This is the tenth article in the series "Popular Risk management". The aim of the series is to describe the main Risk management topics in a simple, but at the same time a clear and concise language.  
Written by Boris Agranovich

Original definition:

Arbitrage is simultaneous purchase and sale of the same commodity or stock in two different markets in order to profit from price discrepancies between these markets.

For example, selling the share of Shell for a higher price in Amsterdam and buying the share Shell in London.

Through increasing globalisation of markets this type of arbitrage strategies have virtually disappeared as trading is conducted now with help of sophisticated automatic systems. There is no “Free lunch” any more!

Therefore arbitrage is often referred now to strategies in which there is an expected positive return.

Arbitrage strategies often entail a short position for which shares must be borrowed.

1. Index arbitrage

Theoretically the difference between the price of a future is formed by the “cash and carry principle”. This principle states that two positions that have the same cash flows must have the same price.

Theoretical Future price = Index price + Interest – dividend – Security lending fee 

Thus the theoretical spread is formed by Dividend, interest rate and security lending fees. 

So if the real  spread  (or difference between the real futures and index price) is not equal to the theoretical one, you can profit by buying the relatively cheap instrument and selling  the relatively expensive one, for example buying the FTSE March 20010 future and selling a basket of FTSE shares.

Main factors in deal profitability are access to shares, low security borrowing and lending rates, favorable funding costs which depends on bank’s rating.

2. Conversions and reversals

This strategy is similar to Index arbitrage. The future is however replaced with an option position.

Here is the put-call parity equation is important.

Future = Long Call + Short Put position

3. Merger arbitrage

Merger arbitrage is the purchase of stock of a company that is to be acquired and the short sale of the stock of the acquiring company if a company pays in its own shares.

Positions are generally initiated when a deal is announced, sometimes even in the anticipation of a takeover.

Normally, the stock price of the target company in a deal trades to a discount, because of the uncertainly of the success of the deal.

Main factors in deal success are:

  1. Analysis of Anti-trust laws;

  2. Analysis of Anti takeover defense;

  3. Shareholders voting anticipation

If a deal goes through, the “discount” for which shares have been bought is the profit in the deal, ignoring dividends, financing and stock borrowing costs.

The inherent risk in a merger arbitrage deal is that the deal falls through and that the shares of the target company can drop to pre-merger levels.

4. Convertible bond arbitrage

Convertible bond is a corporate bond that can be converted into a predetermined amount of shares at certain times during its life. Convertible bonds are hybrid instruments, part equity and part debt.

Convertible bond arbitrage involves the following steps:

  1. Buying a convertible bond

  2. Simultaneously selling the underlying shares (hedging the equity element)

  3. Trading interest rate futures or selling an ordinary bond (hedging the debt element)

  4. Buying credit protection

Motives for convertible bond arbitrage are following:

  1. “Cash and carry”. This means that there is a positive difference to be earned on the difference between the interest earned on the bond less dividend owed to the lender of the short stock. In reality financing and stock borrowing costs must also be considered.

  2. Cheap optionality. This is the case if the trader believes that the implied volatility is too low compared with the historical volatility of the shares or options. To capture this volatility difference, the trader must continuously delta-hedge his share position. He will be buying the share when the share price drops and selling the share when the share price increases.

If in retrospect the market has moved more (the volatility was higher)  then was accounted for in the price of the convertible bond when it was bought, the trader has captured the volatility difference by adjusting his stock position.

  1. New issues. New convertible issues are often very attractive, especially when they are offered at a discount. Often these bonds can be sold in the “gray” market for a higher price immediately.

As convertible bonds are a combination of debt and equity the motives for trading these investments are both related to the equity/stock optionality and the debt element of the instrument.

5.  PAIR trading

If two stocks have a historical price relationship that is temporarily reversed, it is possible to buy the cheaper stock and sell short the most expensive stock in the expectation that the historical relationship will be established. When this happen, the profit is made.

Historical data is used to investigate possible relationships between companies listed on the major European stock exchanges.

Main factors in profitability are the statistical quality of the pair analysis and ability or the price of borrowing stock.


6.  Spin off arbitrage

Listed companies often have interests in other listed companies, like holding company has interests in a company B. Based on published information a trader can calculate the value of both companies.

For example, a holding company might be theoretically under priced in relation to its participants. If so, the trader has an arbitrage opportunity. Logically he will buy the company that is relatively under priced and short the one that is relatively overpriced. Profits will only be realized in this strategy if the trader’s estimations and calculation were correct. 

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