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:

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%). 

But the pricing anomaly persists.  At the close yesterday, 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.

Disclosure: I have no position in any Citigroup securities.

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 call options on 1,000 shares at a cost (according to yesterday’s closing price) of $200, (b) sell put options on 1,000 shares 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.)

25 thoughts on “The Citigroup Anomaly Lives”

  1. When you sell shares short, you have to borrow them from someone. Generally speaking, the shares can be recalled by the lender at any time. That is, the lender of the shares sold short controls when the game ends. The short-term nature of the lending of shares creates a risk to the borrower of those shares (i.e. to the short-seller). Naturally the short-seller expects to earn a return for bearing that risk. The chance that the lender of shares will call the shares in before the borrower/short-seller wants varies with the volatility of the securities markets, and the regulatory and economic climate. So does the financial ability of the borrower/short-seller to sustain that risk. Does that explain why otherwise-expected arbitrage does not always happen?

  2. @Jon: Hi Jon. Yes, potential short sellers do have to price in the various costs and risks of short-selling. Friends have told me that the main one is just the cost of borrowing shares, which might cost as much as 100% at an annualized rate. As the end date for the exchange gets closer, more arbs will be willing to absorb these costs, and we will probably see more shorting.

  3. I believe C’s short interest numbers will be published tomorrow and I’ll be looking to see if it increases from the already colossal 23.8% of float. Just a reminder that we still don’t have firm exchange offer dates filed with SEC and until then, some risk of another swipe from Mama Bair may still be factored in. Man, I’ll be happy to see the back of this arb trade.

  4. No doubt, Donald, the costs have to be factored in. My point is that in addition to whatever has to be paid to the lender of shares is a separate very hard-to-quantify cost, which I think is typically ignored, that the lender of shares will call the shares back in before the trade has converged. Sort of like, there’s an overnight lending rate, but how does one price in the risk that the lender won’t roll the loan over? My suspicion, from talking over the years with people who sell short, is that this cost (or risk, if you like) is often ignored, but it should not be. If in fact shares are commonly lent out with some sort of agreement about the length of the share loan, that’s another matter. Without pretending to be sure, I do not think that is the case. I’m curious what you and others thinks.

  5. Jon- You are right on-
    I have been in this Citi/Preferred Arb trade for 3 months now.. While I somewhow am not paying the “cost to borrow” fees (don’t ask me how), the risk of “buy0in ” is huge. You’ve done a great job of using the analogy of the loan that does not renew. I went 2 months with zero buy-ins (miraculously), but the past 2-3 weeks the buyins have been fast and furious. However, whenver I get a buy-in (I’m talking hunderds of thousands of shares sometimes), I recreate the position by selling in-the-money calls, which of cousrse then get assigned, leaving me short again. It’s a viscious cycle, ut worth the trx ciosts (and the .01-.02 loss per round turn) in order to make the .785/share profit (now closer to .50 as the gap narrowed yesterday).

    Donald, excellent article, as intelligent posts re this are hard to find. You did, however, err slightly, as you used the “last price” when explaining the SEP 4 strike synthetic long position. In fact, if you were buying calls/selling puts, you’d pay the ask (.21) for calls, and get the bid (1.23) for selling puts. This would be a total diff of .04 fr your price, so the synthetic long would yield a 2.98 price, not 2.94. The concept is the same, though.

    It is notable that this “anomaly” exists with many hard-to-borrow stocks,(I can name 10-15 of them right now)and the common can always be bought for less thruu synthetics on those cases.. The interesting thing about C is the third option – no pun intended_ of the the preferred conversion, which adds an unusual twist.

    1. Thanks Jonathan, very interesting to hear this from someone in the middle of this trade. If you would, I would be interested (and suspect others might be too) in a bit more detail on what you mean by the calls being assigned?

    2. Thanks Jonathan — very useful to hear how this is working in practice. And yes, one of the costs of using Yahoo for my option quotes is that the bid and ask sometimes aren’t available (e.g., in the morning before the market close).

      If you have any information on the other anomalies you could share, I’d love to take a look. Several folks have told me that such put-call parity violations are running near record levels.


  6. Donald-
    As to your other question, yes, these put-call volatility skews (as they are called) are definitely much more rampant these days… and I am convinced it is all about the difficulty and the cost of shorting the hard-to-borrow shares. This puts more buying pressure on the puts as a substitute for shorting the shares, (along with the fact that if a market maker sells a put they ned to short the stock to hedge the position), causing the relative cost of the puts to soar. If someone merely wants to own the common in any of these cases, then putting a synthetic long position is always the cheaper way to go.. But few are familiar or comfortable with that.

  7. Jonathan –

    “I have been in this Citi/Preferred Arb trade for 3 months now.. While I somewhow am not paying the “cost to borrow” fees (don’t ask me how)” > If you had not said do not ask, I would have done !

    “I recreate the position by selling in-the-money calls, which of cousrse then get assigned, leaving me short again.” > if you get assigned on the short call, you have to deliver stock. How do you do this ? Ie I understand that you need to recreate the short b/c you have been recalled on (some of) your borrow. So you cannot borrow stock to deliver against your assignment. My understanding is that if you do nothing, you will get bought in (by your clearer) to make delivery on the assigment. Fascinated to hear if / how you can get around this.

  8. Jonathan,

    You can get assigned every day. With a cost of 0.02-0.04(including transation cost) per round turn you might loose all the 0.5 gap in a month.

    Where can I find a list of hard-to-borrow securities?

  9. In previous years when interest rates were high the short seller would earn money on his short position depending on his or her agreement with the clearing broker.With short term interest rates so low this interest is very small.The exception to this idea occurrs when the stock is hard to borrow, like Citigroup.Either the clearing broker can not locate any stock to borrow or he charges a fee of up to %120 to borrow the stock.With the exception of very well connected accounts the short seller is at continual risk of buy-ins.
    The Citigroup deal expires on July 24 with stock being issued about July30. Any arb who hedged the preferreds with June or July options has to roll to Aug or Sept or pray that the stock does not drop below 3.00.

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