Relative Pricing

Many popular trading strategies are based on some forms of fundamental or technical analysis. They attempt to value securities based on some fundamental multiples or technical indicators. These valuation techniques can be considered “absolute pricing”. Arbitrage trading strategies, on the other hand, are based on a so-called relative pricing. So what is relative pricing?

The theory and practice of relative pricing are derived from the principle of no arbitrage. Stephen A. Ross, a renowned professor of finance, is known for saying:

You can make even a parrot into a learned political economist—all he must learn are the two words “supply” and “demand”… To make the parrot into a learned financial economist, he only needs to learn the single word “arbitrage”.

What he was referring to is what financial economists call the principle of no risk-free arbitrage or the law of one price which states that: “Any two securities with identical future payouts, no matter how the future turns out, should have identical current prices.”

Relative pricing based on the principle of no risk-free arbitrage underlies most of the derivative pricing models in quantitative finance. That is, a security is valued based on the prices of other securities that are as similar to it as possible. For example an over-the-counter interest-rate swap is valued based on the prices of other traded swaps and not on, for example, some macro-economic factors. A bespoke basket option is valued based on the prices of its components’ vanilla options.

The principle of no risk-free arbitrage is employed in its original form in trading strategies such as convertible and volatility arbitrage. In statistical arbitrage  it is, however, relaxed; it normally involves stocks  which are similar but not 100% identical.

In summary, relative pricing based on the principle of no risk-free arbitrage is very different from absolute pricing. It is the foundation of many derivative pricing models and quantitative trading strategies.

Correlation Decreasing

Statistical arbitrage trading relies on, among other factors, the correlation between stocks. It is important to note, however, that correlation, like volatility, is not static, but time dependent and changing. Different market condition has a different level of correlation, and this has an important implication for stat-arb trading PnL.

We have been in a bull market lately, and it’s fairly common in bull markets for correlations to relax. The chart below depicts the CBOE Implied Correlation Index for SP500 stocks from November 2011 to March 2013. As we can see from the graph, the correlation is in a downtrend; it decreased from 80 % in Dec 2011 to about 55% in early March 2013.

The decrease in correlation explains in part why we have observed lots of dislocated pair relationships lately.  This dislocation increased the likelihood of pair divergence, hence one should exercise more caution when choosing pairs.

Models for Beating the Market

Edward Thorp is believed to be the first quantitative hedge fund manager. He first developed a winning blackjack strategy, and later started a successful hedge fund that exploited the pricing inefficiencies in the warrant and convertible markets. During the holidays I revisited one of his articles published in 2003 “A Perspective on Quantitative Finance, Models for Beating the Markets”. In this article Thorp recounted stories how he developed models for making money in blackjack and convertible bond hedging, respectively. According to him, developing a successful trading business  involves three steps:

  1. Idea,
  2. Development,
  3. Successful real world Implementation.

Most of the ideas (Step 1) in statistical arbitrage are more or less well known these days. To successfully build a quantitative trading business we need to complete Steps 2 and 3; we would need the following skills:

  1. Visionary,
  2. Quantitative,
  3. Entrepreneurial

Do you have the required relevant skills? If you’re missing one of these skills then learn it, improve it or team up with someone who already has it.

Happy Trading !!!


Arbitrage is the process of buying assets in one market and selling them in another to profit from price differences. True arbitrage is both riskless and self-financing. In today’s modern financial markets with ultra-fast supercomputers riskless arbitrage rarely exists. Arbitrage strategies still work, but they’re often not risk-free. These strategies include (but not limited to):

  • Statistical arbitrage (pairs, basket trading): mostly involves equities and other instruments whose payoffs are linear.
  • Volatility arbitrage: involves different classes of options on a single or multiple underlyings. The payoffs of those options are not linear, i.e. they have convexities.
  • Convertible arbitrage: consists of a hybrid (equity + debt) instrument and a hedge.
  • Sport arbitrage: refers to inter-market arbitrage. It can also mean profiting from a bookmaker’s mispricing of sport matches.