Page | 52 Thurner, Farmer and Geanakoplos (2012) posit that fat tails are caused by the purchasing of assets with leverage and margin calls, maintaining in their study that when funds do not trade with leverage, asset price fluctuations are uncorrelated and normally distributed across time.
Increasing leverage leads to amplified price fluctuations, fat tailed distributions and the display of clustered volatility. This volatility according to Thurner et al. (2012) are as a result of nonlinear feedback which intensifies large downward movement of prices which at the extreme cases cause crashes even though the effect can be seen at every time scale which produces a power law of asset price disturbances.
Page | 53 by the same amount still results in self-similar patterns. Figure 3.2 below is a fractal generated by adjoining the middle points of a triangle to create four different triangles with the one in the centre cut out later. The process is carried on infinitely until the final figure is observed.
Figure 3.2: The Sierpinski Triangle
Source: Mandelbrot and Hudson (2014)
Benoit Mandelbrot, who is regarded as the father of fractal geometry, first discovered the distinguishing characteristics of fractals in financial time series, but many economists rejected his ideas so he lost interest in fractals in finance, and turned to physics. In the field of physics, he developed the fractal geometry of nature (Velasquéz, 2009). Mandelbrot spotted that the variance of prices misbehaved, culminating in abnormally big changes. This behaviour was manifested in “fat-tail” and high-peak distributions, which commonly followed a power law with the implication that graphs will not descend toward zero as strikingly as a Gaussian curve.
However, the most distinctive property was that these leptokurtic (fat-tail and high-peak) distributions seemed unchanged irrespective of time scale (weekly, monthly or yearly).
Mandelbrot therefore concluded that “the very heart of finance is a fractal” (Mandelbrot and Hudson, 2014:147).
However, an MIT professor and efficient market theorist - Paul Cootner – pointed out that
“Mandelbrot, like Prime Minister Churchill before him, promises us not utopia but blood, sweat, toil and tears. If he is right, almost all of our statistical tools are obsolete— least squares, spectral analysis, workable maximum-likelihood solutions, all our established sample theory, closed distribution functions. Almost without exception, past econometric work is meaningless.”
(Cootner, 1964: 337).
Peters (1994), followed up on his earlier criticism of the EMH (Peters, 1991) and proposed the FMH, a hypothesis that offers a new method for modelling the deterministic characteristics and conflicting randomness of financial markets. The FMH appears to be a robust theoretical input
Page | 54 that provides an explanation of the discontinuity, turbulence and non-periodicity that typify financial markets.
The FMH has as its cornerstone, a focus on the heterogeneity of investors with regard to their investment horizons. Financial markets consist of the investors with varying investment horizons spanning a few seconds up to several years. Investors with diverse investment horizons react differently to information. A particular set of information can be interpreted by a short-term investor as a sell signal but interpreted by a long-term investor as a buy opportunity. Differing investment horizons ensures that financial markets function in a stable manner. The presence of investors with various investment horizons is vital for a stability and smooth operation of financial markets (Rachev, Weron and Weron, 1999, Weron and Weron, 2000). FMH posits that during stable periods of financial markets, all the different horizons are equitably represented therefore there is a smooth clearing of demand and supply on the market.
Conversely, during highly volatile periods such as in a crisis, even some long-term horizon investors switch to short-term horizon which becomes the dominant horizon therefore the demand and supply of the differing groups of investors are not cleared efficiently.
Kristoufek (2012) concluded in a study on the three most liquid indices in the United States - DJIA, NASDAQ and S&P 500 – that the EMH does not sufficiently explain the behaviour of financial markets during the Global Financial Crisis, arguing however that the FMH provides an adequate explanation of the behaviour of financial markets during this period. Kristoufek (2013) further posit that short investment horizons characterised the most turbulent periods of the Global Financial Crisis, this mismatch between short and long term investment horizons led to liquidity problems which is in line with the assertions of the FMH. Dar, Bhanja and Tiwari (2015) also test the assertion of a dominant investment horizon during financial crises. Using the wavelet power spectra based on continuous wavelet framework in line with Kristoufek (2013), Dar et al (2015) conclude that equity markets around the world exhibited the dominance of higher frequencies during the period of the crises, thereby, validating the assertions of Fractal Market Hypothesis.
Van der Merwe (2015) defines a liquid market as one in which large volumes of trade can be executed immediately with minimal effect on prices. Fisher Black (1971), co-author of the Black-Scholes option pricing model, defined a liquid market as one where:
Page | 55
• There is always a bid-ask price for investors who want to immediately trade small amounts of stocks.
• There is a small difference between bid and ask prices.
• Investors trading large amounts of stocks, without any special information, can do so over a long period at prices that are on average, not different from current market prices.
• Investors can trade large blocks of stock immediately, perhaps at a premiums or discounts dependent on the size of the block with larger blocks attracting larger premiums or discounts.
Financial markets provide a stable and liquid environment, that facilitate trading activities.
Financial markets create this stability through “investors with different horizons, different information sets, and consequently, different concepts of ‘fair price’” (Peters 1994: 43).
Investors with differing time horizons will evaluate information differently. For example, since day traders are only concerned with the daily prices of securities, they will focus mainly on recent trends while ignoring information concerning prices of such securities in the long-term.
Investors with long-term horizons however, will set long-term investment objectives and will therefore be more interested in the long-term prospects. As a result of this differences in investment horizons, investors will have diverse opinions on what a fair price is. Consequently, information that flows into financial markets impact each investment horizon differently. For example, new information that may lead to a decline in prices in the short-term triggering a sell signal among short-term investors may attract long-term investors who will take the opposite side of the trade and thereby providing stability in the market. They buy these stocks because they regard such information as noise and therefore willing to bear the short term distress (Peters, 1994).
Generally, investors share the same degree of risk once with subsequent adjustments for the range of investment horizons. In fact, such “shared risk explains why the frequency distribution of returns look the same at different investment horizons” (Peters 1994: 46), and is responsible for the fractal nature of financial markets. The market will become unstable if it loses its
“fractal” nature. Market failures may occur when there are major uncertainties in long-term expectations. Wars, political crisis and natural disasters for example, can alter the fundamentals of financial markets. In such periods, long-term investors affected by such events, will adopt a short-term approach or totally avoid investing in the market. Shortening positions leads to a dry
Page | 56 up of liquidity and subsequently a critical period where markets become highly volatile. Peters (1994) posits that so far as market participants with differing investment horizons are active in the market, a panic in one group can be easily contained by other horizons who will view such event as an opportunity to buy or sell. Conversely, if the market wholly assumes the same horizon, or a crucial segment of the market stay away from market activities, then the market will become unstable. In this situation, the non-existence of liquidity eventually culminates in a panic.
Table 3.1: Comparing the EMH and FMH
EFFICIENT MARKET
HYPOTHESIS
FRACTAL MARKET
HYPOTHESIS Emphasis Fair asset prices and efficient markets Liquidity Market cycles
and memory
Past events have no effect on future prices as markets behave in a random manner
The path of the market is determined by past events thereby exhibiting deterministic order making short-term predictions possible.
Market Market has a single equilibrium and always in equilibrium with deviations that are highly infrequent and negligible deviations.
There are different equilibria for each investment horizon therefore the market cannot reach just a single equilibrium
Distribution Normal distribution Fat tails and high peaks
On the JSE, Jefferis and Smith (2005), adopting a GARCH methodology with time varying parameters, and employing a test of evolving efficiency (TEE) over the period 1990 to 2001, concluded that the JSE is weak form efficient. Smith (2008), however, rejects the random walk hypothesis on the JSE, using tests of four joint variance ratios. Adelegan (2003, 2009) also finds the Nigeria Stock Exchange (NSE) to be informationally inefficient, by testing the reaction of market participants to changes in dividend policies of listed firms.
Page | 57