Posts Tagged ‘stock exchange’

Triangular arbitrage

Sunday, February 7th, 2010

Triangular arbitrage (sometimes called triangle arbitrage) refers to taking advantage of a state of imbalance between three foreign exchange markets: a combination of matching deals are struck that exploit the imbalance, the profit being the difference between the market prices.

Triangular arbitrage offers a risk-free profit (in theory), so opportunities for triangular arbitrage usually disappear quickly, as many people are looking for them, or simply never occur as everybody knows the pricing relation.

Example

Consider the three foreign exchange rates among the Canadian dollar, the U.S. dollar, and the Australian dollar. Triangular arbitrage will produce a profit whenever the following relation does not hold:

CD$/US$ * AU$/CD$ = AU$/US$.

For example if you can trade at these exchange rates

* the Canadian Dollar (CD$) against the US dollar (US$) is CD$1.13/US$1.00 (1 US$ gets you CD$1.13)
* the Australian Dollar (AU$) against the US dollar (US$) is AU$1.33/US$1.00 (1 US$ gets you AU$1.33)
* the Australian Dollar (AU$) against the Canadian Dollar (CD$) is AU$1.18/CD$1.00 (1 CD$ gets you AU$1.18)

1.13 * 1.18 = 1.3334 > 1.3300, thus mispricing has occurred.

To take advantage of the mispricing, starting with US$10,000 to invest:

* 1st buy Canadian Dollars with his US Dollars: US$10,000 * (CD$1.13/US$1) = CD$11,300
* 2nd buy Australian Dollars with his Canadian Dollars: CD$11,300 * (AU$1.18/CD$1.00) = AU$13,334
* 3rd buy US Dollars with his Australian Dollars: AU$13,334 / (AU$1.33/US$1.0000) = US$10,025
* Net risk free profit: US$25.00

A profit maximizing trader presented with these prices will trade up to the maximum size possible, or equivalently do the trade as many times as possible, until one of the traders on the other side of one of the deals changes his price. In practice currencies are quoted with a bid ask spread, so a trader should be careful that he is actually buying at the quoted ask price, and selling at the quoted bid price. Other transaction costs, such as commissions often prevent the trade from being profitable.

Efficient-market hypothesis

Saturday, January 23rd, 2010

In finance, the efficient-market hypothesis (EMH) asserts that financial markets are “informationally efficient”, or that prices on traded assets (e.g., stocks, bonds, or property) already reflect all available information, and instantly change to reflect new information. Therefore, according to theory, it is impossible to consistently outperform the market by using any information that the market already has, except through luck. Information or news in the EMH is defined as anything that may affect prices that is unknowable in the present and thus appears randomly in the future. The hypothesis has been attacked by critics who blame the belief in rational markets for much of the financial crisis of 2007–2010, with noted financial journalist Roger Lowenstein declaring “The upside of the current Great Recession is that it could drive a stake through the heart of the academic nostrum known as the efficient-market hypothesis.”

The efficient-market hypothesis was first expressed by Louis Bachelier, a French mathematician, in his 1900 dissertation, “The Theory of Speculation”. His work was largely ignored until the 1950s; however beginning in the 30s scattered, independent work corroborated his thesis. A small number of studies indicated that US stock prices and related financial series followed a random walk model. Research by Alfred Cowles in the ’30s and ’40s suggested that professional investors were in general unable to outperform the market.

The efficient-market hypothesis was developed by Professor Eugene Fama at the University of Chicago Booth School of Business as an academic concept of study through his published Ph.D. thesis in the early 1960s at the same school. It was widely accepted up until the 1990s, when behavioral finance economists, who were a fringe element, became mainstream. Empirical analyses have consistently found problems with the efficient-market hypothesis, the most consistent being that stocks with low price to earnings (and similarly, low price to cash-flow or book value) outperform other stocks. Alternative theories have proposed that cognitive biases cause these inefficiencies, leading investors to purchase overpriced growth stocks rather than value stocks. Although the efficient-market hypothesis has become controversial because substantial and lasting inefficiencies are observed, Beechey et al. (2000) consider that it remains a worthwhile starting point.

The efficient-market hypothesis emerged as a prominent theory in the mid-1960s. Paul Samuelson had begun to circulate Bachelier’s work among economists. In 1964 Bachelier’s dissertation along with the empirical studies mentioned above were published in an anthology edited by Paul Cootner. In 1965 Eugene Fama published his dissertation arguing for the random walk hypothesis, and Samuelson published a proof for a version of the efficient-market hypothesis. In 1970 Fama published a review of both the theory and the evidence for the hypothesis. The paper extended and refined the theory, included the definitions for three forms of financial market efficiency: weak, semi-strong and strong (see below).

Further to this evidence that the UK stock market is weak-form efficient, other studies of capital markets have pointed toward their being semi-strong-form efficient. Studies by Firth (1976, 1979, and 1980) in the United Kingdom have compared the share prices existing after a takeover announcement with the bid offer. Firth found that the share prices were fully and instantaneously adjusted to their correct levels, thus concluding that the UK stock market was semi-strong-form efficient. However, the market’s ability to efficiently respond to a short term, widely publicized event such as a takeover announcement does not necessarily prove market efficiency related to other more long term, amorphous factors. David Dreman has criticized the evidence provided by this instant “efficient” response, pointing out that an immediate response is not necessarily efficient, and that the long-term performance of the stock in response to certain movements are better indications. A study on stocks response to dividend cuts or increases over three years found that after an announcement of a dividend cut, stocks underperformed the market by 15.3% for the three-year period, while stocks outperformed 24.8% for the three years afterward after a dividend increase announcement.