Sunday, April 08, 2007


Arbitrage in its classic form is nothing more complicated than attempting to profit by buying something in one market and then selling it at the same time in another market for a price differential. As practiced in the years before World War II, when communication advantages were still possible, classic arbitrage meant trying to capture discrepancies in different financial markets. For example, the British pound might have been trading at $2.45 in London and $2.46 in New York. If an arbitrageur could buy pounds in London and sell them in New York simultaneously, he would be assured of a profit of $1 for every $245 he put up. The only risk in this kind of arbitrage is not completing the transaction fast enough. During the first half of the century, many firms made a steady income from the minor price differentials for the same currencies and securities trading in different markets.

As time goes by with global communications improving, however, the profits went out of traditional arbitrage. Once everyone knew in real time, people changed their calibration, and thus developed a new form known as “risk arbitrage.” In classic arbitrage, you buy and sell the same thing simultaneously. In the simplest form of risk arbitrage, you buy one stock – call it A – that will be converted into another stock – B – once an already announced event, such as a merger, is completed. At the same time as the purchase, you sell B in order to “hedge” the transaction and lock in your profit. There’s an element of risk, because of the conversion of A into B is not certain – the deal might fall apart rather than close due to a variety of reasons.

From the 1950s, risk arbitrage on Wall Street has meant buying securities that are the subject of some material event, like a merger, a tender offer, a breakup or spin-off, divestiture, or a bankruptcy.

As a hypothetical example, Big Fish might announce a friendly takeover of Acme Industries at the price of one half of a share of Big Fish’s stock for every Acme share. Say Big Fish is trading at $32 per share. The stock of the target company was trading at $13 before the deal was announced and rose to $14.50 after the announcement, based on its being worth $16 per share once the deal is completed (one half of Big Fish assuming if it remained at $32).

In a risk arbitrage transaction, you would buy shares of Acme and “sell short” the number of Big Fish shares you would receive when the takeover closed. Short selling in this context means selling something now that you don’t yet own to hedge against market risk – in other words, to protect yourself against the possibility that by the time the item you’re buying (A) is converted into the item you’re selling (B), B will have gone down in value. To sell something you don’t own, you have to borrow for a fee. Then when the deal closes, you simply take the shares of Big Fish you received in exchange for your Acme shares and deliver them against the short (those you borrowed), replacing what you borrowed and thus closing out your position. Your profit is the difference between the transaction price and the price you initially locked in. Movements of the Big Fish stock subsequent to your short sale don’t matter – if Big Fish goes down 5 points, it doesn’t affect you because you’ve already sold the Big Fish stock short, locking in the spread against the Acme stock you’ve bought. However, you receive the profit only if the transaction goes through.

If the deal falls apart, you’re left with a position that you bought at a deal premium (Acme) and a short position (Big Fish) – with almost certain losses on one or both ends. In this type of transaction, the potential profit is much larger than in a classic arbitrage trade - $1.50 for every share costing $14.50 in this example. But the risk is also much greater, since the takeover might fail to materialize for any number of reasons. In practice, such transactions become enormously more complicated and more interesting.

In a real life example of an arbitrageur, on Sep 4, 1967, Becton Dickinson, a mid-sized manufacturer of medical equipment, announced a friendly takeover of Univis, a somewhat smaller company that made eyeglass lenses. Under the terms of the takeover, Becton would buy all outstanding shares of Univis for about $35 million in stock. Shareholders in Univis would get a 0.6075 share of Becton for each share of Univis they held. Becton Dickinson was trading at around $55 a share and Univis at around $24.50. If the deal was to be completed, A or Univis, would be become B or Becton, and a share of Univis share would be worth $33.50 – at the price of Becton when the deal was first announced ($55 X 0.6075). To decide whether to engage in arbitrage, we have to estimate the odds of the merger coming to fruition, what would we make if it did, and what would we lose if we didn’t.

Such an announced merger could fail to be completed for any number of reasons. It might be called off after either side performed its “due diligence” of examining the others’ books in detail. Or the shareholders of either side might reject the terms of the transaction as not favorable enough. The Justice Department of Federal Trade Commission might decide that a combination of the two companies was anticompetitive. Regulatory issues might surface. One of the firms might have a history of announcing deals, and not completing them, and simply change its mind or be too unwilling to make accommodations on specific matters that arose after the initial agreement in principle. Basing on these, we could weight and balance the different factors to decide whether or not to take an arbitrage position. Intense and rapid research is the first order of the day. But even with as much information and time, risk arbitrage could still fall far short of science. It is a judgment call.

In merger transactions such a Becton-Univis, the projected loss would typically be much larger if the deal fell apart than the projected gain if it went through. That meant the odds had to be substantially in our favor in order for us to participate. But how greatly did they have to be in our favor? Someone who had been to business school would know “expected-value tables,” used to calculate the anticipated outcome of a transaction.

The basic inputs in an arbitrage expected-value table are the 1) price you’ve to pay for a stock, 2) what you’ll get for the stock if a deal goes through (the potential upside), 3) what you’ll have to sell it for if the deal doesn’t go through (the potential downside), and finally – the most difficult factor to assess and the heart of risk arbitrage – 4) the odds that the transaction will be completed.

So here’s how to construct an expected-value table. Univis stock traded at $30.50 (up from $24.50 before the announcement). That meant the upside potential from an arbitrage trade was $3, because a Univis share would be worth $33.50 – 0.6075 of a share of Becton – if the deal went through. If the deal didn’t go through, Univis would likely fall back to around $24.50, giving your investment a downside potential of around $6. Let’s say we rated the odds of the merger being completed as slightly better than six to one (about 85% success to 15% failure). On an expected-value table basis, the potential upside would be $3 multiplied by 85%. The downside risk would be $6 multiplied by 15%.

$3 X 85% = $2.55 upside potential
($6) x 15% = $0.90 downside risk
Expected value = $2.55 – 0.90 = $1.65

The $1.65 was what one could expect to earn by typing up $30.50 of the firm’s capital for three months (the duration estimated to complete the merger). That works out to a return of approximately 5.5%, or 22% on an annualized basis. As a guide, we figured that it wasn’t worthwhile to obligate the firm’s capital for a return of less than 20 percent per annum.

This is a simplification in a variety of ways. You also had to factor in the risk that a merger would break up under conditions that would cause the target stock you’d bought – in this case Univis – to fall lower than its pre-announcement floor or that would drive the acquiring company’s stock – the Becton Dickinson shares you’d sold short – higher. Or, even worse, both could occur at the same time. And you wouldn’t just make the decision to invest in this sort of deal and wait for the result several months later. The odds of a merger changed constantly over time, as risks emerged and receded and share prices fluctuated. To stay on top of the situation, recalculating the odds and deciding whether to commit more, reduce the position, or even liquidate it entirely. Arbitrage is an actuarial business, a lot like insurance. You expect to lose money in some cases but to make money over the long run thanks to the law of averages.

In the case of Becton-Univis, the positive expected-value prompted an arbitrageur to take a position – the arbitrageur sold short 60.75 shares of Becton Dickinson for every 100 shares of Univis he bought. As explained earlier, selling short the acquiring company – which is borrowed for a fee – was a hedge against the market risk. If the stock prices of both companies went down while the merger is under way – perhaps because the sector or market worsened – the profit would still be locked in, as long as the deal went through.

The arbitrageur initially bought 33,233 shares of Univis at an average price of $30.28 and a total of just over $1 million. He also sold short of 19,800 shares of Becton, into which the Univis shares would be converted if the deal falls in place. In the interim, the arbitrageur increased his position, and stood to make around $125,000 if the merger closed. By the end of the year, Becton has risen to around $60, causing Univis to climb to $33.25.

Unfortunately, the deal didn’t work out as the arbitrageur hoped. The merger fell apart in January because an unexpected decline in quarterly earnings at Univis prompted Becton to pull out. When the deal went south, the stock of Univis fell, not only back to its preannouncement price of $24.50 but all the way to $18. As a result, the arbitrageur is staring at a loss on his book of $485,000. He also faced a second loss on his short position because Becton shot up to $64 after the deal fell apart. He would have to buy Becton shares for $64 in the open market to replace the ones he’d borrowed and sold short at $55, which was going to cost him an extra $190,000, in order to close his position. Everything that could go wrong went wrong. This was it: the dreaded arbitrage perfect storm.

In total, the arbitrageur was down by $675,000 – a lot of money back then. But a critical point was that while the result may have been bad, the investment decision wasn’t necessarily wrong. Even a large and painful loss didn’t mean that the arbitrageur had misjudged anything. As with any actuarial business, you will make money on the majority of the deals and occasionally, lose on some other. The essence of arbitrage, as with insurance or investing, is that if you calculate the odds correctly, you will make money on the majority of deals and on the sum total of all your deals. If you take a six-to-one risk, the foreseeable risks will occur, and you’ll lose money every seventh time. To someone who does not understand the workings and sums of such operations, it is viewed as gambling. In fact, it is the opposite of gambling. It is an investment business built on careful analysis, disciplined judgments and the law of averages.

Risk arbitrage although appears risky on the surface, and inevitably at times, involved taking large losses is not what it appears to be. If you take it in reasonable stride by being rigorously analytical in weighing possibilities, do your analysis properly and didn’t get sucked into the psychology of the herd, you could be successful. Intermittent losses – sometimes greatly in excess of your worst case scenarios – are part of the business.

Arbitrage is certainly a way to look at issues probabilistically, very much like investing or in the insurance business. It doesn’t mean the more you invest, the more you make. It is whether the odds are in your favor, irregardless of the sum of investment.

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