Part 16 (2/2)

Merger arb is an arbitrage between the purchasing company (the acquirer) and a to-be-acquired company (the target). This can be traded a number of different ways.

The most successful arbitrageurs try to antic.i.p.ate the acquisition. On the one side, they know a company is not profitable because of debt, overhead, some crisis (such as loss of crops or a tainted product), or a temporary drop in demand that puts pressure on their cash flow. On the other side, there might be companies such as IBM, Intel, or Berks.h.i.+re Hathaway that are looking to either complement their portfolios or add a missing piece of technology to their services. The traders may buy an option on what they perceive as the target candidate that pays off with either higher prices or higher volatility, both of which happen when a buyout or acquisition is announced. The trader who is correct about the acquired company even one in five times gets a very big payout because the price of that stock jumps to near the level of the acquisition price. At that point, they may take their profits or join the second group of arbitrageurs.

The second group is more conservative. They wait until the acquisition is announced and the board of directors has approved the deal. If the acquirer is paying a 100% premium for the stock, say, $30 for a company currently trading at $15, then the price jumps immediately to $28. The $2 difference is the uncertainty factor. If the market thinks the deal has a high probability of closing, then the difference between the stock price shortly after announcement and the target price is very small. If the market doesn't like the deal, then the difference is large.

Some traders buy the target company and sell the acquiring company, under the theory that the purchase adds to debt and uncertainty, thereby lowering the price of the acquiring company. Although that may appear to be a market-neutral trade, the movements of the two stocks are not very predictable; therefore, there is no a.s.surance that one move will offset the other and reduce risk.

The greatest risk in a merger arb trade is that the deal falls through. This most often happens when an audit of the company books produces unacceptable surprises. More recently, it happened because tight money made it impossible for some acquiring firms to borrow enough to close the deal. At that point, the stock of the nearly acquired company collapses, normally back to the preoffer price but many times much lower. The company no longer has its antic.i.p.ated support and, if it was losing money, it might spiral into bankruptcy. A trader who has sold the acquiring company may or may not benefit, but in the best of cases, the benefit would never offset the loss of buying the target company near the target price and then seeing the share price decline by half.

Although a merger arb program can have large risk, it is considered to have a short options profile. That means there are many small profits from successful deals closing and a few large losses. A merger arb program typically generates a return of about 8% annually for investment houses and offers a special type of diversification. Most deals close, so that the large losses are rare and can be absorbed by the higher frequency of small gains.

CREATING YOUR OWN INDEX ARBITRAGE.

If you can create your own stock ranking, can you also create your own index and use it for an arbitrage? In the previous chapters, we've used individual stocks and individual futures markets to create pairs. We've looked at using ETFs as well with some success. An ETF is convenient because there are no restrictions on short selling and it allows leverage. If you subst.i.tute an ETF for the short sales in stocks, you reduce the returns because the distortion in one stock is not reflected in the average of all stocks. Instead of capturing the entry points where two stocks or futures markets diverge, you are only capturing the point where one stock moves away from the index. That may be only half the potential profit. During a high-volatility period, that can still generate profits.

Selecting the two markets to use in the arbitrage can be done in a number of different ways. Many traders test their strategy on a wide choice of stocks and then pick the best performers. That's generally not a good method because you may have overfit the data and squeezed profits out of a few stocks by fine-tuning the parameter choices, which in turn identifies entry and exit points. As we saw in the previous chapters, parameters that are fine-tuned may work beautifully on one period of data but have too many or too few trades during other time intervals, usually because of changing volatility. If we are going to have confidence in a method, then it should produce profits using an arbitrary set of related markets and a wide range of parameters.

Another entirely statistical way of selecting the pairs is to find the correlation in price movement of the two legs. Correlations that are over 0.90 reflect markets that are too similar and have little chance of a profit that exceeds the cost of trading. Correlations below about 0.35 diverge for extended time periods, thereby introducing a very large risk each time you trade. Those markets with correlations of about 0.60 would be ideal, provided it's not just a short-term effect. We've looked at cases where the EURUSD and gold would be highly correlated for short periods due to immediate concerns about inflation. Those are excellent trading opportunities, but they can disappear quickly.

In the next section, we'll look at what happens if we create our own index and use it as one leg of a pair. It's similar to trading one stock against an ETF of that sector, when there is no ETF.

Mining Shares and the PMI Index We were very successful trading pairs of gold, platinum, and copper against the physical commodity in Chapter 6, but not everyone wants to trade futures.

Gold is already familiar to us, and the precious metals sector has a relatively small number of active stocks; therefore, it will be our starting point. By looking at the Yahoo! web site, we can find the precious metals (mining) stocks that are most active. They are shown in Table 9.5, in order of volume.

TABLE 9.5 Six most active precious metals mining stocks.

Symbol Name Current Price CDE Coeur d'Alene Mines Corp $0.63 ABX Barrick Gold Corp $28.76 NEM Newmont Mining Corp $38.90 AUY Yamana Gold Inc $8.70 GG Gold Corp $29.70 NG NovaGold Resources, Ltd $2.70 All other stocks traded fewer than 2 million shares per day. The individual stocks' price histories are shown in Figure 9.1. We create an index that we call the PMI (Precious Metals Index) by equally weighting the prices of the six stocks. That index is shown in Figure 9.2. It is easy to see that the index tracks the rise and fall of precious metals prices in a way that is even more exaggerated than the pattern of gold prices themselves. Besides supply and demand, profitability of mining companies is sensitive to operating margins, labor issues, and corporate management. At the time this index was created, gold was above $900/ounce after touching $1,000 (and on its way higher), and the PMI index is about 17 after topping 35, a drop of 50%.

FIGURE 9.1 Six precious metals mining stocks with the highest daily volume.

FIGURE 9.2 Precious Metals Index (PMI), an equal weighting of six mining stocks.

None of the six companies in the index was chosen based on suitability. You might observe that Coeur d'Alene, CDE, shown as the bottom price line in Figure 9.1, is far different from the other five stocks. It is also trading at the lowest price and might be delisted from the NYSE. It has a large business in silver, which might be reflected in the somewhat different price pattern. Perhaps a better index could be created by paying more attention to fundamentals, but our intention is to show that an arbitrage strategy works on an arbitrary set of stocks and a simple index.

One way to see if the components are reasonable choices is to calculate the cross-correlations, as shown in Table 9.6. Low correlations give us an idea that some of these companies are not affected by the same factors. For example, CDE has a low correlation against all other companies and only 0.163 against the index, while ABX, NEM, and GG are all very highly correlated. Correlations that are this low can occur randomly, but we expect that, being in the same sector, there is some fundamental relations.h.i.+p between CDE and the other stocks. For that reason, we'll leave it in this study because it may offer valuable diversification.

TABLE 9.6 Cross-correlations of six mining stocks and the Precious Metals Index, July 19, 2002, through March 6, 2009.

The Rules As with the other steps that we've followed in previous chapters to identify a trade, we'll follow a standard set of calculations and rules: Standardizing the data so both the stock prices and the index are in the same terms. That should be done by indexing.

Identifying the size of the entry distortion needed to capture sufficient profits to overcome costs.

Trading different quant.i.ties of each in order to equalize the risk.

Deciding at what point to exit the trade.

Because the PMI is an average price, it can be treated in the same way as each of the stocks in the index. We'll need to get the daily returns, based on the prices, using The return, rt, can then be used to calculate the annualized volatility (AVOL) of the two series over the past 10 days, and the ratio of the two volatilities gives the volatility factor, VAF, used to equalize the two series.

The 10-day calculation period is chosen because it is short enough to reflect changes in volatility but long enough to have enough data to be stable. Reducing the period to five days is tempting but would cause the volatility to jump around. Many traders might find that using a 20-day period is more in line with standards such as implied volatility or value at risk. With a much longer period, such as 250 days, the volatility will change very slowly and won't be responsive to some of the exceptionally volatile periods we've seen during 2008 and 2009.

The volatility adjustment factor, VAF, will be used for determining the number of shares to trade for every 100 units of the index. The position size for one side of the arbitrage must be fixed, and the other is then determined from the ratio.

Entry Points Finding good entry points will be the most important step. For this, we again use VAF to equalize the relations.h.i.+p between the index and stock price. The basic way of finding distortions is by using the standard deviation of the differences or, in our case, the returns. These will be called the volatility-adjusted differences (VAD). We will also need the average of the VAD values. This is different from previous methods that used a momentum oscillator to identify extremes.

Both of these calculations, the standard deviation of VAD and the average VAD, are based on only the past 10 days in order to be responsive to changes in volatility. It is now time to choose a key parameter, the standard deviation factor that determines how close or how far away the entry points will be placed. We know from statistics that using 1 standard deviation will capture 16% of these distortions (the part remaining on the outside of the distribution curve to the right). If we choose 2 standard deviations, we will only capture 2.5%, although those distortions will be much larger. We're going to choose a value that is smaller, 0.5 standard deviations, with the intention of having many more trades but enough profit to cover costs. Traders may decide to make this number bigger or smaller depending on their own preference for trading frequency and cost. If the standard deviation factor, F, is 0.5, the entry points are then calculated as follows.

Buy the index and sell the stock if VAD falls below the previous value of the average VAD minus the factor F times the previous value of the standard deviation of VAD.

If then buy the index and sell the stock.

If then sell the index and buy the stock.

In both cases, buying and selling, the exit occurs when the current VAD returns to the average VAD over the past 10 days. If the VAD values drift during the time a position is held, results may be better or worse than expected. There are no stop-losses and no maximum holding period. Risk is reduced primarily by diversification and is naturally minimized because there is no directional exposure.

Implementation and Liquidity The size of the positions is determined by the volatility adjustment factor, VAF. If we always trade 100 units of the index, then the number of shares of the stock is 100 VAF. Because we are using the PMI index that we created ourselves, we would buy or sell 1/6 of 100 (16.67) shares in each of the six companies in the index.

Selling short is always an issue, and not all stocks are available, so we need to know in advance which companies can be readily sold. If they cannot, they should not be part of the index. In this stat-arb example, we haven't checked on the status of any of the companies. It is best that we create the index, or trade the strategy, using the most liquid stocks, and those stocks are most likely to allow short selling. They will also have smaller execution slippage because they have a narrower bid-asked spread.

Precious Metals Results When we test the strategy on the six stocks for the 10 years ending March 2009, we get the results shown in Table 9.7. All results are adjusted to 12% annualized volatility, meaning that one standard deviation of the stock returns calculated over the entire 10-year period, times the square root of 252, will be 12%.

TABLE 9.7 Results of stat-arb using PMI and six mining companies, about seven years.

Of the six stocks, four were profitable, with the average result showing a return ratio of 0.284. There were nearly 100 trades per stock per year. The two companies that posted losses, AUY and NG, did not trade during the first half of the test period. The three stocks with the highest volume all posted profitable returns. Remember that there are no costs taken out of the results, and the stock trades posted a net loss of $0.0278 offset by the index gains of $0.027 on higher volume. These are marginal returns even for professional traders. Electronic trading can be done at very low cost, but profits this small are a concern. The performance pattern of each company can be seen in Figure 9.3. However, there is better news.

FIGURE 9.3 Performance of components and portfolio for the PMI arbitrage.

First, there is the advantage of diversification. In Figure 9.3, two of the stocks, ABX and NEM, continue higher during the last year while the other four swing lower before beginning a recovery. If we combine the six NAV streams into an equally weighted portfolio, the individual NAV volatility of 12% is reduced to 5.8%, less than half. This shows a significant amount of diversification, considering these stocks all belong to the same narrow industrial group. The final portfolio can then be leveraged back up to 12% using a factor of 2.05, yielding an annualized return of 8.18% from July 2002, shown in Figure 9.4.

FIGURE 9.4 Combined performance NAVs of six mining companies traded against the PMI.

Volatility is an important factor in arbitrage. It makes the distortions larger and reduces the impact of costs. It should be no surprise that the volatility of nearly all markets increased dramatically during the past two years, and this is reflected in the performance. During that period, the annualized return of the portfolio of six markets was 22.4%. The trading profiles from January 1, 2006, are shown in Table 9.8. We again see that volatility is an ally of the trader.

TABLE 9.8 Performance of each mining company traded against PMI for the period from January 1, 2006, through March 2009.

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