Wachovia and Wells Fargo Merger – A short study on the market efficiency and no arbitrage theory

In front of me is a copy of the shareholder’s prospectus on the Wachovia and Wells Fargo merger.

Put all the excitement aside (since this is the first time I am voting as a shareholder for a legal entity, although practically I do not hold any stock of Wachovia Corp as this point although I held an insignificant portion of Wachovia Corp common shares as of the recording date), I can not help to wondering whether there is any arbitrage opportunity arises here.

On the prospectus, it was stated that the merger was publicly announced on the 3 October, 2008 and the criteria of the merger is that each of the Wachovia common stock will be converted into 0.1991 of a share of Wells Fargo common stock. Using the law of one price, or the no-arbitrage principle, one should expect the common shares of Wachovia to be traded at 0.1991 times of the Wells Fargo stock. However, a simple Excel spreadsheet would reveal that is not the case.

The following table summarized the daily closing price of Wachovia Corp. (NYSE: WB) relative to the daily closing price of Wells Fargo (NYSE: WFC) from 2 October, 2008 to 12 December, 2008:

Average: 0.18468

St Dev: 0.018232

Count: 52




In the 52 trading days of data available, there is only one day that the share price of Wachovia Corp traded above 0.1991 times of that of Wells Fargo, and the average is slightly below 0.1991, at around 0.1846.

In the textbook, we learnt that in this case, the shares of Wells Fargo is overvalued and the shares of Wachovia Corp is undervalued and we should go short on WFC and long on WB.

However, why such “arbitrage” opportunity has existed for so long if, in theory, the market is efficient enough (the market in reality is a combination of semi-strong efficient and weakly efficient) to balance the demand and supply curve?

In my opinion, there are 2 major issues here
1. The uncertainty of merger. Although almost all major shareholders of Wachovia Corp have mostly accepted the fate of the bank, there are still shareholders who are contending for the merger, claiming that the merger has significantly undervalued the firm. It is very unlikely, but still possible, that such lawsuits will cause the merger to fail.

2. The volatility in the stock market: Although the shareholder’s meeting is going to take place on December 23, 2008, the merger is not expected to be completed  on that day. As a result, there may still be volatility in the share prices of both WFC and WB, which could affect the implied values of the shares.


Note that the market was able to quickly absorb the information and the ratio was relatively stable after the initial fluctuation, indicating the market is still fairly efficient despite that there was significant arbitrage opportunity initially even after the announcement was made to public.

However, it was also noted that out of those 52 days, in 44 days both shares went up and down together, hence it is safe to say that the market has indeed absorbed the information of the merger and is currently considering the two corporations as a pair rather than two unrelated stocks. When comparing to S&P 500 index (which is the proxy for the market portfolio), WB was traded with the movement of the market in only 27 out of the 52 days, indicating that is quite independent of the market movement.