GOLD STOCK MARKET: A REFUGE FOR RATIONAL OR NOISE TRADERS?
EVIDENCE FROM SOUTH AFRICAN GOLD MINING STOCKS
George Ogum
School of Business, La Sierra University
Paper to be Presented at the Southwestern Finance Association 52 nd
Annual Meeting
Albuquerque, NM, March 12 – March 16, 2013
Correspondence to:
George Ogum, School of Business, La Sierra University
4500 Riverwalk parkway
Riverside, CA 92515
Tel: (951) 785-2314
Fax: (951) 785-2700

GOLD STOCK MARKET: A REFUGE FOR RATIONAL OR NOISE TRADERS?
EVIDENCE FROM SOUTH AFRICAN GOLD MINING STOCKS
George Ogum
School of Business
La Sierra University
Abstract
This paper investigates the hypothesis that gold-mining stock market noise traders participate in positive feedback trading. The analysis is based on the Sentana-Wadhwani (SW) model which yields testable implications about the presence of positive and negative feedback traders in stock markets. The hypothesis is tested using data from South Africa’s gold mining stocks. The empirical results suggest that there is significant evidence of positive feedback trading. More importantly, the feedback trading pattern does not exhibit significant asymmetry contingent on market direction. The findings suggest that feedback trading is more intense during market advances than it is during market declines in the gold stock market. Finally, we find no evidence of feedback trading in the post-crisis period. The results indicate significant feedback trading in the pre-crisis period but it vanishes in the post-crisis period. Perhaps after the crisis, the trading process for gold was mostly dominated by informed traders suggesting that this commodity became more credible in the eyes of informed traders.
JEL classification: C32, G10, G11, G14
Keywords: gold, volatility asymmetry, positive feedback trading, South African gold
stock
2

1. Introduction
Since 2007 the world has seen a period of striking economic and financial volatility, featuring the deepest recession since the 1930s and steep declines in the value of many financial assets – both traditional ones such as equities and newly developed ones such as mortgage-backed securities. Against this back ground, however, gold has performed strongly with its price roughly doubling since the global financial crisis began in mid-2007. Gold’s performance in this period has sparked something of a reappraisal of its characteristics as an asset and led some to revisit its proper place in investors’ portfolios. As a store of value, gold has been used for centuries to protect individuals’ wealth. It is relatively immune to inflation, financial crisis and credit default.
These special properties are borne out in the recent performance of gold, and investors may continue to value them given the significant uncertainties still facing the global economy.
An issue bearing interesting policymaking implications in this context is the one related to whether gold-stock trading is dominated by rational or noise traders. The move into gold trading has occurred alongside a broader diversification by asset managers away from equities and bonds into alternative asset classes. But it is unclear to what extent any increased interest in alternative assets, including commodities like gold, represented price motive rather than diversification motive. That is, to what extent were the flows tactical rather than strategic in nature. Given the significant increase in gold prices that occurred during the period 2003-2010, (with gold recently trading well above 1600 US dollars per troy ounce (see Baur and Glover (2011)), it is reasonable to assume that a tactical desire to take advantage of the gold price boom occurred alongside an increase in strategic holdings of gold. Some would argue that the recent strong positive trend in
3

gold prices has attracted trend-chasing investors. These positive feedback or noise traders buy an asset whose price increased in the past thereby enforcing or prolonging the trend. This behavior is in contrast to a fundamentalist (or rational trader). A rational trader buys an asset when it is below the fundamental price and sells the asset when it is above the fundamental price. Thus, a long and positive price trend can only be explained by a continuously changing fundamental price or the presence of positive feedback traders (trend chasers or chartists). We believe the presence of feedback (or noise) traders explains the strong positive trend of gold prices.
This study adds to the existing literature in a number of ways. First, using the original Sentana and Wadhwani (1992) model (hereafter SW model), the paper tests whether gold mining stocks attract noise traders in general and positive feedback traders in particular. To our knowledge, this is the first such empirical work focusing on gold stock market. The result of such an investigation may provide additional insights into the potential determinants of stock return correlation. Second, we consider the impact of the US credit crisis on the positive feedback trading in gold stock market. Third, by employing gold mining stock returns (from an emerging market), this paper departs from the practice (of most papers) which employ gold prices (troy ounces or bullion priced in US dollars). Gold exhibits various roles in global economy. It is used as a financial asset to diversify risk and works as a safe haven during financial turmoil (Baur and
Lucey, 2010). In equity markets, fundamentalists base their estimate of the fundamental value on a detailed analysis of dividends and earnings forecasts or more simply on the expected dividend stream. Since gold does not provide any future cash flow, other than possible capital gain, what can we say about the fundamental price of gold? To circumvent this problem, we employ gold stock returns. It has also been suggested that investors’ positions in gold stocks may be more
4

feasible than positions in gold itself (Jaffe, 1989). We are then able to implement the heterogeneous agents’ model of SW with fundamental traders and noise traders.
This paper tests the hypothesis that some market participants in the gold stock market follow positive feedback trading strategies. The major findings of our study may be summarized as follows. First, the empirical results suggest that there is significant positive feedback trading for all models tested. This implies that noise traders do bear a decisive presence in the gold stock market of South Africa. Second, feedback trading pattern is not asymmetric contingent on market direction. Our results indicate that positive feedback trading is not more intense during market declines than it is during market advances. Third, we find that US credit crisis had an impact on positive feedback trading activity. Noise traders were active during the pre-crisis period but not in the post-crisis period. These results are very interesting as they are of great relevance to the financial market regulators, finance practitioners and investors in gold stock markets.
The rest of the paper is organized as follows. Section 2 describes the positives feedback trading model used. Section 3 describes the data and presents the empirical findings. Section 4 summarizes and concludes the study.
2. The Feedback Trading model and Autocorrelation
To investigate whether the South African gold stock market is dominated by rational or noise investors, we employ the empirical framework introduced by Sentana and Wadhwani (1992). In the spirit of Shiller (1984), Sentana and Wadhwani assumed that there are two types of
5

heterogeneous investors. The first group follow momentum trading strategies, that is, they buy
(sell) following price increases (decreases). Such investors have also been described as trendchasers or feedback traders. Their demand for stocks is given by:
F t
 
R t

1
(1)
Where F t
is the fraction of shares demanded by this group, R t1 is the return in the previous period and the parameter
γ is assumed to be positive. Such a strategy suggests trading on noisy information, which is usually irrelevant of economic fundamentals. This kind of trading behavior pushes asset prices away from their fair (fundamental) values. Hence, negative serial correlation occurs in returns as price increases are followed by increases in demand resulting in even higher prices in the future. Positive feedback trading is not necessarily irrational or noise trading in the sense of De Long, et al. (1990b). It is consistent with portfolio insurance strategies and the use of stop-loss orders. Portfolio insurance is rational if risk aversion declines rapidly with wealth (e.g.
Sentana and Wadhwani, 1992). Obviously, if
γ
< 0, then negative feedback trading is implied whereby traders buy low and sell high. This selling pressure causes the price to close lower than it otherwise would have based on the market information set. In the following days trading, prices will rise to correct for this profit-taking on the part of negative feedback traders, thereby inducing positive autocorrelation.
The second group of investors, information (or smart) traders value shares in the context of the
CAPM, with a demand function for shares given by:
S t

( E t

1
R t
 
) /
 t
(2) where S t
is the fraction of stocks they hold, E t-1
(R t
) -
 is the expected excess return of stocks over the risk-free rate, and
 t measures the risk of stock holding. In a mean-variance framework, this time-
6

varying risk measure is an increasing function of the conditional variance of stock returns,
 t
 
(
 t
2
) with
 
(
 t
2
)

0 .
Without loss of generality, we can follow Koutmos (1997) and assume that risk is linearly related to volatility,

(
 t
2
)
  t
2
. As Sentana and Wadhwani (1992) point out, market equilibrium in a model with investors of this type alone yields the familiar capital asset pricing model of
Sharpe (1964), Lintner (1965), and Mossin (1966).
 t
2 
( E t

1
R t
 
)
(3)
Allowing the existence of both groups in the stock market, all existing stock are either held by information traders (S t
) or by feedback traders ( F t
), i.e.:
S t

F t

1 (4)
In the CAPM setting, with both information traders and feedback traders in market equilibrium, substituting (1), (2) and (3) into (4) yields:
E t

1
( R t
)
    t
2  
(
 t
2
) R t

1
(5)
From Eq.(5), in a market with feedback traders, the return function contains an additional term
R t1 so that stock returns exhibit autocorrelation. The pattern of autocorrelation in returns depends on the type of feedback trader captured by the parameter
γ
. The term
 
(
 t
2
) R t

1
in Eq.(5) implies that the presence of positive feedback trading will induce negative autocorrelation in returns. The higher the volatility the more negative is the autocorrelation. Furthermore, the extent to which returns exhibit autocorrelation varies with volatility
 t
2
. As it is, Eq.(5) does not allow autocorrelation due to nonsynchronous trading and/or market inefficiencies. To account for this possibility, and to test the hypothesis that feedback trading is present, we need to convert
7

Equation (5) into a regression equation. This can be done easily by setting R t

( E t

1
( R t
)
  t
) via rational expectations assumption and substituting into Eq. (5) to get:
R t
= α +  t
2
+ (

0
+

1
 t
2
) R t-1
+ε t
. (6) where the direct impact of noise traders (at a constant level of risk) is dictated by the positive sign of

0 and
   
1
. Thus the presence of positive feedback trading implies that

1 is negative and statistically significant.

0 captures the impact of nonsynchronous trading effects and/or market inefficiencies and frictions. However, to account for the impact of such intense trades during market downturns, it is necessary to augment Eq.(6) as follows:
R t
= α +  t
2
+ (

0
+

1
 t
2
) R t-1
+

2
R t

1
+ ε t
(7) where the existence of positive feedbacks is given by the negative sign of

1
. Moreover, the last term (

2
R t

1
) reflects the possibility of asymmetric trading behavior where negative returns will be followed by a higher volume of feedback trading, if

2
>0. Formally, asymmetry is expressed as:

0
 
1
 t
2  
2
if R t

1

0 (8)

0
 
1
 t
2  
2
if R t

1

0 (9)
The essence of the model is to explore the nature of the relationship between smart money traders and noise traders as captured by the interaction of autocorrelation and volatility in the returns by imposing an a priori assumption about the noise traders’ behavior of positive feedback trading.
8

We also examine whether the US credit crisis had a statistically significant impact on feedback trading in the gold stock market of South Africa. To formally test the hypothesis that changes in

0
and

1 in the post-crisis period are significant, we estimate the following variant of Eq. 6:
R t
= α +
 t
2 + [

0 , 1
( 1 - D t
) +

0 , 2
D t
+

1 , 1
( 1 – D t
)
 t
2 +

1 , 2
D t
 t
2 ] R t-1
+ε t
. (10) where D t
is the dummy variable indicator taking the value of unity in the post-credit crisis period or zero otherwise. This model has the advantage that it utilizes the full sample thereby improving efficiency. It allows for direct testing of the following null hypotheses: H
0,1
:

0 , 1
=

0 , 2
and H
0,2 :

1 , 1
=

1 , 2
, using the Wald test.
Finally, we consider a modified model where serial correlation is an exponential function of conditional volatility as suggested by Lebaron (1992). The mean equation for this exponential model is:
R t
= α + 
2
+ [ t

0

+

1

exp(-
 t
2
/

2
)] R t-1
+ε t
. (11) where

2 is the unconditional variance of log returns, which in empirical applications is replaced by its sample analogue. Our heterogeneous agents model predicts that, if feedback trading is of the positive kind, the parameter estimate of

1

should carry a positive sign, as opposed to the expected negative value for

1
 in the baseline model. Watanabe (2002) estimates this variant of the Shiller-Sentana-Wadhwani model for Japanese stock index returns and finds a better empirical fit than for the baseline model.
It is clear from Eq. 7 that the variance of returns is time varying. Thus, completion of the model requires that the conditional variance be specified. It is now a well-established stylized fact that stock returns are characterized by conditional heteroskedasticity. The model is, therefore,
9

completed using a GARCH specification for the conditional volatility. We conduct extensive tests to compare the symmetric GARCH models with the two most popular asymmetric models.
Symmetric GARCH (1,2) fits the data better than the other models. Consequently, the conditional variance of the returns is modeled as GARCH (1,2) process given by:
 t
2    
0
 t
2

1
 
1
 t
2

1
 
2
 t
2

2
(12) where
 t
2 is the conditional variance of the returns at time t ,
 t is the innovation at time t , and

,

0
,

1
, and

2 are nonnegative fixed parameters. The degree of volatility persistence is measured by

0
+

1
+

2
.
Several parametric specifications have been used in the literature for stock returns, the most common being the standard normal distribution. The standardized residuals obtained from
GARCH models that assume normality appear to be leptokurtic, thereby rendering standard t tests unreliable. As such, distributions with flatter tails, such as the student’s t and the generalized error distribution (GED), have been suggested. In this paper, we employ the GED.
Its density function is given by: f (
 t
,
 t
, v )
 v
2
[

( 3 / v )] 1 / 2 [

( 1 / v )]

3 / 2 ( 1 /
 t
) exp(

[

( 3 / v ) /

( 1 / v )] v / 2
 t
/
 t v
) (13) where

(.) is the gamma function and v is a scale parameter, or degrees of freedom to be estimated. For v = 2, the GED yields the normal distribution, while for v = 1 it yields the Laplace or double exponential distribution. Given initial values for
 t
, and
 t
2 the parameter vector
 
(

,

0
,

0 , 1
,

0 , 2
,

1
,

1 , 1
,

1 , 2
,

2
,

,

0
,

1
,

2
, v ) can be estimated by maximizing the log- likelihood over the sample period, which can be expressed as:
10

L (

)
 t t 

1 log f (
 t
,
 t
, v ) (14) where,
 t and
 t are the conditional mean and the conditional standard deviation, respectively.
Since the log-likelihood function is highly non-linear in the parameters, numerical maximization techniques are used to obtain estimates of the parameter vector. The method of estimation used in this paper is based on the Berndt et al.
(1974) algorithm.
3. Data and Empirical Findings
3.1 Data and Descriptive Statistics
Given their growing significance in global financial markets and its unique characteristics, gold stock markets provide a key opportunity to investigate further the impact of feedback trading on stock returns, and to examine whether positive feedback trading is more intense during market downturns. Since gold mining stocks are directly tradable just like any other stocks, it is expected that noise trading will be easier to identify and the potential asset price “bubble” issue inherent in many previous studies relying on gold prices can be overcome. Therefore, for the empirical analysis, we investigate returns of gold mining stocks of South Africa. Daily closing prices of the gold stock index were obtained from Johannesburg Stock Exchange (JSE) for the period of 01/01/2000 to 12/31/2010.The returns were calculated as the first-difference of the natural logarithm of prices:
R t
= 100*(ln(P t
)-ln(P t-1
)) (15) where ln is the natural logarithm operator; R t
is the return for period t; P t
is the index closing price in period t ; and t is the time measured in days. The summary statistics for the gold-mining stock index are reported in Panel A of Table 1. The statistics reported are the mean, the standard deviation, measures for skewness and excess kurtosis and the Ljung-Box (LB) test statistic for up
11

to 10 lags. The table shows a clear evidence of departures from normality (as implied by significant Jarque-Bera (JB) statistics and significant ARCH(1-2) effects). The skewness and excess kurtosis measures also indicate departures from normality. The return-series are significantly positively skewed and highly leptokurtic. Rejection of normality can be partially attributed to temporal dependencies in the second moment of the series. The positive skewness implies that the return distribution of the gold stocks has a higher probability of being positive.
KPSS stationarity test statistic is insignificant at 5%. This indicates that the return series is stationary, i.e.
I(0).
LB statistic for squared returns is significant, thus, providing evidence of temporal dependencies in the second moment of the returns distribution. This may be due to market inefficiencies. The JOINT test of Engle and Ng(1993) for potential asymmetries in conditional volatility suggests that no significant asymmetries exist in the gold stock return volatility.
3.2 Hypotheses Tested
Several hypotheses are developed and tested within the SW baseline model and its variants discussed above. The hypotheses are:
H1 . There is no significant positive feedback trading in the South African gold stock market:

1
= 0 (see Eq. 6). This implies that noise traders (trend-chasers) do not command a significant position in the gold stock market.
H2
.
Positive feedback trading pattern is not characterized by asymmetry contingent upon market direction.

2
= 0 (see Eq. 7): This implies that positive feedback trading in the gold stock market is not more intense during market downturns than during market upturns.
12

H3 . The level of positive feedback trading in the gold stock market in the pre-US credit crisis period is not significantly different from that of post-crisis period:

0 , 1
 
0 , 2
and

1 , 1
 
1 , 2
(see Eq. 11). This implies that pre-crisis and post-crisis investors do not differ in their information processing and as a result they have similar beliefs and patterns of feedback trading.
3.3 Empirical Results and Discussion
3.3.1 Evidence on the Positive Feedback Trading in the Gold Stock Market
The maximum likelihood estimates for SW model, as described by Eq. (6) and Eq. (12) are reported in Table 2: Panel A. The coefficients describing the conditional variance process,

,

0
,

1
, and

2
are statistically significant at the 1% level. Specifically, coefficient

0
, which represents the autocorrelation in volatility, implies that current volatility is a function of last period’s squared innovation. Coefficients, 
1 and

2
, which represent autoregressive nature of volatility, imply that current volatility is a function of last two periods’ (two days) volatility.
Coefficients,

0
,

1
, and

2
indicate the degree of volatility persistence. Thus, the significance of

,

0
,

1
, and

2
imply that volatility exhibits high autocorrelation and persistence. To illustrate this persistence of volatility, we calculate the half-life of volatility as HL=ln(0.5)/ln(

0
 
1
 
2
) in line with Li, et al (2006). Our results indicate that volatility is persistent since it is found to be almost 60 days. Inspecting now the estimated mean equation (Eq. (6)), we note that parameter

(or GARCH–M) effect is statistically significant. This contradicts the results of
Koutmos and Saidi (2001). Their findings indicate insignificant parameters in the case of emerging stock markets.
13

Continuing our inspection on the estimated parameters, we now focus on mean equation (Eq. 6).
The parameters testing the presence of feedback trading are those governing the autocorrelation of returns (

0
and

1
). Interestingly, as in Koutmos (1997), the parameter of interest

1
, is negative and statistically significant. This suggests that positive feedback trading is present in gold stock markets. Moreover, the estimated scale parameter ν, indicate that the Generalized
Error Distribution yields the Laplace or the double exponential distribution. The estimated value is well below 2 (the value required for normality) and it is very close to unity. This confirms that the departures from normality observed in raw data series cannot be entirely attributed to temporal second moment dependencies. Finally, an array of diagnostics performed on the standardized residuals (Table 2: Panel B) show no misspecification of the SW model (our baseline model). The mean and the variance of the standardized residuals satisfy the white noise requirements. Moreover, Ljung-Box (LB) tests applied onto the standardized residuals and their squared values suggest the absence of temporal dependencies for up to ten lags in their structure.
3.3.2 Asymmetric Feedback Trading Mechanism
We now focus on Table 3: Panel A to examine here whether feedback trading is more intense during market downturns. The parameter of interest here is

2
. It is captured by Eq.7 and Eq.12.
The results reported show that the parameter

2
is negative but statistically insignificant. This implies that feedback trading in gold stocks do not exhibit asymmetric behavior. Given that

1 is negative and statistically significant, the evidence suggests that there is positive feedback trading during market advances. The result is interesting and unique to gold stock returns. It contradicts the results of Sentana and Wadhwani (1992) and Koutmos (1997). They find that for developed
14

markets, including the US, feedback trading is intense during market downturns. Antoniou, et al.
(2005) suggest that the presence of asymmetry in the conditional variance implies that positive feedback trading is more intense during market declines than it is during market advances. For the gold market, Baur (2012) demonstrates that gold stock returns volatility has an inverted asymmetric reaction to positive and negative shocks. Positive shocks increase volatility by more than negative shocks. He argues that this effect is related to the safe-haven property of gold.
Accordingly, this paper argues that gold stock returns do not exhibit asymmetric behavior in feedback trading because volatility of gold stock returns has inverted asymmetric reaction to positive and negative shocks.
3.3.3 Credit Crisis and Positive Feedback Trading
In this section, we investigate the impact of US credit crisis on feedback trading behavior in the gold stock market. Estimation results for the modified baseline model including post-crisis dummy (Eq. 11 and Eq. 12) are reported in Table 4: Panel A. The parameter estimate of

1 , 1 is negative and significant at the 1% level. It confirms the presence of significant positive feedback trading strategies during the pre-crisis period. The post-crisis period coefficient,

1 , 2
, is negative and insignificant. This implies that noise traders did not bear a decisive presence in the gold stock market during the U.S. credit crisis. In addition, we test for changes in model parameters between the two periods. The null hypotheses (

0 , 1
 
0 , 2 and

1 , 1
 
1 , 2
) of the Wald test are rejected based on chi-squared statistics with p-values = 0.0000. This further confirms the absence of significant feedback trading in post-crisis period. Perhaps after the crisis, the trading process for gold was mostly dominated by informed traders suggesting that this commodity became more credible in the eyes of market traders.
15

To verify the robustness of our empirical results, we conduct an additional test based modified model (Table 5: Panel A) where serial correlation is an exponential function of conditional volatility as suggested by Lebaron (1992). The parameter of interest is

1

. It is positive and significantly different form zero at the 5% level. This result lends further support to our conclusion that positive feedback traders bear a significant presence in the gold stock market of
South Africa.
3.4 Model Diagnostics
The results of the models diagnostics are reported in Tables 2B, 3B, 4B and 5B. If our models are correctly specified the normalized residuals and squared residuals of the estimated GARCH models will be free of serial auto-correlation. We use Ljung-Box Q statistics in normalized residual series and squared normalized residuals to test for significant auto-correlations. We employ Engle’s test for ARCH effects on the normalized squared residuals. We also implement the specification (JOINT) tests of Engle and Ng (1993) to capture any asymmetric response of volatility to innovations. The results of the performed specification tests support our conditional volatility specification. We conclude that the models are well specified - the normalized residuals are in general white noise and more importantly are completely free of ARCH effects.
4. Summary and Conclusion
In this paper we provide empirical evidence on whether rational investors or noise traders command a significant position in the gold-mining stock market. This is an issue with farreaching investment and policymaking implications. Using gold stock data from South Africa,
16

we employ Sentana and Wadhwani (1992) model to examine the presence of positive feedback trading process; possible asymmetric behavior in feedback trading contingent on market direction; and the impact of credit crisis of 2007 on positive feedback trading. Our findings indicate the presence of significant positive feedback trading in South African gold stock market.
Noise traders command a significant position in the market. Secondly, our results suggest that feedback trading in gold stock is not characterized by asymmetry contingent on market direction.
We posit that gold stock returns do not exhibit asymmetric feedback trading pattern because their volatility has an inverted asymmetric reaction to positive and negative shocks (Baur, 2012).
Finally, we find that feedback traders had significant influence during the pre-crisis period, but they had no significant impact in the post-crisis period. It is possible that after the crisis, the trading process in the gold stock market was dominated by informed traders.
The results have regulatory and portfolio management implications; sentiment-driven investor behavior is of concern for security market regulators because interaction between positive feedback traders and rational investors can destabilize financial markets (De Long et.al
, 1990b).
Portfolio managers also rely on volatility estimates in risk management and dynamic hedging strategies. Given that noise traders may have substantial influence on market prices, understanding feedback trading pattern an asset is vital in asset allocation strategy.
17

Reference
Antoniou. A., G. Koutmos. and A. Pericli (2005), “Index futures and positive feedback trading:
evidence from major stock exchange.” Journal of Empirical Finance (2005) 12, 219-
238
Baur. D.G. (2012), “Asymmetric Volatility in the Gold Market”, The Journal of Alternative Investments
Spring (2012), 14, 26-38
Baur, D.G. and F. J. Glover,. (2011), “A Behavioral Finance Approach With Fundamentalists and
Chartists In The Gold Market”, Working Paper, Business School, University of Technology,
Sydney.
Baur, D.G. and B.M. Lucey, (2010), “Is Gold a Hedge or a Safe Haven/ An Analysis of Stocks, Bonds and Gold” Financial Review 45, 217-229
De Long, J.B., A. Shleifer, L.H. Summers, and R.J. Waldmann (1990b), “Positive Feedback Investment
Strategies and Destabilizing Rational Speculation”, Journal of Finance 45,379-395
Engle, R.F. and Ng, V.K. (1993), “Measuring and Testing the Impact of News on Volatility”,
Journal of Finance, 48, 1749-1777
Jaffe, J.F. (1989), “Gold and Gold Stocks as Investments for Institutional Portfolios”, Financial Analysts
Journal 45, 53 – 59.
Koutmos, G. (1997), “Feedback Trading and the Autocorrelation Pattern of Stock Returns: Further
Empirical Evidence”, Journal of International Money and Finance 16, 625 – 636.
Koutmos, G. and R. Saidi, (2001), “Positive Feedback Trading in Emerging Capital Markets”,
Applied
Financial Economics 11, 291-297.
LeBaron, B. (1992), “Some Relations Between Volatility and Serial Correlation in Stock Market
Returns”,
Journal of Business, 65, 199-219.
Lintner, J. (1965), “The Valuation of Risk Assets and the Selection of Risky Investments in Stock
Portfolios and Capital Budgets”
Review of Economics and Statistics 47, 13 – 37.
Li, X. J. Miffre, and C. Brooks, (2006), “Momentum Profits and Time-Varying Unsystematic Risk”,
Working Paper, ICMA Centre, University of Reading.
Mossin, J. (1996), “Equilibrium in a Capital Asset Market”,
Econometrica 34, 768 – 783.
Sentana, E. and Wadhwani (1992), “Feedback Traders and Stock Return Autocorrelations: Evidence from a Century of Daily Data”,
The Economic Journal 102, 415 – 25.
Sharpe, W.F. (1964), “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk”,
Journal of Finance 19, 425 – 442.
Shiller, R.J. (1984), “Stock Prices and Social Dynamics”,
Brooking Papers on Economic Activity 2, 457 –
98.
18

Table 1: JSE Gold Mining Daily Stock Returns: January 1, 2000 to December 31, 2010.
Panel A: Descriptive Statistics
Statistics Gold Stock Returns
Observation
Mean
Std. Dev.
Skewness
2870
0.034904
2.5503***
0.24407***
Excess Kurtosis
JB
LB(10)
LB
2
(10)
ARCH(1)
KPSS
3.2642***
1302.2***
12.6650
695.035***
127.26***
0.0749
JOINT 4.6547
Panel B: Auto-correlation
ρ(lag)
ρ(1)
ρ(2)
Daily Returns
0.017
-0.021
Daily Squared Returns
0.246***
0.201***
ρ(3) 0.000 0.133***
ρ(4)
ρ(5)
0.023
-0.056
0.127***
0.146***
NOTES:
*** and ** denote statistical significance at 1% and 5% level respectively.
LB(n) and LB 2 (n) are the Ljung-Box Q test statistics of serial cumulative correlation up to the nth-order in the gold returns and squared gold returns. The test is distributed as χ 2 with n degrees of freedom where n is the number of lags. Critical value (at 5% level) of χ 2 with 10 degrees of freedom is 21.02.
KPSS is the Kwiatkowski, et. al (1992) test for stationarity of the return series. The computed KPSS statistic is 0.0749. This is less than the KPSS critical value (at 5%) of 0.4630. The null hypothesis – the return series are stationary – cannot be rejected.
Skewness estimate is zero in a normal distribution and excess kurtosis is three in a normal distribution.
JB is the Jarque Bera LM test for normality. It tests whether the return series are normally distributed. It has a χ 2 distribution with 2 degrees of freedom under the null hypothesis of normally distributed errors.
The critical value at 5% is 5.99.
ARCH (N) is the Lagrange Multiplier (LM) test for ARCH effects and distributed as an X 2 with N degrees of freedom. The test results for JOINT are Engle and Ng (1993) test for the potential asymmetries in conditional volatility.
19

Table 2: Maximum Likelihood Estimates of the Sentana and Wadhwani (1992) Model
Mean Equation: R t
= α +
 t
2
+ (

0
+
 
1 t
2
) R t-1
+ε t
.
Variance Equation:
 t
2    
0
 t
2

1
 
1
 t
2

1
 
2
 t
2

2
Panel A: Parameter Estimates
Parameter
α
Daily Gold Stock Return
-0.1204
(0.0304)**

0.0224
(0.0220)**

0
0.1034
(0.0012)***

1
-0.0099
(0.0112)***

0.0736
(0.0449)**

0
0.0817
(0.0000)***

1
0.2699
(0.0206)***

2
0.6370
(0.0000)*** v
Log Likelihood
1.3391
(0.0000)***
-6399.1
Panel B: Diagnostic Tests on Model’s Standardized Residuals
Daily Stock Returns
Mean
Std. Dev.
Skewness
Excess Kurtosis
LB(10)
LB 2 (10)
ARCH(1-5)
JOINT
0.0102
1.0008
0.2236***
(0.0000)
1.5750***
(0.0000)
7.5926
8.3307
1.1619
(0.3255)
4.6547
(0.1989)
NOTES:
*** and ** denote statistical significance at 1% and 5% levels respectively.
LB(n) and LB 2 (n) are the Ljung-Box Q test statistics of serial cumulative correlation up to the nth-order of the level gold returns and squared gold returns. The test is distributed as χ 2 with n degrees of freedom where n is the number of lags.
Critical value (at 5% level) of χ 2 with 10 degrees of freedom is 21.02. Skewness estimate is zero in a normal distribution and excess kurtosis is three in a normal distribution. ARCH (N) is the Lagrange Multiplier (LM) test for ARCH effects and distributed as an X 2 with N degrees of freedom. The test results for JOINT are Engle and Ng (1993) joint test for the potential asymmetries in conditional volatility. P- values (t-prob) of the estimated parameters are included in parentheses.
Errors are assumed to follow the Generalized Error Distribution (GED) distribution that nests the normal (for v=2) and the Laplace (for v=1) distributions; v is a scale parameter estimated endogenously.
20

Table 3: Maximum Likelihood Estimates of the Modified Sentana and Wadhwani (1992) Model
Mean Equation: R t
= α +
 t
2
+ (

0
+
 
1 t
2
) R t-1
+

2
R t

1
+ ε t
, ε t ~
GED(0,
 t
2
)
Variance Equation:
 t
2    
0
 t
2

1
 
1
 t
2

1
 
2
 t
2

2
Panel A: Parameter Estimates
Parameter
α


0

1
Gold Stock Return
-0.1297**
(0.0365)
0.0208**
(0.0658)
1.0264***
(0.0027)
-0.0099***
(0.0046)
0.0125
(0.6633)

2



 v
0
1
2
Log Likelihood
Panel B: Diagnostic Tests on Model’s Standardized Residuals
0.0736**
(0.0450)
0.0819***
(0.0000)
0.2649***
(0.0224)
0.6416***
(0.0000)
1.3393***
(0.0000)
-6399
Mean
Std. Dev.
Skewness
Excess Kurtosis
LB(10)
LB 2 (10)
ARCH(1-5)
JOINT
Gold Stock Returns
0.0096
1.0008
0.2225***
(0.0000)
1.5724***
(0.0000)
7.6526
8.4523
1.1808
(0.3160)
4.6932
(0.1957)
NOTES:
*** and ** denote statistical significance at 1% and 5% levels respectively.
LB(n) and LB 2 (n) are the Ljung-Box Q test statistics of serial cumulative correlation up to the nth-order of the level gold returns and squared gold returns. The test is distributed as χ 2 with n degrees of freedom where n is the number of lags.
Critical value (at 5% level) of χ 2 with 10 degrees of freedom is 21.02. Skewness estimate is zero in a normal distribution and excess kurtosis is three in a normal distribution. ARCH (N) is the Lagrange Multiplier (LM) test for ARCH effects and distributed as an X 2 with N degrees of freedom. The test results for JOINT are Engle and Ng (1993) joint test for the potential asymmetries in conditional volatility. P- values (t-prob) of the estimated parameters are included in parentheses.
Errors are assumed to follow the Generalized Error Distribution (GED) distribution that nests the normal (for v=2) and the Laplace (for v=1) distributions; v is a scale parameter estimated endogenously.
21

Table 4: Maximum Likelihood Estiamtes of the Sentana and Wadhwani (1992) Model: Test for Parameter
Changes in the Gold Stock Market Daily Returns Pre- versus Post- Global Subprime Crisis.
Mean Equation: R t
= α +
 t
2
+ [

0 , 1
( 1 – D t
) +

0 , 2
D t
+

1 , 1
( 1 – D t
)
 t
2
+

1 , 2
D t
 t
2
] R t-1
+ε t
.
Variance Equation:
 t
2    
0
 t
2

1
 
1
 t
2

1
 
2
 t
2

2
Panel A: Parameter Estimates
Parameter Gold Stock Return
α


0 , 1

0 , 2

1 , 1

1 , 2


0

 v
1
2
Log Likelihood
-0.1139**
(0.0642)
0.0214**
(0.0523)
0.1565***
(0.0003)
0.0466
(0.2975)
-0.0173***
(0.0012)
-0.0032
(0.3359)
0.0702**
(0.0446)
0.0801***
(0.0000)
0.2758**
(0.0234)
0.6331***
(0.0000)
1.3433***
(0.0000)
-6396.28
H
0
, 1 :

0 , 1
H
0
, 2 :

1 , 1
=

1 , 2
=

0 , 2
Wald Test t-statistics
2.3139**
(0.0000)
-2.5902***
(0.0000)
Panel B: Diagnostic Tests on Model’s Standardized Residuals
Mean
Std. Dev.
Skewness
LB(10)
LB 2 (10)
ARCH(1-5)
JOINT
Excess Kurtosis
Gold Stock Returns
0.0096
1.0007
0.2191***
(0.0000)
1.5456***
(0.0000)
7.6526
8.4523
1.0472
(0.3880)
3.5892
(0.3094)
22

NOTES:
*** and ** denote statistical significance at 1% and 5% levels respectively.
LB(n) and LB 2 (n) are the Ljung-Box Q test statistics of serial cumulative correlation up to the nth-order of the level gold returns and squared gold returns. The test is distributed as χ 2 with n degrees of freedom where n is the number of lags.
Critical value (at 5% level) of χ 2 with 10 degrees of freedom is 21.02. Skewness estimate is zero in a normal distribution and excess kurtosis is three in a normal distribution. ARCH (N) is the Lagrange Multiplier (LM) test for ARCH effects and distributed as an X 2 with N degrees of freedom. The test results for JOINT are Engle and Ng (1993) joint test for the potential asymmetries in conditional volatility. P- values (t-prob) of the estimated parameters are included in parentheses.
Errors are assumed to follow the Generalized Error Distribution (GED) distribution that nests the normal (for v=2) and the Laplace (for v=1) distributions; v is a scale parameter estimated endogenously.
23

Table 5: Maximum Likelihood Estimates for Modified Sentana Wadhwani (1992) Model
Mean Equation: R t
= α +
 t
2
+ [

0

+

1

exp(-
 t
2
/

2
)] R t-1
+ε t
.
Variance Equation:
 t
2    
0
 t
2

1
 
1
 t
2

1
 
2
 t
2

2
Panel A: Parameter Estimates
Parameter
α
Gold Stock Return

 

1





0 v
0
1
2
Log Likelihood
-0.1042*
(0.0871)
0.0186*
(0.0825)
-0.0046
(0.8671)
0.2470*
(0.0819)
0.0749**
(0.0465)
0.0826***
(0.0000)
0.2781***
(0.0185)
0.6277***
(0.0000)
1.3391**
(0.0000)
-6399
Panel B: Diagnostics of the Standardized Residuals from Gold Stock Returns
:
Mean
Std. Dev.
Skewness
LB(10)
LB 2 (10)
ARCH(1-5)
JOINT
Excess Kurtosis
Gold Stock Returns
0.0115
1.0006
0.2284***
(0.0000)
1.5707***
(0.0000)
7.0732
8.5167
1.2351
(0.2898)
4.4343
(0.2182)
NOTES:
*** and ** denote statistical significance at 1% and 5% levels respectively.
LB(n) and LB 2 (n) are the Ljung-Box Q test statistics of serial cumulative correlation up to the nth-order of the level gold returns and squared gold returns. The test is distributed as χ 2 with n degrees of freedom where n is the number of lags.
Critical value (at 5% level) of χ 2 with 10 degrees of freedom is 21.02. Skewness estimate is zero in a normal distribution and excess kurtosis is three in a normal distribution. ARCH (N) is the Lagrange Multiplier (LM) test for ARCH effects and distributed as an X 2 with N degrees of freedom. The test results for JOINT are Engle and Ng (1993) joint test for the potential asymmetries in conditional volatility. p- values (t-prob) of the estimated parameters are included in parentheses.
Errors are assumed to follow the Generalized Error Distribution (GED) distribution that nests the normal (for v=2) and the Laplace (for v=1) distributions; v is a scale parameter estimated endogenously.
24