the price of the preferred is too low or is weighed down by concerns about the conversion.

That view is reinforced by the pricing of the synthetic strategy.  The low price of synthetic shares suggests that sophisticated investors really do believe that the fair value of Citi common shares is less than the going market price. Arbitrageurs, for example, may be using options, rather than short-selling, to hedge long positions in the preferred.  If that’s true, then the discount on the preferred is, in fact, relatively small; on Friday, the preferred closed at only a 3.5% discount to the synthetic price of Citigroup.

These pricing anomalies are interesting from an investment perspective, of course, but they also raise important policy questions.  First, deviations from the law of one price usually indicate that something is wrong in our financial system. Liquid, efficient capital markets generally minimize such obvious pricing disparities. &... either market imperfections or government actions prevent them  from doing so.  If so, what are the specific problems here?  Limited risk appetite among hedge funds?  Implicit and explicit government limitations on short shelling?

There is also a distributional question of who benefits from these disparities and who gets hurt.  Most notably, who is buying the common shares at (what appear to be) inflated prices?  Comments welcome.

(Disclosure: I don’t have any investment position in any Citigroup securities.  That might change, of course, if someone can convince me that the preferred shares are under-valued, rather than the common shares being over-valued.)