G.J.C.M.P.,Vol.4(2):16-21 (March-April, 2015) ISSN: 2319 – 7285

AN EMPIRICAL INVESTIGATION OF RANDOM WALKS IN GOLD PRICE MOVEMENT *S.Shankari & **Dr.S.Manimaran

1. INTRODUCTION The are investing their money in the market with the aim of generating a return on their capital invested. Many investors try not only to make a profitable return, but also to outperform or beat the market. The Efficient Market Hypothesis (EMH), created in the 1970s by , is an investment theory that states it is impossible to "beat the market," and also states that the price of a stock at any given time should reflect all the available information. The actual price of the stock should reflect events that have occurred in the past, and those that are expected to occur in future. For example, if investors expect the interest rates to go down, then the price of the stock should also discount the factor Although it is a cornerstone of modern financial theory, the EMH is highly controversial and often disputed. Believers argue that it is pointless to search for undervalued or to try to predict trends in the market through fundamental-or-Technical-analysis. For example, investors such as Warren Buffett have consistently beaten the market over periods of time, which should be impossible, according to the EMH. Detractors of the EMH also point to events, such as the 1987 crash when the Dow Jones Industrial Average (DJIA) fell by over 20% in a single day, as evidence that stock prices can seriously deviate from their fair values.

1.1. DEGREES OF EFFICIENCY There are three identified classifications of the EMH, which are aimed at reflecting the degree to which it can be applied to markets. 1.Strong efficiency - This is the strongest version, which states that all information in a market, whether public or private, is accounted for in a stock price. Not even insider information could give-an-,-an-advantage. 2. Semi-strong efficiency - This form of EMH implies that all public information is calculated into a stock\'s current share price. Neither fundamental nor can be used to achieve superior gains 3. Weak efficiency - This type of EMH claims that all past prices of a stock are reflected in today\'s stock price. Therefore, technical analysis cannot be used to predict and beat a market. The theory which supports to the Weak Efficiency is known as Random Walk theory

2. RANDOM WALK THEORY Weak form of market gained popularity in 1973 when Burton Malkiel wrote "A Random Walk down Wall Street", a book that is now regarded as an investment classic. Random walk is a stock market theory that states that the past movement or direction of the price of a stock or overall market cannot be used to predict its future movement. Market Efficiency has an influence on the investment strategy of an investor because if securities markets are efficient trying to pick winners will be a waste of time. Since in an efficient market, the prices of securities will reflect the market’s best estimate of their expected return and risk, taking into account all that is known about them. Therefore, there will be no undervalued securities offering higher than deserved expected returns, given their risk. And if markets are not efficient, and excess returns can be made by correctly picking winners, then it will pay investors to spend time finding these undervalued securities.

3. GOLD Gold is one of the oldest precious metals known to man and for years it has been valued as a global currency, an investment, a commodity and an object of beauty and India is not an exception to this. India’s love affair with gold is timeless spanning over centuries and millennia. In India, Gold is not just another precious metal but it is a part of our culture, an inseparable part of our belief system and a matter of pride. Gold has always been considered a sacred item in life and is a must in every religious function- reason being that Gold is pure having passed through fire in its process of evolution. Gold has become an inseparable part of almost every household in Indian Society and infused into the blood of an Indian. It’s being seen as symbol of good fortune and prosperity. Over a few thousands of years, many kings,

16 G.J.C.M.P.,Vol.4(2):16-21 (March-April, 2015) ISSN: 2319 – 7285 emperors and dynasties featuring countless wars, conquests and political upheavals have ruled the Indian subcontinent. Gold acted as a common medium of exchange or store of value across the monetary systems of different kingdoms across the subcontinent and thus resulted into safeguarding wealthin-spite of the various wars and changes in the rulers. The stable purchasing power ability of gold and the intrinsic value feature of gold makes it a safe investment especially during the time of recession with high risk such as inflation,exchange rate fluctuations etc.

3.1. Gold Investment Until the end of last century, Middle class Indians paid a little attention on managing personal during their working life span and consulted their peers or advisors about some deposit schemes with banks or post office or companies only at the time of retirement or at the crisis time (Das, 2012). Now when the growth of the has substantially increased during the past few years, the investor population has also boomed in India. Each investor holds different objective that needs to be accomplished depending on demographic and psychological needs of an individual. Gold has three crucial attributes that, apparently, set it apart from other commodities: firstly, certainly gold is homogeneous; secondly, gold is indestructible and fungible; and thirdly, the inventory of above ground stocks is astronomically large relative to changes in flow demand. Gold is also viewed as a secure and easily accessible savings vehicle by the rural community, where around 70% of the population lives Gold has three characteristics which lure Indians. First, it has held value for so long. Second, it is portable, and a useful hedge against adversity. It is held for distress situations and is easily encashable (Aggarwal and Lucey, 2007). Third, equity has not been a fail-safe deliverer of value for most ordinary Indians. For those who seek safety of capital, gold is the alternative to fixed deposits (Jagannathan, 2013; Singh and Nadda, 2013; Ghosh et.al., 2004).

3.2. Significance of Gold in Indian culture: Gold is a precious metal with which mankind has had a long and very intimate relation. Gold is considered as a symbol of purity and good fortune. Most of the gold that the entire world holds lies in India. The main reasons why Indians consider gold as an investment are:  Gold is considered as equivalent to liquid cash: Gold is considered as a security or asset which can be converted into cash whenever required  Gold is a very good Investment: Due to its consistently increasing value, gold is considered as a safe and secure investment.  Gold, a good gift item: It is precious and worthy. It is given as gift during weddings, birthdays or any other special occasions. It is a symbol of prestige and is considered auspicious.  Gold considered as status symbol: Gold symbolizes wealth. In Indian Weddings, the Bride wears Jewellery as a symbol of family status.  Gold has religious significance: Gold is a symbol of Hindu Goddess Lakshmi. Gold is bought or gifted on occasions of festivals like Dhanteras, Dussera and Diwali.  Gold has great ornamental value: Women and gold jewellery are inseparable from each other. Gold Ornaments are always in fashion and will never become out of fashion. Even the wedding rings are made of gold to mark a long lasting relationship  Gold: An ancestral property: Gold is passed down from generation to generation as an ancestral property.

4. REVIEW OF LITERATURE Richard and Cheung (1994) study the seasonal pattern in of Asian Stock markets and they reported that there exist day-of-the-week variations in volatility in most of the emerging Asian markets. Barnes (1986) tests the weak form market efficiency of the Kuala Lumpur and concludes that the stock exchange exhibited surprisingly high degree efficiency, inspite of thinness of the market. Smith, Jefferis and Ryoo (2002) applied the multiple variance ratio test on eight African stock market price indices(Botswana, Egypt, Kenya, Mauritius, Morocco, Nigeria, South Africa and Zimbabwe) during the period 1990- 1998 and showed that only South Africa was weak-form efficient. Suresh ch. Das, sushil k. pattanaik(2011) studied the randomness of various indices like Nifty, sensex and Nifty Junior and concluded that there is no randomness in Indian indices during their study period.

5. RESEARCH METHODOLOGY Since the test of weak form of EMH, in general, has come from the random walk literature, this paper investigates whether or not successive price changes were independent of each other in the price movement of gold. For this, the researchers employed rigorous parametric and non-parametric tests of the Random Walk Hypothesis. Based on this, the researchers set the objectives as follows:  To comprehend the concept of Random Walk Theory  To investigate the randomness of gold price movement by using run test and auto correlation test. For this, the following Hypotheses are checked with relevant tests

S.No Hypotheses Statistical Tools used 1. Ho: Gold price movement follows random Walk. Run Test

2. Ho: First order auto correlations are not present Auto Correlation

17 G.J.C.M.P.,Vol.4(2):16-21 (March-April, 2015) ISSN: 2319 – 7285 5.1. COLLECTION OF DATA The sample period is January 1994 to December 2014. The data consist of monthly closing values of 1 gram of gold in Indian rupee. The data have been collected from the website of www.ncdex.com.The general details of gold price are obtained using Descriptive statistics.

TABLE NO: 1 Monthly Gold price movement from Jan 94 to Dec 2014

Source:ncdex.com

TABLE NO: 2 Summary Statistics of gold price movement from Jan 94 to Dec 2014

S.No Product N Mean Minimum Maximum 1. Gold 254 1082.56 355 3059

Rate of Return (ROR) is the ratio of money gained or lost (whether realized or unrealized) on an investment relative to the amount of money invested. The money invested may be referred to as the asset, capital, principal, or the cost basis of the investment. Return is usually expressed in percentage. The can be calculated over a single period, or expressed as an average over multiple periods of time. The formula for arithmetic return is:

Where rarith is sometimes referred to as the . The month wise returns for gold has been calculated and it is shown in the following table.

TABLE NO:3 Monthly Gold price returns from Jan 94 to Dec 2014

Source:Calculated data

5.2. RUN TEST A run test is a strong test for randomness in investigating serial dependence in share price movements and compares the expected number of Run from a random process with the observed number of Run. The test is non-parametric and is independent of the normality and constant variance of data. A run is defined as a series of identical signs that are preceded or are followed by a different sign or no sign at all. That is given a sequence of observations, the Run test examines whether the value of one observation influences the values taken by later observations. If there is no influence (the observations are independent), the sequence is considered random. It is assumed that the sample proportion of positive, negative and zero price changes are good estimates of the population’s proportions. The total number of Run is a measure of randomness, since too many or too few Run, suggests dependence between observations. The standardized Z is defined as: Run Test Z= R-X/ σ Where R= number of Run X= 2 n1n2 ______+ 1 n1+ n2

18 G.J.C.M.P.,Vol.4(2):16-21 (March-April, 2015) ISSN: 2319 – 7285 σ=SQRT [2 n1n2 (2 n1 n2-n1- n2)/ (n1+ n2)2 (n1+ n2-1)]

Table No: 4: Run Test Results:

S.No product No. of X σ Z value TV(@95% confidence Run level) 1. Gold 116 126.22 7.84 -1.30 +1.96 to -1.96 Source:Calculated data The results of the Run test are given in Table.No.3. The Run test converts the total number of Run into a Z statistic. Here the observed value of test statistic, Z=-1.30, is higher than the lower critical value, Z=-1.96, the decision is to accept the Null Hypothesis. So, it is inferred that the Gold price movement follows Random Walk Theory.

5.3. AUTO CORRELATION TEST Autocorrelation is one of the statistical tools used for measuring the dependence of successive terms in a given time series. Therefore it is used for measuring the dependence of successive Share price changes. It is the basic tool used to test the weak form of EMH. The autocorrelation function ACF (k) for the time series Y t and the k-lagged series Yt-k is defined as ACF(k)= Σn(t=1-K)( yt - y)(yt-k -y) Σn(t=1) ( yt - y)2 where y is the overall mean of the series

Table No: 5: Auto Correlation results

Source:Wessa.net

19 G.J.C.M.P.,Vol.4(2):16-21 (March-April, 2015) ISSN: 2319 – 7285

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Source:Wessa.net For both random variable series and series with trends, ACF (k) are very high and decline slowly as the lag value (k) increases. At the same time the ACF (k) of the first difference series (price changes or returns) are statistically insignificant when the series is a random walk series. A random walk series drifts up and down over time. In some situation it may be difficult to judge whether a trend or drift is occurring. Hence to determine whether a series has significant trend or whether it is a random walk, the t-test is applied on the series of first differences. For gold price , the auto correlation coefficient for lag 1 is -.018 and 0.017 respectively which is very much lower to te standard error 0.036(2*0.018).Thus the auto correlation are not significantly differ from Zero. And so, it is inferred that the first order auto correlations are not present which is supporting to the Random walk Theory.

6. CONCLUSION The assumption that gold prices are random is basic to the efficient market hypothesis and capital models. This study has presented evidence concentrating on the weak form efficiency in the gold price movement under the consideration that variance is time dependent. Gold price data shows that there is no relationship between the each day’s return again which is supporting to the Random Walk Theory in gold price movement.

7. REFERENCES  Sharma J. L. and Robert E. Kennedy [1977] "A Comparative Analysis of Stock Price Behaviour on the Bombay, London and New York Stock Exchanges", Journal of Financial and Quantitative Analysis Sep 1977, p-35-43.  Suresh ch. Das, sushil k. pattanaik(2011),” testing random walk hypothesis for bombay stock exchange and national stock exchange”, journal on banking financial services & insurance research, September 2011,Finance India, September 1996,p-605-616.  Sunil poshakwale(2011),”Evidence on Weak Form Efficiency and Day of the Week Effect in the Indian Stock Market”  Rogalski, R., 1984, “New Findings Regarding Day of the Week Returns over Trading and Non-trading Periods”, Journal of Finance, 39, 1603 -14.  Solnik, B. and Bousquet, L., 1990, “Day of the Week Effect on the Paris Bourse”, Journal of Banking and Finance, 14, 461-68.  Smith, G., Jefferis, K., & Ryoo, H-J. (2002). African stock markets: multiple variance ratio tests of random walks. Applied , 12 (7), pp.475-484.  www.nseindia.com cited on 28.02.2015  www.sse.com cited on 28.02.2015 20 G.J.C.M.P.,Vol.4(2):16-21 (March-April, 2015) ISSN: 2319 – 7285  www.yahoofinance.com on 24.02.2015  www.wessa.net cited on 29.02.2015

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