### That Wacky Wells Deal – What the Spread Says

October 04, 2008
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RELATED TICKERS: WFC
, WB.DL2
, C

On Friday morning Wells Fargo (WFC) and Wachovia (WB) announced that WFC was purchasing WB in a stock transaction at 0.1991 of WFC per WB share. The press frequently reports these deals at the equivalent total or per share price when the deal is announced; you probably saw reports saying WFC was paying $7 per share or $15 billion for WB. It’s important to know that those valuations are based on the price of WFC stock at a given point in time and will fluctuate. This Marketwatch announcement does it right, giving the valuations along with the basis. I haven’t checked, but I’m sure the Yahoo boards are full of posts wondering why WB isn’t trading closer to $7.

A possible problem here is that Citigroup (C) had already agreed to buy parts of WB in an agreement brokered by the FDIC. WFC is buying the entire WB operation. C was only buying the WB banking operations, their deal included FDIC guarantees capping losses on WB assets at $42 billion and C was issuing $12 billion of preferred stock to the FDIC. C is challenging the WFC deal. Since I’m not an expert in corporate law and haven’t seen any of the agreements in the C – WB offer, I can’t comment on the merits of Citi’s challenge. However, the arbitrage spread will give some insight into the odds.

Anytime two different assets represent the same thing, an arbitrage trade is possible. Investopedia defines arbitrage as “… simultaneous purchase and sale of an asset in order to profit from a difference in the price.” In this case, if the deal goes through, WB shares are equivalent to 0.1991 shares of WFC. That ‘if’ is an important qualifier. When the big market players are certain a deal will happen, they will sell one stock and buy the other anytime the spread between the two prices gets far enough apart to make the transaction and holding costs worth it. Regardless of what the markets do, the arb trader has locked in a guaranteed small profit as long as whatever is linking the two assets doesn’t fall apart. In this case, the arbitrage trade is somewhat limited by the short sale ban, however I’m sure the pros have no problem duplicating the trade with options.

Friday’s closing price for WFC, $34.56, values WB at $34.56 x 0.1991 or $6.88 per share. WB closed Friday at $6.21 per share, a discount of 10.8%. A spread that wide indicates the market has doubts about the deal. We have WB prices that included the details of the C offer prior to WFC making its bid and we can use that to come up with an estimate of the odds the market is giving this deal.

The closing prices for WB on 30 Sep – 2 Oct were 3.50, 3.55 and 3.91. I’m going to use the average of those prices, 3.65, as the value of WB if C is successful in challenging the bid. Citi’s offer is $1 a share, but there is some value to AG Edwards and other parts of WB that C isn’t buying. I’ll use the 6.88 based on Friday’s WFC close as the value of WB if the WFC offer goes through as announced on Friday.

In an efficient market, the price of WB would be its expected value based on the probability of various events happening. In this case there are only two likely events, either C buys WB or WFC buys them. Other very remote possibilities include both deals falling apart, a third bidder entering the picture or one of the current bidders upping the price. For this exercise, I’m giving those remote outcomes probabilities of zero. I’m also ignoring dividend payments that might be made between now and the deal closing. Someone making a risk-arb trade would need to factor them in, but their impacts on what I’m doing are in the noise.

Using Friday’s closing price for WB as its expected value and the assumptions stated above, the following equation would hold:

3.65 * Pc + 6.88 * Pw = 6.21

where Pc is the probability Citi’s offer succeeds and Pw is the probability WFC’s offer succeeds.

Since the assumption is one and only one of these two outcomes will occur, Pc + Pw = 1 and we can solve the equation to get a probability. The equation above becomes:

3.65 * (1-Pw) + 6.88 * Pw = 6.21 which reduces to

Pw = (6.21-3.65)/(6.88-3.65) = 79%

That shouldn’t be considered a precise number, several factors like market action over last week, the dividends, trading and carrying costs, etc. would need to be known and included in the math, but the trading tells us the market thinks there’s about an 80% chance the WFC deal will go through.

Individual investors typically can’t trade the huge volumes necessary to play an arbitrage spread. However, someone considering buying WFC should pay attention to the spread and consider buying WB instead. That consideration needs to include the risks of the deal falling apart.

At Friday’s close, buying WB would be equivalent to buying WFC at a 10% discount if WFC's deal goes through. For example, the price of 100 shares of WFC would have purchased 555 shares of WB at Friday’s close with a few bucks left over. Assuming the deal closes, the 555 shares of WB would convert to 110 shares of WFC plus a little cash. Of course, if C wins, the 555 shares of WB would only be worth about half the purchase price.

None of this should be considered a recommendation to buy or sell any of these securities. I am long WFC at the time of posting.