emh01 information, not panic contributes to the price change

International Research Journal of Finance and Economics

ISSN 1450-2887 Issue 43 (2010)

© EuroJournals Publishing, Inc. 2010

http://www.eurojournals.com/finance.htm

Inefficiency in Gold market

Mohsen Mehrara

 

Kargar-e-Shomali Avenue, Faculty of Economics, University of Tehran, Tehran, Iran

 

Tel: [phone]

E-mail: [e-mail]

Ali Moeini

 

Address: Enghelab Street, Department of Algorithms and Computation, Faculty of Engineering,

University of Tehran, Tehran, Iran

 

Tel: [phone]

E-mail: [e-mail])

Mehdi Ahrari

 

Address: Kargar-e-Shomali Avenue, Faculty of Economics, University of Tehran, Tehran, Iran

 

Tel: [phone]

E-mail: [e-mail]

Vida Varahrami

 

Address: Kargar-e-Shomali Avenue, Faculty of Economics, University of Tehran, Tehran, Iran

 

Tel: [phone]

E-mail: [e-mail], [e-mail]

Abstract

 

The efficient market hypothesis gives rise to forecasting tests that mirror those

adopted testing the optimality of forecast in given information set. It seems obvious that

profitable trading opportunities may exist, when the gold market is not efficient. In this

paper, among the models such as GMDH and MLFF neural network, Technical analysis

rule, Buy and hold rule, Treasury bill tested and Random walk rule, GMDH and MLFF

neural network models with moving crossover inputs are determined to produce better

results in the gold market. Results also indicate that high returns are possible by using

GMDH neural network and at the end, we show that the gold market is not efficient in

Fama sense.

Keywords:

 

Multi Layered Feed Forward (MLFF) and Group Method of Data Handling

(GMDH) neural network, Gold prices, Technical Analysis.

1. Introduction

 

Allan Timmermann and Clive W. J. Granger[41] note in their paper " Transaction costs and trading

restrictions change tests of market efficiency in some important ways. Most obviously, if transaction

costs are very high, predictability is no longer ruled out by arbitrage, since it would be too expensive to

take advantage of even a large, predictable component in returns." They note in other section of this

paper" The earlier definition of market efficiency is purely based on asset returns independently of how

International Research Journal of Finance and Economics - Issue 43 (2010)

 

59

these are related to the underlying ‘intrinsic’ asset value. In fact, prices and values need not be closely

related. This definition of market efficiency focuses on the size of deviations of asset prices from true

‘value’. Investors’ information can be so ‘noisy’ at times that price are far removed from fundamentals.

However, the market is still efficient in this definition provided that such deviations do not last ‘too

long’ or become ‘too big’ before they are corrected."

Jensen [21] in his paper notes "A market is efficient with respect to information set

t if it is

impossible to make economic profits by trading on the basis of information set

t" and Malkiel [26]

notes " A capital market is said to be efficient if it fully and correctly reflects all relevant information

in determining security prices. Formally, the market is said to be efficient with respect to some

information set,

t, if security prices would be unaffected by revealing that information to all

participants. Moreover, efficiency with respect to an information set,

t, implies that it is impossible to

make economic profits by trading on the basis of

t".

Gold markets are a zero sum game, where for every long position there must be a short

position. Every price movement in market that creates a profit for one participant will result in an equal

loss for another participant. With heavy participation of informed traders on both sides, trading should

perform particularly well as a price discovery mechanism based on the known market fundamentals.

Thus neoclassical economic theory suggests that markets should be highly efficient, with no room for

excess returns. What then explains traders' enthusiasm for short-term bets on prices? [36]

Long before the contributions of behavioral finance, technical analysts have claimed the ability

to generate excess returns solely on the basis of interpretations of historical price patterns. Technical

analysis has evolved from looking for patterns on price charts to using computer programs based on a

variety of weighted and unweighted price averages, to the current state of the art which employs

artificial intelligence [AI] techniques. A branch of AI technology that has been experiencing strong

expansion in its application to commodity trading is the field of GMDH and MLFF neural networks.

If historical price patterns can indeed be used to predict future prices, the market would not fit

the strict definition of efficient markets laid out by Fama [10]. If inefficiencies exist, there could be

profitable trading opportunities.

Problems of complex objects modeling such as analysis and prediction of stock market, gold

price and other, cannot be solved by deductive logical-mathematical methods with needed accuracy.

The task of knowledge extraction from data is to select mathematical description from data. But the

required knowledge for designing of mathematical models or architecture of neural networks is not at

the command of the users [27]. In mathematical statistics it is need to have a priori information about

the structure of the mathematical model. In neural networks the user estimates this structure by

choosing the number of layers, and the number and transfer functions of nodes of a neural network.

This requires not only knowledge about the theory of neural networks, but also knowledge of the

object's nature and time. Besides this the knowledge from systems theory about the systems modeled is

not applicable without transformation into an object in the neural network world. But the rules of

translation are usually unknown [18, 19].

GMDH type neural networks can overcome these problems. It can pick out knowledge about

object directly from data sampling. The GMDH is the inductive sorting-out method, which has

advantages in the cases of rather complex objects, having no definite theory, particularly for the objects

with fuzzy characteristics. GMDH algorithms found the only optimal model using full sorting-out of

model-candidates and operation of evaluation of them, by external criteria of accuracy or difference

types [17, 24].

The purpose of this paper is to examine the possibility that the gold market is not an efficient

market in that subtle price patterns that can be exploited for profitable trading. To explore this question

we estimate GMDH and MLFF neural network model for the price of nearby gold with technical

analysis rules as inputs. We find that, without transaction costs and disregarding slippage, the GMDH

model can produce profitable trading signals for several years, thus casting doubt on the efficiency of

the gold market.

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International Research Journal of Finance and Economics - Issue 43 (2010)

 

In Section 2 below, we reference selected literature as background, including studies which

have used neural network models in technical analysis. Section 3 provides the non-parametric

modeling approach adopted here as per MLFF neural network with back-propagation algorithm and

GMDH neural network with genetic algorithms which are briefly discussed and describes a network

with technical analysis rules as inputs. Benchmark models are given in Section 4. Empirical results are

presented in Section 5, and concluding remarks in Section 6.

2. Literature Survey

 

Gencay (13) uses foreign exchange markets to pioneer the use of technical analysis rules as inputs for

neural networks, which are flexible, nonlinear models with powerful pattern recognition properties. In

a series of articles, Gencay (14) and Gencay (15) and Gencay et al. (16) show that simple technical

rules result in significant forecast improvements for current returns over a random walk model for both

foreign exchange rates and stock indices.

Doran [9] employing a survey distributed to over 4,000 professors, they obtain four main

results. First, most professors believe the market is weak to semi-strong efficient. Second, twice as

many professors passively invest than actively invest. Third, their respondents’ perceptions regarding

market efficiency are almost entirely unrelated to their trading behavior. Fourth, the investment

objectives of professors are, instead, largely driven by the same behavioral factor as for amateur

investors–one's confidence in his own abilities to beat the market, independent of his opinion of market

efficiency. Sohel Azad [37] empirically tests the random walk and efficiency hypothesis for 12 Asia-

Pacific foreign exchange markets. The hypothesis is tested using individual as well as panel unit root

tests and two variance-ratio tests. The study covers the high (daily) and medium (weekly) frequency

post-Asian crisis spot exchange rate data from January 1998 to July 2007. The inferential outcomes do

not differ substantially between the unit root tests and the variance-ratio tests when using daily data but

differ significantly when using weekly data.

The use of gold price as an economic indicator drew the attention of many economists.

Mirmirani [27] asserted that more than 70% of the change in inflation rate can be explained by the

price movements of gold.

In the field of engineering decision systems, techniques based on inductive human behavior

have been developed. Among such systems are neural networks, the genetic algorithm and their

integration. These engineering-based systems have gradually found their way into business and

economics [8]. A thorough literature review of neural network applications in finance and business are

provided by Wong and Yakup [44].

In time series analysis, a review of the methodological linkage between statistical techniques

and neural networks is given by Cheng and Titterington [7]. Recently, some studies have been done

with neural networks. One of them has been done with S. Mirmirani and H.C. LI [27], concentrates on

a non-parametric study of gold prediction with neural network and genetic algorithm. Sarafraz

and.Afsar [35] has done another study with neuro-fuzzy networks. They have studied gold price in

Iran.

3. Modeling using Neural Network

 

Artificial Neural Networks (ANN) is biologically inspired network based on the organization of

neurons and decision making process in the human brain [26]. In other words, it is the mathematical

analogue of the human nervous system. This can be used for prediction, pattern recognition and pattern

classification purposes. It has been proved by several authors that ANN can be of great used when the

associated system is so complex that the underline processes or relationship are not completely

understandable or display chaotic properties [31]. Development of ANN model for any system

involves three important issues: (i) topology of the network, (ii) a proper training algorithm and (iii)

transfer function. Basically an ANN involves an input layer and an output layer connected through one

International Research Journal of Finance and Economics - Issue 43 (2010)

 

61

or more hidden layers. The network learns by adjusting the inter connections between the layers. When

the learning or training procedure is completed, a suitable output is produced at the output layer. The

learning procedure may be supervised or unsupervised. In prediction problem supervised learning is

adopted where a desired output is assigned to network before hand [20].

3.1. MLFF Neural Network

 

MLFF neural network is one the famous and it is used at more than 50 percent of researches that are

doing in financial and economy field recently [1]. This class of networks consists of multiple layers of

computational units, usually interconnected in a feed-forward way. Each neuron in one layer has

directed connections to the neurons of the subsequent layer. In many applications the units of these

networks apply a sigmoid function as a transfer function (

x

 

e

f x

 

−

+

=

1

1

( )

 

). It has a continuous derivative,

which allows it to be used in back-propagation. This function is also preferred because its derivative is

easily calculated:

y '= y (1− y )

Multi-layer networks use a variety of learning techniques; the most popular is back-propagation

algorithm (BPA). The BPA is a supervised learning algorithm that aims at reducing overall system

error to a minimum [22]. This algorithm has made multilayer neural networks suitable for various

prediction problems. In this learning procedure, an initial weight vectors

0 w  is updated according to

[21]:

i i i i i i i

 

w

 (k  +1) = w  (k ) + μ (T  − O  ) f  ' (w x  )x  (1)

Where,

i

 

w

 The weight matrix associated with ith neuron;

i

 

x

 Input of the ith neuron;

i

 

O

 Actual output of the ith neuron;

i

 

T

 Target output of the ith neuron, and μ is the learning rate

parameter.

Here the output values (

i O  ) are compared with the correct answer to compute the value of some

predefined error-function. The neural network is learned with the weight update equation (1) to

minimize the mean squared error given by [23]:

2 2

 

[ ( )]

2

1

( )

2

1

i i i i i

 

E

 = T  −O  = T  − f w x

 

By various techniques the error is then fed back through the network. Using this information,

the algorithm adjusts the weights of each connection in order to reduce the value of the error function

by some small amount. After repeating this process for a sufficiently large number of training cycles

the network will usually converge to some state where the error of the calculations is small. In this case

one says that the network has learned a certain target function. To adjust weights properly one applies a

general method for non-linear optimization that is called gradient descent. For this, the derivative of

the error function with respect to the network weights is calculated and the weights are then changed

such that the error decreases [24].

The gradient descent back-propagation learning algorithm is based on minimizing the mean

square error. An alternate approach to gradient descent is the exponentiated gradient descent algorithm

which minimizes the relative entropy [38].

3.2. GMDH Neural Network

 

By means of GMDH algorithm a model can be represented as sets of neurons in which different pairs

of them in each layer are connected through a quadratic polynomial and thus produce new neurons in

the next layer. Such representation can be used in modeling to map inputs to outputs [3, 12, 17, 18, 25].

The formal definition of the identification problem is to find a function

f ˆ so that can be approximately

used instead of actual one,

f  , in order to predict output y ˆ for a given input vector ,..., )

3

,

2

,

1

(

n

X

 

 

= x x x x

 

as close as possible to its actual output

y  [19,28]. Therefore, given M observation of multi-inputsingle-

output data pairs so that

62

International Research Journal of Finance and Economics - Issue 43 (2010)

 

,..., )

3

,

2

,

1

(

in

x

i

x

i

x

i

f x

i

y

 

 

= (i=1,2,…,M)

it is now possible to train a GMDH-type neural network to predict the output values

i

y

 

 

ˆ for any given

input vector

( , , ,..., )

i

 

 

1 i 2 i 3 in

X

 

 

= x x x x  , that is

,..., )

3

,

2

,

1

ˆ ˆ (

in

x

i

x

i

x

i

f x

i

y

 

 

= (i=1,2,…,M).

The problem is now to determine a GMDH-type neural network so that the square of difference

between the actual output and the predicted one is minimized, that is

min

2

,..., ) ]

3

,

2

,

1

ˆ (

1

 

 

[ − ®

=

i

y

in

x

i

x

i

x

i

f x

M

i

 

.

General connection between inputs and output variables can be expressed by a complicated

discrete form of the Volterra functional series in the form of

...

1 1 1 1 1 1

0

 

=

 

=

 

 

+

=

 

=

 

=

 

 

+ +

=

= +

n

i

n

j

n

i

n

j

x j xk

n

k

xi aij xi x j aijk xi

n

i

y a ai

 

 

(2)

Which is known as the Kolmogorov-Gabor polynomial [3, 18, 19]. This full form of

mathematical description can be represented by a system of partial quadratic polynomials consisting of

only two variables (neurons) in the form of

2

5

2

y

 

 

ˆ = G (xi  , x j  ) = a 0 + a 1xi  + a 2 x j  + a 3 xi x j  + a 4 xi  + a x j  (3)

In this way, such partial quadratic description is recursively used in a network of connected

neurons to build the general mathematical relation of inputs and output variables given in equation (2).

The coefficient

i a  in equation (3) are calculated using regression techniques so that the difference

between actual output, y, and the calculated one,

y ˆ , for each pair of i x  , j x  as input variables is

minimized. Indeed, it can be seen that a tree of polynomials is constructed using the quadratic form

given in equation (3) whose coefficients are obtained in a least-squares sense. In this way, the

coefficients of each quadratic function

i

G

 

 

are obtained to optimally fit the output in the whole set of

input-output data pair, that is [18, 28]

1 min

( )2

®

 

=

−

=

M

M

i

i

G

i

y

E

 

 

(4)

In the basic form of the GMDH algorithm, all the possibilities of two independent variables out

of total n input variables are taken in order to construct the regression polynomial in the form of

equation (3) that best fits the dependent observations (

i

y

 

 

, i=1, 2, …, M) in a least-squares sense.

Consequently,

2

( 1)

2

−

=

 



 





n n n

 

neurons will be built up in the first hidden layer of the feed forward

network from the observations {

( , , );

iq

x

ip

yi x

 

 

(i=1, 2,… M)} for different p ,q Î{1,2,...,n } . In other

words, it is now possible to construct M data triples { (

yi  , xip  , xiq  ); (i=1, 2,…, M)} from observation

using such

p ,q Î{1,2,...,n } in the form

 

 

 

 

 



Mp Mq M

p q

p q

x x y

x x y

x x y

 

2 2 2

1 1 1

International Research Journal of Finance and Economics - Issue 43 (2010)

 

63

Using the quadratic sub-expression in the form of equation (3) for each row of M data triples,

the following matrix equation can be readily obtained as

A

 

a  = Y

 

where

a  is the vector of unknown coefficients of the quadratic polynomial in equation (3)

{ , , , , , }

0 1 2 3 4 5 a  = a a a a a a  (5)

and

T

M

 

Y

 {y  , y , y ,..., y } 1 2 3 = is the vector of output’s value from observation. It can be readily seen that

 

 

 

 

 



=

2 2

2

2

2

2 2 2 2 2

2

1

2

1 1 1 1 1

1

1

1

Mp Mq Mp Mq Mp Mq

p q p q p q

p q p q p q

x x x x x x

x x x x x x

x x x x x x

A

The least-squares technique from multiple-regression analysis leads to the solution of the

normal equations in the form of

A A A Y

T

1 T ( )− a = (6)

which determines the vector of the best coefficients of the quadratic equation (3) for the whole set of M

data triples. It should be noted that this procedure is repeated for each neuron of the next hidden layer

according to the connectivity topology of the network. However, such a solution directly from normal

equations is rather susceptible to round off errors and, more importantly, to the singularity of these

equations [2, 5, 29, 30].

Our approach is to construct GMDH and MLFF neural networks model using a technical

analysis rule as an input. We assume that technical analysis rules may have merit because there may be

exploitable patterns which can result in profitability. The patterns may not be identifiable by traditional

means but may be uncovered by the pattern recognition capabilities of GMDH neural networks.

Empirical evidence of profitability will be confirmation of this approach and evidence of inefficiencies

in the gold market.

2 lags of the 5[MA

5,MA5(-1),MA5(-2)], 50[MA50,MA50(-1),MA50(-2)], day moving average

crossover

1, as input variables to the neural networks. Moving average crossovers have long been used

as buy– sell signals for trend-following trading systems. The assumption that a short-term moving

average is higher than a long-term moving average indicates that prices are trending higher, thus

signaling an uptrend. The opposite case signals a downtrend. First we use the neural network with

moving average crossover inputs to forecast what will happen to gold prices. A long position is taken

when prices are predicted to be higher, and a short position when prices are predicted to be lower. Then

profitability is calculated from actual returns based on these positions. For tractability, we utilize a

neural network with two hidden nodes and a direct connection between the lagged moving average

crossovers and return. The price data are NYMEX database. Observations are the daily nearby gold

prices. Predicted prices from the model are compared with the actual prices for 01/01/2006 until

31/6/2009 period separately. Prices are converted to returns using the daily difference in the logs of the

prices.

4. Other Trading Strategies

In this paper, in addition to the GMDH and MLFF neural network, three benchmark models are used

for comparison purposes. The first benchmark model, referred to as the buy-and-hold [BH] model,

simply assumes that the nearby contract is purchased and rolled over as a new contract month becomes

the nearby contract. The second benchmark model [TA for “twenty-day average”] is a simple moving

1

 

Such models are all based on rules using moving averages of recent prices. A typical moving average is simply the sum

of the closing prices for the last

 

n number of days divided by n, where n may be from 1 to 200 days the rules for using

these tools are very similar and usually involve making a decision when a short-term average crosses over a long-term

average. For example, the rule may be to buy when the 5-day moving average exceeds the 50-day moving average and to

sell when the 5-day average is below the 50-day average.(Gencay et al. 1996)

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International Research Journal of Finance and Economics - Issue 43 (2010)

average crossover model where a long position is established when the price exceeds the 20-day

moving average by one standard deviation, and a short position is taken when the price is at least one

standard deviation below the 20-day moving average. This second model has been popular with

technical analysts, who believe it has the ability to capture and profit from trending markets. The third

model [RW for “random walk”] incorporates a naïve trading rule based on the current day's movement.

If the price is above the previous day's closing price, the trader goes long. If the price is below the

previous day's price, the trader goes short, for more details referred to Shambora and Rositer [36].

In Table 1, we summarize the neural network given in Section 3 as well as the benchmark

trading strategies discussed in this section.

Table 1:

 

 

Summary of trading strategies

Model Description Strategy

GMDH & MLFF neural

network

Inputs to the network are the

differences between the 5- and the

50-day moving average of price (1–5

lags)

Take a long position if forecast from the network is

that price will increase; take a short position if

forecast is that price will decrease.

TA; Technical analysis

rule

Conventional moving average

crossover rule

Take a long position if price exceeds the 20-day

moving average by one standard deviation; take a

short position if price is at least one standard

deviation below the 20-day moving average.

BH; Buy and hold rule Assumes price will always increase Go long and continuously roll position over.

T-bill 90-day; Treasury

bill

Risk-free rate Measure equal to change in log price of 90-day

Treasury bill

RW; Random walk rule Naïve trading rule Take a long position if price is above previous

day's price; take a short position if price is below

previous day's price.

5. Empirical Results

We use trading signals from the four models to generate daily profit and loss expressed as percent

returns and summarize the returns for each strategy in Table 2.

Table 2:

 

 

Comparison of profitability

Model 2006 2007 2008 2009 Bear Bull Cumulative

GMDH 0.675 0.689 0.623 0.594 0.376 0.612 2.581

MLFF 0.631 0.642 0.568 0.526 0.298 0.537 2.367

TA 0.456 0.523 0.496 0.437 0.228 0.453 1.912

BH 0.231 0.213 0.275 0.356 -0.237 0.654 1.075

RW -0.102 0.032 0.125 -0.117 -0.215 -0.0231 -0.508

T-bill 0.031 0.032 0.046 0.066 0.024 0.062 0.175

As shown in table 2 cumulative returns for GMDH and MLFF are 258% and 232%, but for TA,

BH, RW and T-bill are 191%, 108%, -51% and 18%, then GMDH and MLFF neural network generate

overall returns much better than other models and GMDH model is the most profitable.

In this paper, we define period from Jun 10, 2007 to February 14, 2008 as a bear market

because prices were generally falling in this period and the period from February 14, 2008 to

December 31, 2008 is defined as a ball market which prices generally rising thru this period. Results

show that return of BH model in the ball market is 65%, but return of this model in bear market is -

24%. Returns of GMDH and MLFF in bull market are lower than BH but in bear market returns of

these models are higher than other models.

International Research Journal of Finance and Economics - Issue 43 (2010)

 

65

In table 3 we compare average daily returns of 6 models. The average daily returns of GMDH

and MLFF are 26% and 23% that are higher than other models. We use volatility for comparing

returns. Volatility is measured with standard deviation of returns. In table 3 standard deviation of

GMDH, MLFF and TA are quite high relative to other models; coefficient of variation is used for

measuring comparative risk / reward. When there is small risk, CV is low. In table 3, the lowest CV

and the highest risk is for GMDH model. Sharp ratio is another method for comparing returns relative

to risk. The sharp ratio for GMDH is higher than other models; therefore neural network produces

much better return for risk than other models.

The t-static is identified for null hypothesis that average daily returns are significantly zero for

overall period. Neural networks and T-bills' returns are significantly different from zero at 5% level.

Table 3:

 

 

Statistical Comparisons 2006-2009

GMDH MLFF TA BH RW T-bill

Average daily returns (%)

 

 

0.26 0.23 0.14 0.12 -0.046 0.01

Standard deviation

 

 

0.0278 0.0285 0.0229 0.0189 0.0092 0.0017

Coefficient of variation

 

 

10.69 12.39 16.36 15.75 -20 17

Sharpe ratio

 

 

0.0823 0.0778 0.0532 0.0485 -0.0345 NA

t-Stat

 

 

2.56* 2.34* 1.72 1.65 1.27 2.45*

Correct Trades (%)

 

 

66.4 63.7 62.3 53.2 48.1 NA

* Significant at 5% level.

Correct trader is presented in table 3. GMDH and MLFF are correct 66.4% and 63.7% of the

time that they are better than other strategies.

In table 4, we compare correct trades and overall returns for three different opportunity costs.

When opportunity cost increases, correct trades increases and overall return decreases. Overall results

are shown that GMDH neural network dominates the other trading strategies

Table 4:

 

 

Effect of opportunity cost filter trading rule on GMDH

Opportunity cost % Correct Trades Overall return

0.005% 77.23 2.28

0.01% 79.68 1.75

0.015% 83.35 1.21

7. Conclusion

Efficient market theory claims that the efficient use of all available information are reflected by current

prices. Strictly speaking, if markets are efficient, exploitable historical price patterns should not exist.

Technical analysis, on the other hand, is the ability to identify patterns and profit from their repetition.

Neural networks are especially well-suited to identifying patterns and making predictions based

on those patterns. In this paper, we trained GMDH and MLFF neural network model for nearby gold

prices with technical analysis crossover rules as inputs. By contrasting this model with a buy-and-hold

(BH) strategy, a traditional technical trading (TA) strategy, a naïve “random walk” (RW) strategy and

the return on Treasury bills (T-bill), we show that high returns are possible by using GMDH neural

network. Overall returns, year-to-year returns, returns over a market cycle, and Sharpe ratios all favor

the GMDH neural network model by a large factor. Additionally, daily returns using the neural

networks and TA models are significantly different than zero, while the returns from the other models

are not. There for the gold market is not efficient in the Fama sense.

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International Research Journal of Finance and Economics - Issue 43 (2010)

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