The Complete Arbitrage Deskbook (book review)

This book is pretty informative for anyone new to arbitrage. Stephane Reverre explains a fairly comprehensive field of existing means of arbitrage (up to the year of the book, 2001), covering a very wide range of instruments and explains both technical and economical grounds behind the mentioned market inefficiencies.


Prerequisite knowledge

A good understanding of statistics is necessary to fully understand some of the concepts from this book. The reader is also expected to have basic understanding of corporate finance and familiarity with intermediate financial mathematics.


Some interesting things from the book

Mathematical explanations for Index Arbitrage opportunities and expected mispricings (Index futures vs. Spot ETF, component portfolio, etc.)

Risk arbitrage exploiting scheduled corporate events (mergers and acquisitions)

Existing statistical arbitrage (e.g. pair trading) means

Examples of actual arbitrage opportunities and exploitations­­ off empirical data

Is complicated math necessary for profitable trading?

An old blog post from Paul Wilmott addresses the too often accepted belief, "the more complicated the mathematics the better". An example he gave involves the Heston Stochastic Volatility Process, where you need to solve a PDE (Partial Differential Equation) involving numerical integration in complex space, i.e.

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So the next logical question remains, does all that work improve forecast accuracy significantly? More importantly, would it offer significantly more efficient volatility arbitrage strategies? We need empirical findings!


The fact that the above applies "standard arbitrage arguments", an assumption of no arbitrage, makes it not as desirable. Wilmott makes a really good point here, "So, many know all the ins and outs of the most advanced volatility models based in the classical no-arbitrage world. Well, what if your job is to find volatility arbitrage opportunities?"

Classical Arbitrage Strategies Explained

Now that I have described pair trading, the next topic of interest lies in “risk-free” arbitrage strategies. Due to generally limited literature, this subject remains heavily veiled behind institutional trading.

Classical arbitrage defined

Classical arbitrage applies to any business strategy where one exploits market inefficiencies for a risk-free, self-financed profit. Discrepancies in offered values of same underlying commodities/services present the said “market inefficiencies”.

I had provided some examples a while ago on the blog. They present some direct and practical business models or trading schemes applied by real life people.

Are they really entirely risk-free?

No, but it takes much less effort to control the risks arbitrage strategies face, as profitable trades occur regardless of market movement or volatility exposure. In other words, common risks associated with naked stock positions disappear.

Liquidity, price impact, and transaction costs (associated with transaction sizes) generally become manageable via adequate calculations. Mathematical finance helps to optimize arbitrage strategies via things like linear programming or vector space representations, but to become basically profitable (just not maximized), anyone with basic algebraic understanding can manage it.

Do you need huge capital to apply arbitrage strategies?

No. Many opportunities exist for traders of all levels of account sizes. Though of course the larger the trades, the more insignificant transaction-costs become which makes rewards more attractive.

Quick example:

A NZ company is listed on both the NZSX and ASX, and today at close you see the following prices for the stock:

(Hypothetical prices)

· At NZSX: $10.00NZD/share

· At ASX: $10.50NZD/share

You sell 300 shares short on the ASX (requires $3,150 cash in account), then buy 300 shares of the stock long on NZSX. When prices converge you close both positions.

· Total initial cash requirement: $6,300

· Total profit: $150

· Total transaction cost (at $30/trade): $120

· Total net profit: $30

At $30/trade, the brokers here charge way too much, hence making arbitraging in this manner not-so-attractive.

So, with a few thousand dollars, anyone can make money in these markets regardless of market movement.

Reasons why not all traders apply these strategies

Some simply do not understand it or never bothered looking it up. Then for others, the returns remain too low. While arbitrage strategies offer double digit returns per year with very low-risk, ambitious traders aim for much higher targets.

Exceptionally high returns require strategies of highly active management and innovation. Though once found, the mentioned arbitrage models do not look attractive anymore. I have met traders who make over 1% per day, consistently, so yes it is all possible.

Pair Trading Explained

Market neutral, pair-trading strategies allow traders to reap profit off stock markets regardless of directional forecasting. It embraces simple principles, though the reward does not come easily.

Basic Tenet

Some institutional traders consider Pair-Trading a type of statistical arbitrage (like this one). It first takes two stocks or ETFs of very high positive correlation, i.e. they basically move in concert, and when their prices deviate you short the high, long the low, and close both positions for a profit when (and if) their prices converge.

The fundamental steps entail importing historical prices into statistical software, and then enter when they diverge by 2-3 standard deviations, closing positions if and when prices converge later on.

Main Risks

No adequate exit strategy if the pair never converges. Remember Long Term Capital Investments run by those Black-Scholes Nobel Prize winners? They lost a fortune betting on a pair of oil based stocks.

Too much time may lapse before convergence. Naturally if it takes several years for a pair to converge, the loss in opportunity cost may become quite significant.

Potential volatility may cause margin issues with open positions. To effectively manage this, potential reward becomes lowered, an uncomfortable trade off.

Liquidity issues still stand, especially with short positions becoming potentially squeezed. Some could argue that having a pair highly negatively correlated may solve this issue, yet while working with large volumes, liquidity and price impact matters will not go away.

Profitable?

Yes it can be, but not via simply entering and exiting based on guesses. It takes meticulous planning and active execution. It will not generate all winners, but as long as you can provide yourself a statistical edge, it will work.