The Citigroup Anomaly Lives On

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

Later this week, Citigroup (C) 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:

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. Two weeks ago, however, they gave radically different prices, with purchasers of common shares paying about 20% more than purchasers of the preferred shares. Of course, that comparison assumed that the preferred shares would convert into common shares on the terms that Citigroup had previously announced, but not implemented.

In principle, the price disparity between the common and the preferred might have reflected concerns about the terms of the deal. Except for one thing: the pricing of the synthetic strategy was similar to the pricing of the preferred strategy. In other words, investors in the option market were also acting as though Citigroup’s common shares were overvalued.

Those pricing disparities thus suggested that something was amiss in the market for the Citigroup securities. That something was a failure of arbitrage. Media reports indicated that potential arbitrageurs were finding it expensive, or even impossible, to sell common shares of Citigroup short. As a result, they couldn’t arbitrage away the pricing disparity by selling the common and buying the preferred. Thus, two clienteles of investors existed side-by-side, with the smart money buying preferred shares and the dumb money buying common shares.

Which brings us to today’s question: How are prices behaving now that Citigroup has announced that it will go ahead with the exchange?

That announcement, which hit the wires about 2:15pm on Monday, had the qualitative effects you would expect: the gap closed, with common shares promptly falling (down about 2.3% from 2:15 to the close) and preferred shares rising (the Series F preferred was up about 3.3%). Monday, you could have bought 1,000 shares of Citigroup for three different prices (using price quotes from Yahoo and ignoring transaction costs):

Simple $3,420

Preferred $2,898

Synthetic $2,940

Note: The preferred calculation is based on the Series F, while the synthetic is based on options that mature in September 2009 with a strike price of $4.

In other words, investors in the common stock appear to be overpaying by as much as 18% relative to investors in the preferred.

It will be fascinating to watch how this gap evolves as Citigroup moves to implement the exchange offer. If you take the options pricing seriously, the smart money expects the common price to decline towards the preferred, much more than the reverse. But yesterday, at least, the increase in the preferred was a bit larger than the decline in the common. Stay tuned.

Update: A reader suggested that it would be helpful to provide details on the synthetic calculation. Good idea. Here’s my math: To synthesize 1,000 shares of Citigroup common stock using options that have a $4 strike price and expire in September, you would (a) buy 1,000 call options at a cost (according to yesterday’s closing price) of $200, (b) sell 1,000 put options at $1,260, and (c) set aside the $4,000 you would need to exercise the call option if it ends up in the money. Putting that together, you have a net cost to you of $2,940 = $4,000 + $200 – $1,260. (This calculation ignores the fact that you could earn a small amount of interest by placing the $4,000 in a bank account, which would reduce the cost a tiny amount.)

Disclosure: I have no position in any Citigroup securities.

Comments

[Alex Trias:]

Fascinating article. Thanks for pointing this out. It would be very interesting to put this arbitrage failure into a broader context. For example, there have been a number of arbitrage opportunities cropping up within the fixed income and credit default swap markets over the last year and a half. An interesting (but very time consuming question) to examine would be to examine the cause for these market inefficiencies - which you have done in your article on Citigroup stock pricing. Late last year, I studied (and wrote a couple of articles on) panic being a cause of (or enabling factor for) inefficient asset pricing. I argued that panicking bulls enabled bearish investors to benefit from a number of arbitrage opportunities that should not exist for more than a nanosecond in an efficient market. Today, could it be that bearish investors are somewhat panicked, creating price anomalies as in the case of Citigroup's common share price relative to the synthetic/ preferred convertible share price? If so, then has the pendulum swung too far?

Jun 10 04:29 PM

[Jasper M:]

Actually, Cetin, it's a Fine time to short the market. (using your guidelines, I would have been afraid to add to my shorts all through '06 to '08) Leave yourself plenty of margin, to keep from being squeezed out, but there is a cavernous amount of down side potential.
Though, for those with some experience, I would recommend puts, instead of short positions, as the VIX is so low right now, premiums are next to nothing.
As for the "powers that be", you will find they are impotent before the combined might of the world's frightened bond holders. That's a pretty huge herd right now.

Jun 10 06:19 PM

[buff butler:]

this cetin guy is such a little parasite...

Jun 10 06:54 PM

[Michael Shu...:]

The difference in price between the common and the preferred is quite simple -- short covering, the purchase of stock based on a value different than the calculation you are making.

Jun 10 08:02 PM

[Jasper M:]

buff,
Not so little. Seen his picture?

668: The Neighbor of The Beast

Jun 11 02:34 AM