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# Pairs MACD

Pair's MACD is an auxiliary indicator that can be used in conjecture with Pair's Spread, Pair's RSI and Pair's Momentum Indicators for optimizing the timing of opening or closing a position in a Pair's trading strategy. Pair's MACD is an ordinary MACD indicator with the only difference being the way its price is derived.

While a simple MACD indicator uses the closing prices of only one instrument, Pair's MACD uses the Pair's Spread closing prices (see equation 2).

Let's assume that we have identified a long-term relationship between Microsoft and Intel Corporation. Additionally, let's assume that after applying an econometric research we have found that the long-term relationship between Microsoft and Intel is given by the following equation:

MSFT=-13.8362+2*INTC+error  (1)

Pair's Spread= MSFT-(-13.8362+2*INTC) (2)

Where the error is normally distributed with mean zero and unit standard deviation.

The above econometric equation uses daily time frame!

In more detail in our example, Pair's MACD price is derived using the following inputs:

• Pair A symbol: Is the symbol of the first pair component. For example, MSFT for the Microsoft Corporation. Its value should be a string.
• Pair B symbol: Is the symbol of the second pair component. For example, INTC for the Intel Corporation. Its value should be a string.
Before typing any pair symbol, please make sure that the corresponding investment instrument is added to the navigator window. To add an instrument, you should right-click on navigator window, go to Symbols, select the desired instrument and then click Show button.
• Mean: Is the long-term mean.  In our example -13.8362. Its value is a double.
• Integrating Coefficient: Is the co-integrating coefficient. In our example 2. Its value is a double.
• FastEMA: Is the fast exponential moving average with its default value set to 12.
• SlowEMA: Is the slow exponential moving average with its default value set to 26.
• SignalSMA: Is the signal moving average with its default value set to 9.

### What is Pairs Trading?

This trading strategy looks for pairs of assets that historically have moved together and tries to exploit cases of relative mispricing. More specifically, it assumes that a long-term pricing relationship exists between the two stocks and that the time series of their price spread is stationary. If their spread deviates from its long-term mean by more than a pre-specified threshold, a trader shorts the asset which is overpriced and goes long the relatively underpriced one.

This procedure is referred to as “opening a position”. When the spread converges to its long-term mean the trader unwinds or "closes" his position, making a profit. In case the spread diverges by more than a specific threshold or the spread has not converged before a pre-specified time threshold, then the position is closed. It is worth noting that pioneers of this disarmingly simple concept were Nunzio Tartaglia and his team of former academics, who in the mid 80's by trading such pairs made a \$50 million profit, only in their first year (Gatev, Goetzmann, & Rouwenhorst, 2006).

According to Vidyamurthy (2004), there are two types of pairs trading in equity market: statistical arbitrage and risk arbitrage. Statistical arbitrage is based on the idea that two stocks which have similar characteristics and are exposed to similar risks, for example two banks, might be priced more or less the “same”. This does not mean that the two banks should have the same price but that their price spread should have a long-term mean and move within a given band. The greater the divergence from this mean, the greater the profit potential.

On the other hand, risk arbitrage happens in the context of every corporate event that alters the capital structure of a firm. Such examples are tender offers, mergers, exchange offers, spinoffs and recapitalizations. A tender offer is a situation in which a company, the bidder, tries to buy another company, the target. Shareholders of the target firm are offered the opportunity to exchange their shares for cash at a pre-specified price and time. Spinoffs occur when a firm divides its business into separate units. The shareholders of the initial company will receive new stock in the spun-off entity in addition to the shares currently owned by them.

In the merger case, which is the most common, the price ratio and thus the price spread between the two stocks, bidder and target, is locked to a pre-specified level after the completion of the merger. As a result any deviation from this parity relationship gives rise to potential profitable opportunities. However, the completion of a merger is not always a certainty. Thus, the realized price spread corresponds to the market implied probability that the merger will be successful. A risk arbitrage portfolio is created by shorting the bidding stock and buying the target stock. It is worth mentioning that in this case the created portfolio is a market neutral one since after the merger, the two stocks will have the same exposure to the market and thus our portfolio will have a beta of zero.

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