Summary: Both Citigroup and Berkshire Hathaway continue to violate the law of one price.
Citigroup
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.
Those pricing differences have declined somewhat over time as the likelihood of the preferred conversion has risen and as the closing date has gotten closer (the offer expires July 24 and closes the following week).
Nevertheless, the spread in prices remains substantial. At Thursday’s closing prices you could have bought 1,000 shares of Citigroup for three different prices (using price quotes from Yahoo and ignoring transaction costs):
Simple $2,880
Preferred $2,517
Synthetic $2,650
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 $3.
In other words, investors in the common stock appear to be overpaying by as much as 14% relative to investors in the preferred. That’s down from the 18% I calculated in my previous post, but it is still much wider than normal for these kinds of deals.
As best as I can tell, the only explanation for this anomaly is the difficulty of shorting Citigroup common stock, coupled with some clientele effect that leads certain investors (presumably not the “smart money”) to buy only the common.
Berkshire Hathaway
Berkshire’s pricing anomaly is small compared to Citi’s, but still interesting. As I discussed in my original post, the source of the anomaly is that Berkshire Hathaway has two classes of shares: A and B. The B shares receive 1/30 the economic payoff of the A shares (there are also some differences in voting rights).
As a result, you might expect that the price of an A share should be about 30 times the value of a B share — the law of one price in action. And you would be right; the prices have often traded around a 30:1 ratio since the class B shares were introduced. But not always.
In recent months, for example, the ratio has increased noticeably, with Class A shares trading at a notable premium to the Class B:
On Thursday, the ratio finished the day at 30.8. The A shares closed at $89,384, while the B shares closed at $2,893. At that price, 30 B shares would cost you $86,790, almost $2,600 less than a single A share. If you think that the prices will converge, you might be able to profit by shorting an A share and buying 30 B shares (that’s not a recommendation, and no I haven’t tried).
I originally thought the Berkshire anomaly might be a sign of stress in the financial markets; notice, for example, how the spread widened in the summer of 2007 and the fall of 2008. More recently, however, the wide spread has persisted despite calmer financial conditions. That suggests that the spread is being driven by Berkshire specific factors. A leading hypothesis — as suggested in several emails from readers — is that it may be related to Warren Buffett’s donation of Class B shares to the Gates Foundation.
Disclosure: As research, I am currently long a small amount of Citigroup preferred and short some call options on the common. I have no positions in Berkshire securities.
Interesting update. You say that it may be difficult to short the common stock, but yet you yourself claim to have shorted it yourself. Are you claiming that an institutional investor would have a difficult time shorting a larger position?
Hi Chappy — I would have loved to be short the common if I could find a way to do that cheaply enough. Unfortunately, I couldn’t, so I am short some call options on the common, not the common itself. Some readers have told me they’ve gotten short the common in various ways but it’s either (a) expensive or (b) temporary, with the short shares being called back with some frequency.
Oops. Sorry I should have noticed that difference. Is this actually a better hedged position? If you actually shorted the stock your downside risk is that the ‘spread’ reverses, correct? With a call option you are under no obligation to buy at your agreed strike price, but I guess you are out the premium you pay for the option? I’m just trying to figure out how the two different methods functionally differ in terms of your costs/risks.
Good questions. I will probably cover these more fully in a future blog post, but here’s the gist of what I learned in my research (I don’t find these surprising, by the way, but I wanted to see if reality tracked theory):
1. On paper, the best way to simulate a short position in the common would seem to be to write (i.e., short sell) a deep-in-the-money call, which is effectively a share of stock. Of course, everyone else has already figured this out. In this case, that translates into the following scenario: you write the option and then wake up to discover it’s been exercised the next morning (darn American options).
2. The next best is to write a distant near-the-money option. You pocket the premium, but you have to bear the basis risk — i.e., the option not tracking the stock price. You also have to deal with the changing delta — i.e., the quality of hedge changes as the underlying stock price changes. In this case, as the price of C has fallen, the quality of the hedge has weakened. I’ve been too lazy to short more options, so that means I’ve fallen behind on the deteriorating quality of the hedge.
Thanks!
Per your answer in 1: Doesn’t this imply that the price of the stock is going up if the call buyer is immediately exercising the option? If it is so obvious that this is the prevailing wisdom, why don’t they just buy the stock itself and cut out your premium? Does this mean that the call buyer thinks that the price is going up, but the perceived volatility of the (common) stock makes it worth the premium?
Anyway, thanks much for your helpful answers.
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