The Adaptive Markets Hypothesis: Analysis from the Commodity Market
Name: Pieter Arjan de Vries Student Number: 2230615
Supervisor: Dr. I. Souropanis Study Program: MSc Finance
Date: 10-06-2019
Abstract
2
1. Introduction
The growing global demand for goods makes commodity prices very important. In one way or another, indirectly and directly there are almost no products in the world that do not depend on raw materials. In addition, the profits of many companies depend on commodity prices. Such as car manufacturers and airlines. As a consequence, commodity trading is essential to many aspects of the world economy. Understanding or predicting commodity prices is highly important for companies. Companies hope that they buy commodities when prices are low and sell when prices are high. A key challenge for companies is to ensure stable prices (Tevelson et al., 2013b). Ensuring stable prices, by using options or future contracts, enables especially manufacturing companies to optimize their production costs and deliver stable prices to consumers. Additionally, ensuring stable prices mitigates a major risk for companies since they can plan and forecast their expenses (IHS, 2013). If managers can estimate how prices of raw materials will develop, they have also an idea on how the prices of their products will evolve. Therefore, understanding commodity markets can be a competitive advantage for companies. However, there is an important hypothesis on price developments, which is called the efficient market hypothesis. The efficient market hypothesis states that in an efficient market all current information must be contained in today’s price and hence only new, unknown and uncertain information will influence tomorrow’s price. Price developments should follow a random walk. So, the price tomorrow might as well increase as decrease because it is unknown what will happen tomorrow (Fama, 1970). Therefore, the efficient market hypothesis states that it should not be possible to make predictions of future price developments of commodity prices.
Decades ago, the efficient market hypothesis was widely accepted. It was generally believed that security markets were extremely efficient in reflecting information about individual stocks and about the stock market as a whole. The accepted view was that when information arises, the news spreads very quickly and is incorporated into the prices of securities immediately. As a result, prices fully reflect all known information (Malkiel, 2003).
Even after several decades of research, economists have not yet reached a consensus about whether financial markets are efficient. Especially, the emerging discipline of behavioral economics and finance has challenged this hypothesis, arguing that markets are not rational, but are driven by fear and greed instead (Lo, 2004). There is a growing amount of literature which criticized the efficient market hypothesis. The first line of criticism is based on the fact that an investor can’t generate an excess return from trying to predict the market. Namely an investor would not receive any reward in compensation for the costs of seeking information to make predictions. When there is no gain from information search, no trader will seek information; hence all information available will not be reflected in the prices and prices will as such not be efficient (Grossman and Stiglitz, 1980).
3 Lo 2004, proposed a new perspective on the efficient market hypothesis, the adaptive market hypothesis. The adaptive market hypothesis adjusts the efficient market hypothesis view of the world, arguing that learning, competition, and evolutionary selection pressures prices to their efficient levels. Individual agents are no longer the rational beings of the standard paradigm, but rather bounded rational satisfiers.
The adaptive market hypothesis has two relevant findings for this paper. First, price developments of commodities should be predictable and profitable to some extent. And secondly, the forces of learning and competition will gradually erode these profitable opportunities. In other words when those market opportunities are exploited, they will disappear.
Empirical studies have investigated the efficient market hypothesis on a variety of markets. Most studies concentrate on stock markets (Smith and Ryoo, 2003) and foreign exchange markets (Ning, Wang and Su, 2017). A smaller number of studies analyze the commodity futures markets. Several important studies have shown that stock prices do not follow a random walk (Urquhart and Hudson, 2013). Statistical tests are used to evaluate market efficiency over some predefined period. This means that market efficiency is treated as an all or nothing condition. But it is reasonable to expect market efficiency to evolve over time due to varying underlying market factors, such as institutional, regulatory and technological changes and possibly the demography behavior of market participants. The purpose of this paper is to extend the literature on the adaptive market hypothesis by examining the changing efficiency of the commodity market.
To examine the efficiency of the commodity market six statistical test will be used on four commodities. The statistical tests include three linear tests namely the autocorrelation test, runs test and the variance ratio test. The other three tests are nonlinear tests which include; the McLeod Li test, the Engle LM test and the BDS test. Four commodities are subjected to these tests; silver, Brent crude oil, gold and the WTI oil price. This thesis contributes to the literature by making use of daily spot price instead of future prices. Also by making use of a dataset which ends on 01-01-2019, the data used is very recent. Finally the commodities used for this research have never been used in relation to the adaptive market hypothesis in this way.
4
2. Literature
The efficient market hypothesis (EMH) has served as the theoretical foundation for many modern finance theories (Bodie et al., 2011). The general belief is that prices follow a random walk, and it is unknown what the future price will be. Despite the research done on the EMH, it is still unclear if the EMH holds and in which form. Fama (1991), for example, argues that asset prices in an efficient market fully reflect all available information. This means that the market processes information rationally, and that relevant information is not ignored, and systematic errors are not made. As a consequence, prices are always at levels consistent with their fundamentals (Beechey et al., 2000).
Samuelson (1965) points out that if traders know that prices will increase tomorrow, they will buy the asset today, and thereby increase the price today. In other words, all relevant information is contained in current market prices because traders act rationally. Nevertheless, Fama (1970) argues that the condition, that the market fully reflects all information is not strictly necessary. The reasoning behind it is that the necessary conditions are; 1) that investors still consider all relevant information despite transaction costs, 2) that a sufficient number of investors have access to readily available information, and 3) that investors not make different and better evaluations than others.
According to Fama (1970) market efficiency can be divided into three categories that describe the degree of market efficiency in terms of reflecting and adjusting to information: the weak, semi-strong and strong forms of efficiency.
Weak-form market efficiency describes a market that fully incorporates historical price movements in future ones. This means that the price movements must be serially independent of each other over time. If this would not be the case, agents could make profits by forecasting future prices based on historical ones. In statistical terms, the weak market efficiency is often referred to as the random walk model.
Semi-strong market efficiency implies that in addition to the properties of a weak efficient market, the prices also reflect all public information. In this case there is no possibility for investors to realize excess returns neither by analyzing historical or public information.
The strong form of market efficiency is the higher level of efficiency and it basically impossible to achieve in the real word. In a market that is strongly efficient prices reflect all information available, including insider information. The consequence for a strongly efficient market is that no excess returns can be made even when in possess of superior information, since this is already incorporated into the price.
The efficient market hypothesis is getting more criticism. The most enduring critique comes from psychologists and behavioral economists who argue that the EMH is based on counterfactual assumptions regarding human behavior, which should be rational. A common explanation for deviations from the efficient market hypothesis is that investors not always react in a proper way to new information. In some cases for example, investors may overreact to performance. Investors sell stock that have experienced recent losses or buy stocks that have enjoyed recent gains. These kinds of overreaction tends to push prices beyond their fair market value (Lo, 2008). Which is in conflict with the efficient market hypothesis. Investors investigate market behavior by using technical analysis with the aim to predict such future market trends (Zhu et al., 2015).
5 varies in strength at different times (Lo, 2005). The author claims that it is unrealistic to expect that markets are perfectly efficient as assumed by the efficient market hypothesis. An important implication of the AMH is that return predictability may arise from time to time, due to changing market conditions by for example cycles, bubbles, crashes, crises and institutional factors.
The discussion about market efficiency is also relevant for the commodity markets. Samuelson (1965) pointed out that properly anticipated prices will act randomly or in other words follow a random walk. However, for commodity markets it can be stated that a vast number of factors influence the prices. Next to supply and demand, factors such as demographics, weather and technological developments could have a significant influence on commodity prices. In line with the efficient market hypothesis it should be assumed that at least a sufficient amount of traders in the market will consider the effect of those factors and will trade based upon information of those factors. For example, traders have information about expectations of future weather developments and their impact on commodity prices (Stevenson & Bear, 1970). If traders have such information and use it to anticipate price developments, than it should be reflected in the spot price (Samuelson, 1965). Traders who have such information and make use of it should have a market advantage.
There is increasing evidence that understanding commodity markets will improve the performance of companies (Tevelson et al., 2013a). For example, when a company fails understanding of the commodity markets and its own demands, it can end up wasting resources on hedging activities or ordering too large quantities. Or worse, the company can end up being in a critical situation, when its storage are short and prices have increased exorbitantly (Busch, 2013). Commodity market understanding as a capability can help companies avoid buying raw materials at peaks of market prices, setting false expectations for the management in terms of future developments, being unprepared for changes in prices, and being pressured into drastic, rash purchasing decisions (IHS, 2013).
A study done by the Boston Consulting group showed that some of the main objectives for commodity management in companies were to achieve stable price and lowest costs (Tevelson et al., 2013b). Arnold and Minner (2011) found that being able to acquire commodities in advance can provide companies with a competitive advantage. However, for companies being able to exploit this advantage means that commodity prices should at least be partially predictable.
Despite all the reasoning for commodity market understanding many companies believe they do not have the necessary understanding in order to make reliable predictions of future price developments in the markets (Tevelson et al., 2013b). Commodity markets have been researched before because of their high volatility (Baffes and Haniotis, 2010). McKenzie and Holt (2002) tested the efficiency of the USA futures markets for cattle, hogs, corn, soybean meal and broilers. Their results showed that futures markets for all the commodities except broilers were efficient in the long run. Nevertheless, that has not prevented the use technical analysis tools that from which is expected to predict future movements in commodity prices (Bundgaard, 2013).
6 As Houthakker (1961) mentioned, it is not possible to prove the EMH, it is only possible to disprove it. This thesis will analyze if commodity markets are behaving efficient, and if the adaptive market hypothesis holds for the commodity market. Charles et al., (2012) conducted a research on the foreign exchange market and assumed that major events alter the market conditions, which in turn change the degree of return predictability. In the literature, especially on foreign exchange markets, there is accumulated evidence that events change the conditions and ecology of markets (Charles et al., 2012). This strengthens the assumption that the adaptive market hypothesis holds for foreign exchange markets.
The majority of work, in testing the efficient market hypothesis in commodity markets has been conducted on the commodity futures markets. Kristoufek and Vosvrda (2014) analyzed the market efficiency of 25 commodity futures across various groups namely; metals, energies, soft commodities, grains and other agricultural commodities. They found that market efficiency differs among commodity groups. Energy commodities are the most market efficient and other agricultural commodities (composed mainly of livestock) the least efficient.
This research differs from the literature because daily spot prices are used instead of futures. According to Kaminska (2013) futures markets are to a higher extent used for hedging and speculation. While spot market participants buy for use and sell for gain (Houthakker, 1961). Research on commodity futures indicates that the futures do not behave outright randomly but rather exhibit some form of long-term dependence (Stevenson et al., 1970).
7
3. Data
For the data we selected a number of commodities that will be used. The chosen commodities are relevant for many companies on a global level. Namely; WTI oil, gold, Brent crude oil and the silver price index. The data is retrieved from DataStream and Fred. The initial dataset of this thesis consists of 7824 daily spot price observations, for the time period 01-01-1989 to 01-01-2019. Table I below describes the data and the data source of the underlying assets.
Table I
Serial codes for a sample of commodity prices in the period 1989 to 2019
Variable Series Source
S&P GSCI Silver Spot - Price index GSSISPT DataStream
Crude Oil Prices: West Texas Intermediate (WTI) DCOILWTICO Fred Gold Fixing Price London Bullion Market GOLDAMGBD228NLBM Fred
Crude Oil Prices: Brent – Europe DCOILBRENTEU Fred
Notes: The data is retrieved from DataStream and Fred for the period 01-01-1989 to 01-01-2019.
In figure I below we plot the daily spot prices in dollars of the four commodities used in this thesis. The time period of the plots is from 01-01-1989 to 01-01-2019. For the silver spot price index it is observed that the index moves sideways from the period 1989 to 2005. After 2005 the index is increasing and reaching its highest level in 2011 with a value of 1519. After to 2013 the index has fallen to a level of around 750.
From 1989 to 2002 the WTI crude oil price is moving around the twenty dollar per barrel. After 2002 the oil price is increasing and reaching nearly a price of 100 dollar per barrel in 2008. However, a year later the WTI oil price has fallen to a level 44 dollar in 2009. After 2009 the price of WTI is increasing again, almost again reaching a price of 100 dollar per barrel in the period 2012 to 2014. After 2014 the prices has fallen to a level 45 dollar per barrel at the beginning of 2019. The decline of the oil price is probably explained by an increased supply of oil.
The gold spot price is relative following a similar pattern as the silver price index. The gold price is 409 dollar per ounce is 1989. The price reaches its lowest value in 2001 with a price of 272 dollar per ounce. After 2001 the price starts to increase reaching its highest level in 2013 with a price 1665 dollar per ounce. After 2013 the price drops to its current level of around 1300 dollar per ounce of gold.
8
Figure I
Plots of the commodity prices
Notes: Figure 1 commodity prices. This figure plots the values of the commodity prices retrieved from DataStream and Fred. The charts include the daily spot prices of silver index, WTI crude oil, gold and the Brent crude oil price. The prices are measured in US dollar, over the time period 01-01-1989 to 01-01-2019.
Table II shows the descriptive statistics of variables used in this thesis, for the period 01-01-1989 to 31-12-2018. All the variables have 7824 daily observations. The sample is also split into four sub samples. In order to analyze the efficiency of the commodity market we use different periods. These sub samples have the length of five years, the exact dates of the samples are as follow; 01-01-1989 to 31-12-1993, 1994 to 31-12-1998, 1999 to 31-12-2003, 2004 to 31-12-2008, 01-01-2009 to 31-12-2013 and 01-01-2014 to 31-12-2018. For this samples the daily returns are used. For the purpose of this thesis we use the daily logarithmic returns.
For the full sample all the commodities show a positive mean return. For the first two subsample periods the mean returns are negative for all commodities. The highest mean return is generated for Brent crude oil in the period 2009 to 2013 with 0.086 percent. The returns show high deviations from the mean with minimum and maximum peaks up to twenty percent. However these values are not surprising due to the volatility that characterizes the commodity market. All the full sample periods have a negative skewness meaning that large negative returns tend to be greater than large positive ones. All the sample periods show a value of kurtosis that is in excess of that of normal distribution (3) indicating that the distribution of returns is leptokurtic, which means that the distributions show higher peaks than a normal distribution.
0 500 1000 1500 2000 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019
Silver Spot Price Index
0,00 20,00 40,00 60,00 80,00 100,00 120,00 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019
WTI Crude Oil Price
0,000 500,000 1000,000 1500,000 2000,000 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019
Gold Spot Price
0,00 20,00 40,00 60,00 80,00 100,00 120,00 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019
9
Table II
Descriptive statistics for the sample of commodities in the period 1999 to 2019
Sample period Observations Mean Std. Dev. Min. Max. Skew. Kurtos.
S&P GSCI Silver Spot - PRICE INDEX
Full Sample 7824 0.00012 0.0174 -0.1948 0.1247 -0.778 11.24 1989 - 1993 1303 -0.00014 0.0134 -0.0960 0.0568 -0.510 8.03 1994 - 1998 1305 -0.00002 0.0150 -0.0953 0.0923 0.045 6.80 1999 - 2003 1303 0.00013 0.0116 -0.0533 0.0746 0.113 6.93 2004 - 2008 1305 0.00049 0.0232 -0.1479 0.1092 -1.046 9.14 2009 - 2013 1304 0.00041 0.0229 -0.1948 0.1247 -0.870 9.11 2014 - 2018 1304 -0.00016 0.0142 -0.0761 0.0705 -0.286 7.01
WTI Crude Oil Prices: West Texas Intermediate (WTI)
Full Sample 7824 0.00012 0.0242 -0.4063 0.1886 -0.731 18.32 1989 - 1993 1303 -0.00016 0.0270 -0.4063 0.1886 -2.729 48.15 1994 - 1998 1305 -0.00012 0.0225 -0.0141 0.0154 0.032 9.52 1999 - 2003 1303 0.00074 0.0258 -0.1709 0.1244 -0.655 7.21 2004 - 2008 1305 0.00024 0.0251 -0.1282 0.1641 0.006 7.90 2009 - 2013 1304 0.00061 0.0213 -0.1274 0.1330 0.063 8.55 2014 - 2018 1304 -0.00059 0.0229 -0.1119 0.1128 0.132 5.78
Gold Fixing Price 10:30 A.M. London Bullion
Full Sample 7824 0.00014 0.0098 -0.0891 0.0964 -0.007 12.46 1989 - 1993 1303 -0.00048 0.0079 -0.0513 0.0407 -0.382 8.21 1994 - 1998 1305 -0.00024 0.0062 -0.0319 0.0438 0.392 7.52 1999 - 2003 1303 0.00028 0.0258 -0.0435 0.0964 1.724 19.31 2004 - 2008 1305 0.00055 0.0135 -0.0875 0.0955 -0.281 8.82 2009 - 2013 1304 0.00052 0.0119 -0.0891 0.0507 -0.646 8.37 2014 - 2018 1304 0.00050 0.0209 -0.0273 0.0378 0.186 4.32
Crude Oil Prices: Brent
Full Sample 7824 0.00014 0.0224 -0.3612 0.1813 -0.596 17.36 1989 - 1993 1303 -0.00017 0.0249 -0.3612 0.1733 -2.510 44.54 1994 - 1998 1305 -0.00017 0.0207 -0.0915 0.1626 0.540 8.20 1999 - 2003 1303 0.00078 0.0252 -0.1989 0.1285 -0.676 7.46 2004 - 2008 1305 0.00012 0.0227 -0.1683 0.1146 -0.243 7.37 2009 - 2013 1304 0.00086 0.0197 -0.1132 0.1813 0.538 11.52 2014 - 2018 1304 -0.00059 0.0209 -0.0808 0.0989 0.327 5.58
10
4. Methodology
As mentioned before, weak-form market efficiency describes a market that fully incorporates historical price movements in future ones. This means that the price movements must be serially independent of each other over time. In statistical terms, the weak market efficiency is often referred to as the random walk model. In order to examine whether prices follow a random walk, the returns of four commodities are examined using six tests for independence. First three linear tests will be conducted on dependence in returns, while three tests examine the nonlinear dependence of the returns. In line with Urquhart and Hudson (2013) a five yearly subsample method is favored to capture the changing efficiency of the four commodity prices.
In line with Urquhart and Hudson (2013) we employ five-type classification of the behavior of commodity markets over time. These types depend on the independence of the returns over time. The five types are as follow; 1) efficient, 2) moving toward efficiency, 3) switching to efficiency/inefficiency, 4) adaptive and 5) inefficient. A market is efficient if the returns are independent with no dependence throughout the sample period. A market is moving toward efficiency if returns were dependent but the dependence over time has trended to reduce. A market has switched to efficiency/inefficiency if returns were independent (dependent) but become dependent (independent), this could be evidence of an early stage of an adaptive market. A market is considered adaptive if returns have gone through at least three different stages of dependence, for example; dependent, independent, dependent. Lastly, a market is inefficient if it has no independence in returns throughout the sample. So, the classification incorporates all possible types of return behavior. In this thesis the dependency will be primarily analyzed from a statistical point of view.
4.1 Linear tests
4.1.1 Autocorrelation test
The autocorrelation test is used for investigating the independence of random variables in series. If autocorrelations are found in the data, returns are not independent. As Samuelson (1965) pointed out properly anticipated prices will act randomly therefore our first test is the autocorrelation test. Autocorrelations are found when the covariance and correlations between different disturbances are not all non-zero. In other words; where 𝐶𝑜𝑣(𝜀𝑖, 𝜀𝑗) = 𝜎𝑖𝑗 for all 𝑖 ≠ 𝑗 where 𝜀𝑡 is the value of the
disturbance term in the 𝑖th observation. The autocorrelation coefficient at lag k is defined as follows; 𝜌𝑘 =
𝛾𝑘
𝛾0
(1)
Where 𝜌𝑘 is the autocorrelation at lag 𝑘. And 𝛾𝑘 is the covariance at lag 𝑘, and 𝛾0 is the variance. The
first order autoregressive process contains values of 𝜀𝑡 lagged by one period, indicating that the
disturbance in period 𝑡 is influenced by the disturbance in the previous period, 𝜀𝑡−1. If 𝜌 > 0 there is
positive autocorrelation and if 𝜌 < 0 than there is negative autocorrelation. The null hypothesis is that 𝜌 = 0 which implies a random walk process.
4.1.2 Runs test
11 of runs, irrespective of signs. So a run is a sequence of positive or negative returns. The formula to calculate the expected number of runs is;
𝐸(𝑢) =2𝑃𝑁(𝑃 + 𝑁)
(𝑃 + 𝑁) + 1 (2)
Where, 𝐸(𝑢) is the expected number of runs. The number of positive runs is denoted by 𝑃, while the number of negative runs is denoted by 𝑁. The variance of runs is calculated by;
𝜎2= 2𝑃𝑁(2𝑃𝑁 − 𝑃 − 𝑁)
(𝑃 + 𝑁)2(𝑃 + 𝑁 − 1) (3)
Where the 𝜎2 is the variance of the runs. The number of positive runs is denoted by 𝑃, while the number of negative runs is denoted by 𝑁. If 𝑁 is large enough then the returns will approximately follow a normal distribution with a test statistic defined as:
𝑍 =𝑟 − 𝐸(𝑢)
√𝜎2(𝑟) (4)
Where 𝑍 is the Z statistic, 𝑟 is the number of runs, 𝐸(𝑢) is the expected number of runs and 𝜎2 the variance of the runs. The null hypothesis is that the series are independent. The null hypothesis of independence of the series will be rejected when the z-value is greater than the critical values. Otherwise, it will be concluded that the returns are independent. Furthermore, the sample will not be independent if it consists of too many or too few runs. Hence, the independence of returns can be assessed by analyzing the distribution of the duration of runs. If the actual number of runs exceeds (falls below) the expected runs, a positive (negative) z-value is obtained.
4.1.3 Variance ratio test
Lo and MacKinlay (1988) proposed the variance ratio test, the variance ratio test is a primary tool in examining whether returns are serially uncorrelated. The variance ratio test has also been used by Smith and Ryoo (2003) for testing the random walk hypothesis on emerging European stock markets. They examined the stock market of Greece, Hungary, Poland, Portugal and Turkey, using the variance ratio test. In four of the markets, the random walk hypothesis has been rejected because of autocorrelation in the returns. Only for the Turkey stock market the random walk hypothesis was not rejected. This makes it an interesting test to apply it to the commodity market as well.
Under Random walk hypothesis for returns 𝑟𝑡, the variance of 𝑟𝑡+ 𝑟𝑡−1 is required to be twice the
variance of 𝑟𝑡. The variance ratio test can be used for testing this requirement, by using the single
variance ratio, denoted by 𝑉𝑅(𝑘). If 𝑟𝑡 is the asset return at time 𝑡, where 𝑡 = 1,2,3 … 𝑇. Then the
variance ratio 𝑟𝑡, with holding period 𝑘 is;
𝑉𝑅(𝑘) = 𝜎𝑘
2
𝑘𝜎2 (5)
Where 𝑘 is the holding period, 𝜎𝑘2 is the variance of the return in the holding period 𝑘. The expression
above can be rewritten as;
𝑉𝑅(𝑘) = 1 + 2 ∑ (1 − 𝑗 𝑘
𝑘−1
𝑗=1 )𝜌(𝑗) (6)
Where 𝜌(𝑗) is the autocorrelation of 𝑟𝑡 of order 𝑗. The variance ratio is 1 plus a weighted sum of
12 uncorrelated with 𝜌(𝑗) = 0. On the other hand, value for 𝑉𝑅(𝑘) greater the one imply a positive serial correlation and values less than one imply negative serial correlation or mean reversion.
Lo and Mackinlay (1988) determined the asymptotic distribution of 𝑉𝑅(𝑥; 𝑘) by assuming that 𝑘 is fixed when 𝑇 → ∞. Lo and Mackinlay (1988) showed that if 𝑥𝑡 is independent and identically
distributed under the assumption of homoscedasticity. Then the null hypothesis that V(𝑘) = 1, the test statistic 𝑀1(𝑘) is given by;
𝑀1(𝑘) =
𝑉𝑅(𝑥; 𝑘) − 1
ф(𝑘)1/2 (7)
Which follows the standard normal distribution asymptotically. The asymptotic variance, ф(k), is given by;
ф(𝑘) =2(2𝑘 − 1)(𝑘 − 1)
3𝑘 (8)
To accommodate the returns exhibiting conditional heteroscedasticity, Lo and Mackinlay (1988) proposed the heteroscedasticity robust test statistic 𝑀2(𝑘);
𝑀2(𝑘) =
𝑉𝑅(𝑥; 𝑘) − 1
ф(𝑘)1/2 (9)
Which follows the standard normal distribution asymptotically under the null hypothesis that 𝑉(𝑘) = 1 where; ф∗(𝑘) = ∑ [2(𝑘 − 𝑗) 𝑘 ] 2 𝑘−1 𝑗=1 𝛿(𝑗) (10) 𝛿(𝑗) =[∑ (𝑥𝑡− û) 2(𝑥 𝑡−𝑗− û)2 𝑇 𝑡=𝑗+1 ] [∑𝑇𝑡=𝑗(𝑥𝑡− û)2]² (11)
The 𝑀2(𝑘) test is applicable to returns of price series and this thesis uses 𝑀2(𝑘) due to the
heteroscedasticity property of the return series of the commodities studied. In estimating 𝑉𝑅(𝑘), a choice has to be made on the number of holding periods 𝑘. In this study the holding periods 2, 4, 8 and 16 will be analyzed.
4.2 Nonlinear tests
The previous tests examined the linear dependence of commodity market returns. However, nonlinear dependence may not be detected. The presence of a unit root is not per se sufficient to conclude that a market is efficient since the return series must be serially uncorrelated or serially independent (Lim et al., 2009). Besides that, unit root tests are not developed to detect return predictability (Lim and Hooy, 2012). If there is persistent nonlinear dependence in commodity returns, it could be exploited by making use of different trading strategies.
13 for time based dependence in series has power against a variety of possible deviations from independence including linear dependence, non-linear dependence, or chaos. The features of these tests make them useful to find dependence in the returns.
First the linear structure will be removed of the data through a pre-whitening model. An 𝐴𝑅(𝜌) model is fitted to the data with the optimal lag length in such a way that the standardized residuals are no longer correlated through the Ljung-Box statistic up to 20 lags. The 𝐴𝑅(𝜌) model in which the Q-statistic at 20 lags is not significant at the significance level of 10% will be chosen. The residuals of the pre-whitened model will be tested on the following nonlinear tests, the McLeod and Li (1983), Engle (1982) and Brock, Dechert, and Schieinkman (1996) tests.
4.2.1 McLeod Li test
McLeod and Li’s (1983) portmanteau test of nonlinearity seeks to discover whether the squared autocorrelation function of returns is non-zero. The test statistic is given by the following formula;
(𝑄)𝑚= 𝑛(𝑛 + 2) 𝑛 − 𝑘 ∑ 𝑟𝑎 2(𝑘) 𝑚 𝑘=1 (12)
Where 𝑇 is the sample size, 𝑛 the number of observations and 𝑘 the number of lags. And where 𝑟𝑎2 is
the autocorrelation of the squared residuals. 𝑟𝑎2(𝑘) =
∑𝑛𝑡=𝑘+1𝜀𝑡2𝜀𝑡−𝑘2
∑𝑛 𝜀𝑡2 𝑡=1
(13)
With 𝑘 = 0,1, … , 𝑛 − 1 and where, 𝜀𝑡2is obtained after fitting appropriate 𝐴𝑅 (𝑝). McLeod-Li tests for
2𝑛𝑑 order nonlinear dependence. If the series 𝜀𝑡 is independently and identically distributed the
asymptotic distribution of (𝑄)𝑚 is 𝜒2 with 𝑚 degrees of freedom. The null hypothesis is independence
of returns and if it is rejected, it indicates the presence of ARCH or GARCH nonlinear effects in the series.
4.2.2 Engle Lagrange Multiplier test
The Engle Lagrange Multiplier test was proposed by Engle in 1982 to detect the ARCH distributive. The residuals of the 𝐴𝑅(𝜌) model are tested for heteroscedasticity. The Engle LM statistic is computed from an auxiliary test regression, which is;
𝑒𝑡2= 𝛼
0+ ∑ 𝛼𝑖 𝑝
𝑖=1
𝑟𝑡−𝑖2 + 𝑣𝑡 (14)
Where 𝑒 is the residual from the pre-whitened 𝐴𝑅(𝜌) model. The F-statistic is an omitted variable test for the joint significance of lagged squared residuals. The 𝑁𝑅2 is the Engle LM test statistic. Where 𝑁 is the number of observations times the 𝑅2 from the test regression. Under the null hypothesis of a linear generating mechanism for 𝑒𝑡, the 𝑁𝑅2 for this regression follows a asymptotically 𝜒2(𝑝)
distribution. There is evidence for ARCH of GARCH effects in the data when the null hypothesis is rejected.
4.2.3 BDS test
14
a time series”(Brock et al., 1987). The test is founded on the concept of spatial correlation from chaos
theory.
The null hypothesis of the BDS test is that the data generating processes are independent and identically distributed. While the alternative hypothesis states that the model is not appropriate (Brock et al., 1996). If the null hypothesis cannot be accepted it assumed that there is no market efficiency of the sample. The correlation integral is the probability that any two points are within a certain length ‘𝑒’ apart in phase space. When ‘𝑒’ is increased, the probability scales according to the fractional dimension of the phase space. The correlation integrals are calculated according to;
𝐶𝑚(𝑒) = [
1
𝑁2] × ∑ 𝑍(𝑒 − |𝑋𝑖− 𝑋𝑗| 𝑇
𝑖,𝑗=1 ) (15)
With 𝑖 ≠ 𝑗, where, 𝑍(𝑒) = 1 if [𝑒 − |𝑋𝑖− 𝑋𝑗| > 0], otherwise 0. 𝑇 is the number of observations, 𝑒 is
the distance, 𝐶𝑚 is the correlation integral for dimension 𝑚, and 𝑋 is the commodity series. The 𝑚 dimension is a point in 𝑚 dimensional space where 𝑚 is the embedding dimension given by;
𝑀1: 𝑥𝑡1= 𝑥𝑡 (16)
𝑀2: 𝑥𝑡2= (𝑥𝑡, 𝑥𝑡+1) (17)
𝑀𝑚: 𝑥𝑡𝑚= (𝑥𝑡, … , 𝑥𝑡+(𝑚−1)) (18)
The function 𝑧 counts the number of points within a distance 𝑒 of one another. The correlation integral calculates the probability that two points that are part of two trajectories in phase space are ‘𝑒’ units apart. The BDS statistic, where 𝑊 is normally distributed with a mean of zero. 𝑊 is given by;
𝑊𝑛(𝑒, 𝑇) = |𝐶𝑛(𝑒, 𝑇) − 𝐶1(𝑒, 𝑇)𝑁| × √[
𝑇 𝑆𝑛(𝑒, 𝑇)
] (19)
Where 𝑆𝑛(𝑒, 𝑇) is the standard deviation of the correlation integrals. The BDS statistic, 𝑊, has a
limiting normal distribution under the null hypothesis of IID when the data series consists of more than five hundred observations. Hsieh (1991) states that structural changes in the data series can cause a rejection of the null hypothesis of IID on the basis of the BDS test. This is a good reason for splitting the full sample into subsamples, which is done in this thesis. To conduct the BDS test the value of “𝑒” has to be chosen. The "𝑒" value represents the maximum distance for the pair (𝑋𝑖, 𝑋𝑗). The developers
15
5. Results
The results of the autocorrelation, runs and the variance ratio test are presented in table III. The results show that for the silver price index and the gold price the first order autocorrelation are negative and significant. For the Brent crude oil price the first order autocorrelation is positive and significant which indicates that the returns are not independent on the basis on their full past price history. However, for the WTI oil price the first autocorrelation is insignificant.
Table III also shows the autocorrelations for the subsamples. For the silver spot price index the first two subsamples show no significant autocorrelations of the returns. However, in the period from 1999 to 2003 the autocorrelation of the first order to be negative and significant. In this period the autocorrelations are significant up to lag 5. Nevertheless the following two subsample period show no significant autocorrelation coefficients. Indicating that the silver spot price index returns were independent during this period. In the last period from 2014 to 2018 the first order correlation turns out to be negative and significant. Thus during this period the silver price appears to be predictable. These results suggest that silver price index returns have gone through sub periods of being independent and sub periods of being dependent, suggesting the adaptive market hypothesis is a good description of the data.
For the WTI oil price the first two subsample periods show no significant first order autocorrelation. However, the autocorrelations for the third and the fifth lag turn out to be negative and significant. For the period of 1999 to 2003 there is no significant autocorrelation. Which indicates that the WTI oil price returns are independent in this period. Followed by a period of significant autocorrelations up to lag 5. In the period 2009 to 2013 the returns show no significant autocorrelations and finally in the last sub sample period the first order autocorrelation in negative and significant. Also the WTI oil price returns seem to switch between periods of dependent and independent returns which is in favor of the adaptive market hypothesis.
The gold price returns show no significant autocorrelations in the first subsample period. However the second and third subsample show significant autocorrelations up to lag 5. However, the last three subsamples show no significant autocorrelations, which indicates independence of the gold price returns. Also here the test results indicate that the independence of returns in this market fluctuate over time, confirming the adaptive market hypothesis.
For the Brent crude oil price returns only the first two subsample periods show significant autocorrelation returns. The last four subsamples periods show no significant autocorrelation in the returns. This indicates that the Brent crude oil prices were independent in the last four subsamples. However, a market is considered adaptive if returns have gone through at least three different stages of dependence. This is not the case for the Brent crude oil price. Thus the results for the Brent crude oil price are not in favor of the adaptive market hypothesis. However, this switch from inefficiency to efficiency, could be the first stage of the adaptive market hypothesis.
16
Table III
Results for linear correlation tests Autocorrelation Runs VR Start
Year
End Year
Lag 1 Lag 3 Lag 5 z-statistic K=2 K=4 K=8 K=16
S&P GSCI Silver Spot - PRICE INDEX
Full Sample -0.022** 0.004 0.009 5.326*** 1.003 1.007 1.014 1.035 1989 - 1993 0.004 -0.026 0.039 2.017** 1.016 1.024 1.022 0.931 1994 - 1998 -0.034 0.004 -0.022 4.494*** 0.982 0.980 0.960 0.907 1999 - 2003 -0.096*** 0.015*** -0.001*** 2.627*** 0.903** 0.889* 0.897* 0.811 2004 - 2008 -0.003 0.029 -0.003 0.677 1.015 1.072 1.007 0.972 2009 - 2013 -0.011 -0.013 0.018 3.017*** 1.010 0.997 1.028 0.961 2014 - 2018 -0.063** 0.003 0.022 0.468 0.946* 0.947 1.003 0.961
WTI Crude Oil Prices: West Texas Intermediate (WTI)
Full Sample -0.018 -0.022*** -0.030*** 1.064 0.954 0.915 0.902 0.899 1989 - 1993 -0.002 -0.134*** -0.037*** 2.239** 0.986 0.860 0.681 0.608 1994 - 1998 0.035 -0.108*** -0.001*** -1.052 1.023 0.944* 0.820* 0.660** 1999 - 2003 -0.025 0.019 0.002 -1.044 0.963 0.917 0.866 0.770 2004 - 2008 -0.048* 0.072*** -0.119*** 1.136 0.922 0.875 0.855 0.920 2009 - 2013 -0.002 0.008 0.010 -0.494 1.000 0.978 0.969 0.919 2014 - 2018 -0.063** 0.012 -0.005 1.165 0.923** 0.889* 0.932 1.028
Gold Fixing Price London Bullion
Full Sample -0.037*** 0.018*** 0.027*** 3.435** 0.976 0.954 0.930 0.924 1989 - 1993 -0.035 -0.009 0.028 4.751*** 0.928 0.945 0.967 1.026 1994 - 1998 -0.069** 0.022* -0.005* 1.560 0.936* 0.907 0.843 0.797 1999 - 2003 -0.016*** 0.004*** -0.001*** 2.509** 0.870** 0.921* 0.998* 0.959 2004 - 2008 -0.016 0.035 0.031 -0.763 0.974 0.987 0.927 0.891 2009 - 2013 -0.031 0.004 0.050 0.883 0.695 0.924 0.878 0.880 2014 - 2018 0.029 0.039 0.020 -0.205 1.030 1.030 1.112 1.141
Crude Oil Prices: Brent
Full Sample 0.029** -0.020** -0.007* -2.344** 1.030* 1.037* 1.058 1.110 1989 - 1993 0.057** -0.117*** -0.028*** -1.491 1.042 1.022 0.852 0.796 1994 - 1998 0.051* 0.021* -0.055*** -0.962 1.055 1.047 0.942 0.876 1999 - 2003 0.035 -0.005 0.003 -1.171 1.041 1.064 1.097 1.178 2004 - 2008 -0.016 0.029 0.024 -2.347** 1.052 1.057 1.121* 1.279* 2009 - 2013 0.002 -0.060 0.015 0.285 1.001 0.983 0.961 0.921 2014 - 2018 0.031 0.016 0.002 0.118 1.020 1.045 1.148* 1.298**
Notes: Test results for linear correlation tests of the full sample and 5 year sub samples for the silver price index, WTI crude oil prices, gold prices and the Brent crude oil prices. The first two columns present the start date and the end date of the sub samples. Columns 3 to 5 indicate the autocorrelation at lag 1,3 and 5. The sixth column shows the z-statistic for the non-parametric runs test. The last four columns show that variance ratio for 𝑘 equal to 2,4,8 and 16. ***, ** and * represents significance at the 1%, 5% and 10% level respectively.
17 The results for the gold price suggest that the adaptive market hypothesis yields for the gold market. The z statistic for the full sample is positive and significant. Suggesting that the gold price returns are generally not independent and the observed number of runs is significantly higher than the expected number of runs. Also the first and the third subsample period are positive and significant. But for the other periods the z statistic is not significant. Suggesting that the gold price returns are independent for those periods.
Finally, the runs test for the Brent crude oil price is negative and significant for the full sample. Which indicates that the Brent crude oil price returns are generally not independent. Also for the period 2004 to 2008 the z statistic is negative indicating that the observed number of runs is significantly fewer than the expected number of runs. However, for the other periods the z statistic is insignificant. These results indicate that the Brent crude oil price returns have switched between efficiency and inefficiency which is in favor of the adaptive market hypothesis.
Finally, the variance ratio test is included in table III. The silver price index results for the variance ratio test show that there that there is no mean reversion in the full sample period for all four test 𝑘’s. The results for the subsample periods show only for the subsample period 1999 to 2003 three significant results. And for the period 2014 to 2018 there is a positive significant result which implies that there is some mean reversion in the returns. All other subsamples do not have any k's that are significant, indicating that returns are independent. Thus the silver price variance ratio test results indicate that returns do conform to the adaptive market hypothesis.
For the WTI oil price returns the variance ratio test shows only in the period 1994 to 1998 and 2014 to 2018 significant results. For the full sample there are no significant returns. Also, all other subsamples do not have any 𝑘's that are significant, indicating that returns are independent. Thus the WTI oil price variance ratio test results indicate that returns do conform to the adaptive market hypothesis.
The variance ratio test result for the gold returns indicate independence for the full sample. The subsample 1999 to 2003 cannot reject the null hypothesis of independence for two or more values of 𝑘. Also in the period 1994 to 1998 there is one significant result. For the other subsample periods there is no evidence of dependence in the returns. These results are in favor of the adaptive market hypothesis.
Finally, the variance ratio test for the Brent crude oil returns indicate that the returns conform to the adaptive market hypothesis. For the full sample the period 2004 to 2008 and 2014 to 2018, two 𝑘 results are positive and significant. These periods provide significant evidence of positive persistent dependent behavior since the variance ratio statistic is greater than one. For the other sub samples there is no significant evidence of dependence in the returns.
18
Table IV
Results for nonlinear correlation tests
Ljung-Box test statistics Mcleod-Li test statistics Engle LM statistics AR Qr (5) Qr (10) Qr (20) Qrr (5) Qrr (10) Qrr (20)
Lag 2 Lag 4 Lag 6
S&P GSCI Silver Spot - PRICE INDEX
Full Sample 1 1.534 9.809 29.608* 533*** 852*** 1361*** 271.13*** 341.27*** 437.28*** 1989 - 1993 1 3.923 13.162 31.097* 42.1*** 60.3*** 78.9*** 17.56*** 23.39*** 26.04*** 1994 - 1998 0 5.440 12.845 30.06* 7.83*** 19.7*** 71.8*** 4.96*** 5.74*** 6.69*** 1999 - 2003 3 3.566 6.740 19.77 43.9*** 48.0*** 65.9*** 27.15*** 39.64*** 45.81*** 2004 - 2008 0 1.473 7.689 33.566* 88.2*** 175*** 310.3*** 34.03*** 48.61*** 98.10*** 2009 - 2013 0 1.448 6.386 15.546 58.3*** 62.5*** 66.9*** 45.17*** 50.07*** 51.60*** 2014 - 2018 1 1.209 16.352 28.375 9.08*** 16.0*** 36.0*** 9.13*** 9.46*** 16.38***
WTI Crude Oil Prices: West Texas Intermediate (WTI)
Full Sample 8 0.003 0.885 17.501 3937*** 5852*** 7423.9*** 994.66*** 1770.66*** 1840.7*** 1989 - 1993 8 0.043 0.833 19.353 131*** 176*** 202.7*** 46.61*** 77.52*** 96.31*** 1994 - 1998 6 0.045 3.610 28.239* 670*** 725*** 790.2*** 297.49*** 306.54*** 310.52*** 1999 - 2003 4 1.306 7.039 16.683 164*** 171*** 174.2*** 242.67*** 266.35*** 271.50*** 2004 - 2008 5 0.106 3.602 17.037 693*** 888*** 1454*** 283.58*** 331.56*** 446.12*** 2009 - 2013 7 0.613 3.701 28.179 314*** 566*** 1008*** 95.91*** 152.24*** 202.45*** 2014 - 2018 1 3.834 4.653 10.902 227*** 356*** 607.3*** 89.75*** 123.50*** 130.19***
Gold Fixing Price 10:30 A.M. London Bullion
Full Sample 11 0.004 0.011 8.253 2820*** 4743*** 7330*** 1244.8*** 1339.91*** 1543.9*** 1989 - 1993 1 5.08 12.38 17.13 42.6*** 83.8*** 165.7*** 10.29*** 28.22*** 33.21*** 1994 - 1998 9 0.070 3.276 11.218 938*** 1327*** 1472*** 259.16*** 427.94*** 428.10*** 1999 - 2003 7 0.034 4.940 13.501 91.3*** 125*** 140.8*** 156.09*** 240.04*** 336.09*** 2004 - 2008 0 5.412 12.741 21.865 127*** 213**** 459.2*** 34.09*** 74.46*** 96.89*** 2009 - 2013 0 7.459 16.807* 32.63** 31.3*** 55.7*** 75.4*** 16.31*** 26.17*** 27.08*** 2014 - 2018 0 4.934 17.357 22.542 32.7*** 55.8*** 70.3*** 10.69*** 20.13*** 31.37***
Crude Oil Prices: Brent
19
Table V The BDS test results
Dimension 2 6
Embedding Dimension
AR 0.5σ 1σ 1.5σ 2σ 0.5σ 1σ 1.5σ 2σ
S&P GSCI Silver Spot - PRICE INDEX
Full sample 1 0.0072* 0.0142* 0.0131* 0.0095* 0.0002* 0.0322* 0.0608* 0.0567* 1989 - 1993 1 0.0083* 0.0152* 0.0114* 0.0065* 0.0020* 0.0313* 0.0634* 0.0562* 1994 - 1998 0 0.0032* 0.0078* 0.0081* 0.0051* 0.0005* 0.0124* 0.0302* 0.0278* 1999 - 2003 3 0.0035* 0.0075* 0.0082* 0.0059* 0.0007* 0.0115* 0.0303* 0.0336* 2004 - 2008 0 0.0084* 0.0186* 0.0191* 0.0136* 0.0017* 0.0317* 0.0771* 0.0815* 2009 - 2013 0 0.0014* 0.0044* 0.0061* 0.0067* 0.0005* 0.0105* 0.0258* 0.0356* 2014 - 2018 1 0.0005* 0.0009* 0.0032* 0.0035* 0.0000* 0.0013* 0.0078* 0.0121* WTI Crude Oil Prices: West Texas Intermediate (WTI)
Full sample 8 0.0067* 0.0152* 0.0156* 0.0114* 0.00185* 0.0314* 0.0736* 0.0821* 1989 - 1993 8 0.0172* 0.0316* 0.0249* 0.0135* 0.00755* 0.0912* 0.1415* 0.1149* 1994 - 1998 6 0.0031* 0.0063* 0.0066* 0.0061* 0.00117* 0.0179* 0.0436* 0.0536* 1999 - 2003 4 0.0021* 0.0075* 0.0100* 0.0089* 0.00207* 0.0069* 0.0258* 0.0383* 2004 - 2008 5 0.0040* 0.0109* 0.0145* 0.0126* 0.00086* 0.0171* 0.0556* 0.0820* 2009 - 2013 7 0.0072* 0.0172* 0.0172* 0.0114* 0.00169* 0.0321* 0.0820* 0.0934* 2014 - 2018 1 0.0089* 0.0201* 0.0189* 0.0130* 0.00212* 0.0343* 0.0765* 0.0818* Gold Fixing Price London Bullion
Full sample 11 0.0098* 0.0175* 0.0161* 0.0115* 0.00372* 0.0404* 0.0785* 0.0774* 1989 - 1993 1 0.0049* 0.0095* 0.0089* 0.0061* 0.00184* 0.0264* 0.0537* 0.0513* 1994 - 1998 9 0.0105* 0.0162* 0.0135* 0.0086* 0.00440* 0.0421* 0.0725* 0.0625* 1999 - 2003 7 0.0087* 0.0177* 0.0163* 0.0113* 0.00154* 0.0307* 0.0670* 0.0667* 2004 - 2008 0 0.0121* 0.0248* 0.0225* 0.0153* 0.00318* 0.0466* 0.0908* 0.0872* 2009 - 2013 0 0.0031* 0.0071* 0.0072* 0.0053* 0.00072* 0.0154* 0.0402* 0.0492* 2014 - 2018 0 0.0018* 0.0044* 0.0042* 0.0028* 0.00016* 0.0057* 0.0189* 0.0236* Crude Oil Prices: Brent
Full sample 16 0.0052* 0.0114* 0.0110* 0.0079* 0.00167* 0.0275* 0.0604* 0.0625* 1989 - 1993 5 0.0153* 0.0269* 0.0201* 0.0135* 0.00825* 0.0897* 0.1293* 0.1049* 1994 - 1998 4 0.0034* 0.0914* 0.0111* 0.0083* 0.00057* 0.0122* 0.0371* 0.0455* 1999 - 2003 7 0.0017* 0.0040* 0.0049* 0.0047* 0.00031* 0.0083* 0.0281* 0.0375* 2004 - 2008 0 0.0042* 0.0018* 0.0025* 0.0027* 0.00025* 0.0077* 0.0249* 0.0344* 2009 - 2013 0 0.0057* 0.0136* 0.0142* 0.0105* 0.00198* 0.0336* 0.0804* 0.0864* 2014 - 2018 0 0.0068* 0.0135* 0.0123* 0.0098* 0.00234* 0.0314* 0.0612* 0.0632*
Notes: This table presents the results of the BDS test for nonlinearity in the residuals of the pre-whitening AR model. The first row reports the dimension while the second row documents the embedding dimension by values of the standard deviation of the sample. * represents significance at the 1%, level.
20 0 0,005 0,01 0,015 0,02 0 20 40 60 80 100 1993 1998 2003 2008 2013 2018
Silver Spot Price Index
McLeod Li test Engle LM statistic BDS
Figure 2
Plots of nonlinear test statistics results
Notes: This figure plots the values of the following selected statistical tests for the silver price index, WTI crude oil, gold and the Brent crude oil price: McLeod–Li statistic up to lag (5), Engle LM statistic up to lag 4 and the BDS test with dimension 2 and embedding dimension 1σ. The left axis provides the values of McLeod-Li and the Engle LM statistic, while the right axis gives the values of the BDS test. The graphs beginning points are the end of the first subsample.
From figure 2 it can be observed that there is changing magnitude in nonlinear dependence. For the silver spot price index the nonlinear dependence is increasing from the period 1998 to 2008. Where it is declining after 2008. Also the nonlinear dependence for the WTI oil price has not been constant throughout the period. Especially the McLeod Li test statistic is fluctuating over the period 1993 to 2013. For the gold spot price returns the test statistic indicate that the degree of nonlinear dependence is not constant over time. The McLeod-Li statistic spikes in 1998 and is relatively stable in the period after 2003. Which could indicate a shift to less nonlinear dependence and so a beginning to market efficiency. The statistical test for the Brent crude oil price returns follow a relative similar pattern. The values of the statistics increase from 1993 to 1998, where after they start to decrease until 2008.
0 0,005 0,01 0,015 0,02 0,025 0,03 0,035 0 200 400 600 800 1993 1998 2003 2008 2013 2018
WTI Crude Oil Price
McLeod Li test Engle LM statistic BDS 0 0,005 0,01 0,015 0,02 0,025 0,03 0 200 400 600 800 1000 1993 1998 2003 2008 2013 2018
Gold Spot Price
McLeod Li test Engle LM statistic BDS 0 0,02 0,04 0,06 0,08 0,1 0 50 100 150 200 250 300 350 1993 1998 2003 2008 2013 2018
Brent Crude Oil Price
21 This thesis is closely linked to research done by Urquhart and Hudson (2013). We use the same statistical tests and apply the five type classification model. Our contribution to the literature is that we use a different asset class and a more recent time period. In table VI the summary of the test results are presented. By making use of the five type classification model and analyzing the patterns of dependence and independence of the returns we can analyze if the AMH is a proper description for the commodity market.
Table VI
Summary of the test results
Sample Period Autocorrelation Runs Variance ratio Mcleod Li LM Engle BDS test S&P GSCI Silver Spot - PRICE INDEX
Full sample D D I D D D 1989 - 1993 I D I D D D 1994 - 1998 I D I D D D 1999 - 2003 D D D D D D 2004 - 2008 I I I D D D 2009 - 2013 I D I D D D 2014 - 2018 D I I D D D
Classification AMH AMH AMH Inefficient Inefficient Inefficient
WTI Crude Oil Prices: West Texas Intermediate (WTI)
Full sample I I I D D D 1989 - 1993 I D I D D D 1994 - 1998 I I D D D D 1999 - 2003 I I I D D D 2004 - 2008 D I I D D D 2009 - 2013 I I I D D D 2014 - 2018 D I D D D D
Classification AMH Switch to
efficiency
AMH Inefficient Inefficient Inefficient
Gold Fixing Price London Bullion
Full sample D D I D D D 1989 - 1993 I D I D D D 1994 - 1998 D I I D D D 1999 - 2003 D D D D D D 2004 - 2008 I I I D D D 2009 - 2013 I I I D D D 2014 - 2018 I I I D D D
Classification AMH AMH AMH Inefficient Inefficient Inefficient
Crude Oil Prices: Brent
Full sample D D D D D D 1989 - 1993 D I I D D D 1994 - 1998 D I I D D D 1999 - 2003 I I I D D D 2004 - 2008 I D D D D D 2009 - 2013 I I I D D D 2014 - 2018 I I D D D D Classification Switch to efficiency
22
6. Conclusion
In this thesis the adaptive market hypothesis has been investigated on the commodity markets. By making use of a sample of thirty years historic data for the silver, WTI oil, gold and Brent crude oil spot price. To examine if the adaptive market hypothesis holds for the commodity markets the sample has been divided into subsamples to test if market efficiency changes over time. To validate this issue empirically the data was subjected to linear and nonlinear tests. Table VI presents a summary of the results for the tests that have been conducted.
The adaptive market hypothesis requires that at least three different stages of dependency are required. For the silver price index three linear tests namely the autocorrelation, the Runs and variance ratio test indicated that the market efficiency changes over time. Which suggests that the commodity market behaves in line with the adaptive market hypothesis. So the linear results suggests that the silver price index is adaptive however, the tests do not fully agree on which periods are efficient and inefficient.
For the WTI crude oil prices the autocorrelation and variance ratio test indicate that the market behaves adaptive. However analyzing the subsamples of the WTI indicates that the market has not gone through three different stages of efficiency. The first period shows dependence of the returns where after the results switch to independence of the returns. Therefore, according to the runs test the market has switched towards efficiency.
The linear tests for the gold price returns indicate that the market prices of gold behave adaptive. Although the different tests disagree for the first three periods on which periods are efficient or inefficient. Which also happens by other commodities.
Finally, the Brent crude oil prices show mixed evidence for the adaptive market hypothesis. With the variance ratio test and the nonparametric runs test providing evidence for the adaptive market hypothesis but autocorrelation test only indicating a switch to efficiency. This could be evidence of the AMH, but at this point can only be deemed as a switch to efficiency.
In this thesis also nonlinear dependence was tested. The nonlinear tests indicated that for each commodity and sample period there appears to be strong significant nonlinear dependence, which indicating inefficiency. Because the nonlinear tests show strong dependence for each commodity market, the degree of nonlinear dependence over time has been plotted. The results show that the degree of nonlinear dependence is not constant over time. However, the graphs show that the dependence looks like to decrease at the end of the time period. Which could indicate a change towards market efficiency.
By making use of the five type classification of commodity market returns over time, it can be concluded that none of the commodity markets has been constantly efficient. This yields for the linear and the nonlinear tests. The linear tests show that the markets have generally gone through periods of efficiency and inefficiency. The nonlinear tests show that the commodity markets have been inefficient throughout the time. In summary the statistical evidence from the linear tests seems to be very supportive of the adaptive market hypothesis whereas the nonlinear tests indicate continuing, inefficiency.
23 outcome of the research. Nevertheless, the data can still be used for a certain degree of generalizations. While this thesis covers some of the key commodities, only four commodities have been used in this thesis.
24
7. References
Arnold, J., Minner, S., (2011). Financial and Operational Instruments for Commodity Procurement in Quantity Competition. International Journal of Production Economics, Volume 131, pp. 96-106. Baffes, J., Haniotis, T., (2010). Policy Research Working Paper 5371: Placing the 2006/2008 commodity Price Boom into Perspective, The World Bank Development Prospects Group.
Beechey, M., Gruen, D., Vickery, J. (2000). The efficiency market hypothesis: A survey, Research
Discussion Paper, Reserve Bank of Australia.
Bodie, Z., Kane, A., Marcus, A. J., (2011). Investments and Portfolio Management. Global ed. New York: McGraw-Hill/Irwin.
Brock, W. A., Dechert, D. W., Schieinkman, J, A., (1987). A test for independence based on the correlation dimension Department of Economics, University of Wisconsin at Madison, University of Houston and University of Chicago.
Brock, W. A., Dechert, D. W., Schieinkman, J, A., (1996). A test for independence based on the correlation dimension Econometric Reviews, 15, pp. 197-235
Bundgaard, T., (2013). Commodity Risk Management III - Technical Analysis, Copenhagen: Kairos Commodities.
Busch, J., (2013). Spend Matters Perspective - Beyond Sourcing and Supply Chain: Commodity Management Solution Fundamentals.
Charles A, Darne, O, Kim, H, (2012). Exchange-rate predictability and adaptive market hypothesis: evidence from major exchange rates. J Int Money Finance, Vol; 31: pp. 1607-1626.
Engle, R. F., (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation Econometrica, Vol:50, pp. 987-1007.
IHS, (2013). Pricing Risks - Be Prepared for the Next Round of Commodity Price Swings, HIS Global Insights.
Fama, E. F., (1970). Efficient Capital Markets: A Review of Theory and Empirical Work. Journal of
Finance, Vol: 25(2), pp. 383-417.
Fama, E. F., (1991). Efficient Capital Markets: II, Journal of Finance, 46(5), pp. 1575–1617.
Grossman, S. J. & Stiglitz, J. E., (1980). On the Impossibility of Informationally Efficient Markets.
American Economic Review, Vol; 70(3), pp. 393-408.
Hsieh, D. A., (1991). Chaos and nonlinear dynamics: Application to financial markets Journal of Finance, Vol 46, pp. 1839-1877.
Houthakker, H. S., (1961). Systematic and Random Elements in Short-Term Price Movements. The
American Economic Review, 51(2), pp. 164-172.
25 Kristoufek L., Vosvrda M., (2014). Commodity futures and market efficiency, Energy Econ., Vol: 42, pp. 50-57.
Lim, K. P., Hooy, C. W., (2012). Non-linear predictability in G7 stock index returns The Manchester School.
Lim, K. P., Luo, W., Kim, J., H., (2013). Are US stock index returns predictable? Evidence from automatic autocorrelation-based tests, Applied Economics, Vol: 45 (8), pp. 953-962.
Lo, A.W., MacKinlay, A. C., (1988), Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test, Review of Financial Studies, 1, pp. 41-66.
Lo, A. W., (2004). The adaptive markets hypothesis: market efficiency from an evolutionary perspective, Journal of Portfolio Management, 30, pp. 15–29.
Lo, A. W., (2005). Reconciling efficient markets with behavioral finance: The adaptive markets hypothesis. J. Inv. Consulting, 7, pp. 21–44.
Lo, A. W., (2008). Efficient markets hypothesis. In L. Blume & S. Durlauf (Eds.), The new Palgrave: A
dictionary of economics. New York: Palgrave Macmillan.
Malkiel, B. G., (2003). The Efficient Market Hypothesis and Its Critics. Journal of Economic Perspectives, Vol: 17(1), pp. 59-82.
Malkiel, B. G., (2012). A Random Walk Down Walk Street: The time-Tested Strategy for Successful
Investing. W.W. Norton & Company.
McLeod, A.I., Li, (1983). Diagnostic checking ARMA time series models using squared-residual autocorrelations. J Time Ser Analysis. Vol: 4, pp. 269-273.
Mckenzie, A. M., Holt, M. T., (2002). Market efficiency in agricultural futures markets, Applied
Economics 34, pp. 1519–1532.
Ning, Y., Wang, Y. M., Su, C.W., (2017). How did China’s foreign exchange reform affect the efficiency of foreign exchange market? Physica A, 483, pp. 219-226
Samuelson, P. A., (1965). Proof that Properly Anticipated Prices Fluctuate Randomly. Industrial
Management Review, Vol; 6(2), pp. 41-49.
Smith, G., Ryoo, H. J., (2003). Variance ratio tests of the random walk hypothesis for European emerging stock markets, The European Journal of Finance, Vol; 9(3), pp.290-300.
Stevenson, R. A., Bear, R. M., (1970). Commodity Futures: Trends or Random Walks?. Journal of
Finance, Vol; 25(1), pp. 65-81.
Tevelson, R., Alsén, A., Ganeriwalla, A., Bennett, S., (2013a). Building Advanced Capabilities in Procurement, Boston Consulting Group.
Tevelson, R., Paranikas, P., Hemmige, H., (2013b). Key Challenges in Managing Commodity Risk, perspectives, Boston Consulting Group.
