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Testing the Efficient Market Hypothesis S&P 500 and Hang Seng Index

London South Bank University Prepared for : Dr. Howard Griffiths Course Unit : Advanced Investment Analysis Due Date : 26.03.2010

2010

February Amelia Curry 1/1/2010

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Table of Contents

I. INTRODUCTION ....................................................................................................................3

II. DATA AND METHODOLOGY .................................................................................................3

III. DISTRIBUTION OF WEEKLY RETURNS ..................................................................................4

IV. WEAK-FORM EFFICIENCY TESTS ...........................................................................................5

IV.1. Autocorrelation Function Test ......................................................................................5

IV.2. Runs Test ......................................................................................................................6

V. DISCUSSION ..........................................................................................................................7

V.1. EMH and Trading Rules..................................................................................................7

V.2. Volatility and Stock Market Crash .................................................................................9

V.3. Changing Market Expectation .................................................................................... 12

VI. CONCLUSION ..................................................................................................................... 13

BIBLIOGRAPHY .................................................................................................................................. 14

APPENDIX .......................................................................................................................................... 16

3

I. INTRODUCTION

The current crisis gives emphasis to the efficient market hypothesis (EMH). If the EMH holds,

government intervention into the financial system is deemed to be unnecessary (Cuthbertson, 1996).

Based on the premise that the market “gets the price right”, financial deregulations in late 1990s

(Sherman, 2009) did not meet many resistance; until the bubble burst in 2007 revealing what

appears to be a contradiction to EMH. Opponents of the EMH argue that although the fundamental

value of securities fully reflects all available information, it does not mean the market price is always

right (Siegel, 2009).

Empirical studies supporting and questioning the merit of the EMH are enormous. However,

consolidating these two opposing views in relation to the current crisis is beyond the purpose of this

paper. We attempt to test the implication of weak-form efficiency of two market indices and analyse

the results based on the statistical evidence. Additionally, tests of trading rule and volatility are

produced as comparison.

II. DATA AND METHODOLOGY

The returns of analysed in this paper are calculated from daily and weekly indices of S&P 500

and Hang Seng Index (HSI), representing prices of major shares in the USA and Hong Kong

respectively. The weekly indices are collected from 04.01.2006 to 10.03.2010 which is sub-

categorized into pre-crisis period of 04.01.2006 – 01.10.2008 and crisis period of 08.10.2008 –

10.03.2010. This sub-categorization is chosen based on the assumption that the onset of stock

market crash is on the second week of October 2008 when the indices of two markets experienced

the largest decline, 15.18% for S&P 500 and 14.35% for HSI (own calculation, source: (Yahoo!

Finance, 2010; Standard & Poor's, 2010), during the period under consideration.

These returns are analysed based on the random walk theory and tested using

autocorrelation function (ACF) and runs tests to investigate the returns predictability. Distribution

and descriptive statistics of the weekly returns are produced by using SPSS. The tests are carried out

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based on the argument that evidence supporting the random walk hypothesis is evidence of weak-

form efficiency (Elton, Gruber, Brown, & Goetzmann, 2011).

The daily indices and trading volume are collected from 03.01.2006 – 10.03.201, consisting of

two subsets: pre-crisis and crisis for the calculation of Moving Average (MA). MA of returns are

calculated to test one of the trading rules called variable length moving average (VMA) with short-

period of one day and long-period of 200 days. Volatility analysis is limited to the S&P 500 returns

and performed based on absolute price fluctuation, skewness regression and historical variance to

illustrate the volatility of the S&P 500 returns prior to the crisis. Finally, yearly and monthly skewness

of returns distribution are calculated and compared to see whether changing market expectation

exists after the crash in October 2008.

III. DISTRIBUTION OF WEEKLY RETURNS

The histogram shows that the weekly returns of S&P 500 for all periods are fat-tailed and

negatively-skewed distributed1. By performing one-tail tests, the negative skewness and excess

kurtosis of S&P returns for all periods under consideration are statistically significant for = 5%. The

expected returns for all periods are also determined to be not significantly different from the

calculated averages. On the other hand, the return distributions of HSI are not significantly skewed

except for that of pre-crisis period which is significantly negatively skewed; the t-values of skewness

for overall and crisis periods are -0.24 and 0.87 respectively, which fall within 95% confidence limits

(Siegel A. F., 2003). However, the excess kurtosis is significant for all periods.

The normality of the return distribution is also examined by performing the Jarque-Bera ( )

test with the null hypothesis (Rachev, Mittnik, Fabozzi, Focardi, & Jasic, 2007):

1 See Appendix for Statistics Summary and Histograms

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All of the calculated coefficients for S&P 500 and HSI are larger than critical values of

distribution with 2 degree of freedom for 5% (Siegel A. F., 2003); thus, the deviation from

normal distribution for return of both markets is significant.

IV. WEAK-FORM EFFICIENCY TESTS

IV.1. Autocorrelation Function Test

The autocorrelation function (ACF) test is a parametric test applied to test the statistical

independence of return observed at time t (Rt) from return observed at lagged time t-k (Rt-k)

(Cromwell, Labys, & Terraza, 1994; Islam & Watanapalachaiku, 2004). The results of ACF test (k = 1 –

6) for S&P 500 and HSI are summarized as follows2:

S&P 500 OVERALL HSI OVERALL

Lag Upper Limit Lower Limit Upper Limit Lower Limit

1 0.0051 0.1351 -0.1351 -0.0503 0.1351 -0.1351

2 -0.0655 0.1351 -0.1351 -0.0767 0.1351 -0.1351

3 0.0312 0.1352 -0.1352 0.1140 0.1352 -0.1352

4 0.0691 0.1352 -0.1352 0.0595 0.1352 -0.1352

5 0.1263 0.1352 -0.1352 0.0438 0.1352 -0.1352

6 0.0647 0.1352 -0.1352 0.0059 0.1351 -0.1351

Q 6.61 5.89

S&P 500 PRE-CRISIS HSI PRE-CRISIS


1 -0.1555 0.1666 -0.1666 -0.0702 0.1666 -0.1666

2 0.1614 0.1668 -0.1668 0.0965 0.1667 -0.1667

3 -0.0472 0.1666 -0.1666 -0.1095 0.1666 -0.1666

4 0.0547 0.1667 -0.1667 0.2029 0.1668 -0.1668

5 -0.0384 0.1666 -0.1666 0.0655 0.1667 -0.1667

6 -0.0080 0.1667 -0.1667 -0.1237 0.1666 -0.1666

Q 8.21 12.53

2 See Appendix for Autocorrelation Coefficient Charts

6

S&P 500 CRISIS HSI CRISIS


1 0.0417 0.2310 -0.2310 -0.0761 0.2308 -0.2308

2 -0.1506 0.2307 -0.2307 -0.1592 0.2307 -0.2307

3 -0.0036 0.2309 -0.2309 0.1723 0.2312 -0.2312

4 0.0038 0.2309 -0.2309 -0.0350 0.2309 -0.2309

5 0.1714 0.2312 -0.2312 0.0272 0.2310 -0.2310

6 0.1087 0.2311 -0.2311 -0.0397 0.2309 -0.2309

Q 4.92 4.83

Table 1. Autocorrelation Function Test (Own Calculation, Source: (Standard & Poor's, 2010; Yahoo! Finance, 2010))

The correlation coefficients of market return are within the chosen confidence intervals

(±2SE), except for that of HSI pre-crisis for k = 4. The squared autocorrelation coefficient ( )

indicates the proportion of the variability of that can be explained by e.g. 0.0015% of S&P

500 return at time t can be explained by return at time t-1. To test whether these coefficients are

statistically different from zero i.e. no serial correlation, Box-Pierce Q statistic for each market is

calculated. The null and alternative hypotheses are defined as (Cromwell, Labys, & Terraza, 1994):

From distribution table (Siegel A. F., 2003); the Q statistics of both markets for all periods are less

than the critical value for 5% and 6 degree of freedom. Therefore, we do not reject the null

hypothesis, i.e. the autocorrelation coefficients for all time lags in both markets are not significantly

different from zero.

IV.2. Runs Test

The weakness of ACF test is that it is affected by outliers, i.e. extreme value of observations

(Elton, Gruber, Brown, & Goetzmann, 2011) which can be found in fat-tailed distribution with higher

probability than in Gaussian distribution. It also assumes that the time-series data are stationary,

which is often not the case (Liu, 1999). Therefore runs test, a non-parametric test, is performed to

examine the independence of our market returns (Siegel & N. John Castellan, 1988). The null

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hypothesis is the independence of the time-series data from previous outcome. The results of runs

test for both market indices are as follows:

S&P 500 HSI

Overall Pre-Crisis Crisis Overall Pre-Crisis Crisis

Actual Runs 117 79 38 99 63 36

Expected Runs 109.49 72.65 37.69 108.58 70.65 38.44

Std. Deviation 7.31 5.95 4.21 7.25 5.78 4.29

Z-Score 1.03 1.07 0.07 1.32 1.32 0.57

Table 2. Runs Test (Own Calculation, Source: (Standard & Poor's, 2010; Yahoo! Finance, 2010))

For all period observed, the actual runs of S&P 500 are higher than the calculated expected

runs. The opposite is observed in HSI, indicating a relatively stronger autocorrelation (Islam &

Watanapalachaiku, 2004). However, all of the Z-scores are within 95% confidence limit of one-tail

test (Siegel A. F., 2003); therefore we do not reject H0 and conclude that there is no significant

clustering of returns for both markets.

V. DISCUSSION

V.1. EMH and Trading Rules

From the results of the ACF and runs tests, it can be presumed that the random walk theory

holds for both markets and thus, the pricing of S&P 500 and HSI are weak-form efficient. The EMH

asserts that if return cannot be forecasted from past returns because all past information already

incorporated into the current price, systematic arbitrage opportunities do not exist (Blake, 2000), i.e.

traders cannot gain excess return relative to that of buy-and-hold strategy. To test this, VMA 1-200

rule is applied to daily return from both markets34. The strategy of this trading rule is to buy when the

short-period MA rises above the long-period MA and to sell when the short-period MA is below the

long-period MA (Brock, Lakonishok, & LeBaron, 1992). Average returns from this trading rule are

calculated for all period under consideration. The results for S&P 500 are summarized as follows:

3 See Appendix for Moving Average Charts

4 See (Brock, Lakonishok, & LeBaron, 1992) for VMA t-tests

8

S&P 500 OVERALL PRE-CRISIS CRISIS

Mean Market Return 0.005% -0.025% 0.065%

Std. Deviation 1.64% 1.17% 2.29%

Variance 0.03% 0.01% 0.05%

Sample Size 1,053 696 357

No. of BUY 622 431 191

Return (BUY) 0.107% 0.088% 0.149%

t-test 1.2213 1.5702 0.4103

(Return) BUY > 0 0.5932 0.5870 0.6073

No. of SELL 431 265 166

Return (SELL) -0.141% -0.209% -0.032%

t-test -1.5587 -2.1685 -0.4505

Return(SELL) > 0 0.4733 0.4641 0.4879

Return(BUY) - Return (SELL) 0.247% 0.297% 0.181%

t-test 2.4076 3.2381 0.7455

Table 3. Variable Moving Average 1-200 for S&P 500 (Own Calculation, Source: (Standard & Poor's, 2010))

The t-values for the difference of average daily buy and sell return are highly significant for

overall and pre-crisis periods; however, we reject the significance for crisis period. By performing

two-sample tests for the averages of buy-return and market return, it can be concluded that they are

not significantly different. However, the sell-return for pre-crisis period is significantly different from

that of the market. These results suggest that the pricing of S&P 500 was not efficient and arbitrage

could benefit from this asymmetry, at least in the pre-crisis period under consideration.

The same procedures are performed for HSI returns, and the results are as follows:

HSI OVERALL PRE-CRISIS CRISIS

Mean Market Return 0.056% 0.032% 0.101%

Std. Deviation 2.09% 1.71% 2.68%

Variance 0.04% 0.03% 0.07%

Sample Size 1,053 694 359

No. of BUY 191 531 207

Return (BUY) 0. 149% 0.145% 0.171%

t-test 0.5708 1.1384 0.298893

(Return) BUY > 0 0.5593 0.5593 0.5121

No. of SELL 166 163 152

Return (SELL) -0.032% -0.334% 0.005%

t-test -0.4983 -2.4565 -0.3671

Return(SELL) > 0 0.4698 0.4356 0.5066

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HSI OVERALL PRE-CRISIS CRISIS

Return(BUY) - Return (SELL) 0.181% 0.478% 0.165%

t-test 0.8152 3.1208 0.5768

Table 4. Variable Moving Average 1-200 for HSI (Own Calculation, Source: (Yahoo! Finance, 2010))

The same conclusion can be made for HSI; the significant t-value during pre-crisis period

indicates that the sell-return of 0.334% is significantly above the market average. However, the

pricing of the market appears to be increasingly efficient during the crisis period; with all t-values are

insignificant, we do not reject the null hypothesis that the average returns from this trading rule are

not significantly different from the market average.

V.2. Volatility and Stock Market Crash

The calculated coefficients suggest that the departure from normality for S&P 500 returns

is larger than that for HSI. It is implied that the S&P return is relatively more volatile than that of HSI,

i.e. extreme values can be observed with relatively higher frequency. The higher negative skewness

of S&P 500 returns also signifies the probability of returns being smaller than the expected returns is

higher in S&P 500 than in HSI. Therefore, the analysis of the volatility of return is limited to S&P 500.

As an illustration of the price fluctuations of S&P 500 from 2006-2010, 4-day moving average

of absolute daily returns (Liu, 1999) is calculated. From Figure 1. below, the relatively calm episode in

2006 started to show choppy pattern in late 2007. A jump of 2.08% of volatility in S&P 500 on

September 11, 2008 preceded the announcement of Lehman Brothers bankruptcy (Sorkin, 2008)

which appears to be in line with empirical studies that insinuate market often adjusts its perception

of risks ahead of news announcement (Blake, 2000).

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Figure 1. Volatility of S&P 500 (Own Calculation, Source: (Standard & Poor's, 2010))

There are several forecasting methods that can be applied to stock return volatility. In terms

of asset risk, volatility can be measured from the standard deviation, skewness and kurtosis of its

returns (Jokipii, 2006). Therefore, multiple regression of skewness is performed based on the

heterogeneity of investor beliefs theory5 and the results are as follows:

Lag

(Returns

SKW)

(SDV. Of Return)

(Returns)

(Trading Volume)

(SDV. Of Volume)

(SKV

Volume)

0 0.148 ***-0.745 0.126 0.023 **-0.110

t-test -1.468 -13.666 0.926 0.383 -1.968

1 -0.059 -0.043 0.023 *-0.249 -0.034 -0.041

t-test -0.771 -0.403 0.264 -1.688 -0.570 -0.730

2 *0.151 0.057 0.018 0.115 -0.079 -0.008

t-test 1.920 0.537 0.200 0.754 -1.324 -0.139

3 -0.033 -0.028 0.058 0.180 **-0.118 -0.072

t-test -0.395 -0.285 0.598 1.149 -2.032 -1.260

4 -0.047 -0.152 -0.028 0.099 -0.011 0.045

t-test -0.573 -1.592 -0.310 0.616 -0.192 0.793

5 0.017 0.010 0.067 -0.154 0.065 0.053

t-test 0.206 0.104 0.761 -1.101 1.092 0.943

*, **, and **** denotes significance at 10%,5% and 1% respectively

Table 5. Skewness Regression for S&P 500 (Own Calculation, Source: (Standard & Poor's, 2010)

5 See (Jokipii, 2006) for Details

2.08%

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

03/01/2006 03/01/2007 03/01/2008 03/01/2009 03/01/2010

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Although only significant at 10% level, the trading volume at t-1 appears to have an inverse

impact on the skewness of return at time t ( ). The regression model employed can explain

62.4% of variation in with F-test confirms that all of these regression coefficients are

significantly different from zero6. More interestingly, there are significant positive correlations

between return’s spread from its expected value at time t and all lagged trading volume and volume

standard deviation7. The analysis on forecasting power of this model is far from being complete;

however, it appears that large trading volume in previous days increases the volatility of return.

There was a jump in trading volume leading to the crash in first week of October 2008 as can be seen

below:

Figure 2. Trading Volume of S&P 500 in Jan – Sep 2008 (Standard & Poor's, 2010)

Additionally, forecast volatility ( ) and realized volatility ( ) are calculated based on

historical variance method (Minkah, 2007). The model shows increasing volatility predicted by end of

September 2008 although it underestimated the jump of volatility on October 14, 2008. The results

for year 2008 are illustrated in the figure below:

6 See Appendix for ANOVA

7 List of Correlation Coefficients cannot be presented here due to the limitation of this paper

3.5E+09

4.5E+09

5.5E+09

6.5E+09

7.5E+09

8.5E+09

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Figure 3. Historical Variance S&P 500 Year 2008 (Own Calculation, Source: (Standard & Poor's, 2010))

V.3. Changing Market Expectation

To see whether we have hit the “bottom” of the stock market crash, yearly and monthly

skewness of daily returns are measured and the results are summarized in the table below:

Skewness (SK) SE of SK t-test SK

Returns 2006 0.1333 0.1537 0.8675

Returns 2007 -0.4483 0.1537 -2.9166

Returns 2008 0.1898 0.1531 1.2394

Returns 2009 0.0360 0.1534 0.2348

Returns Jan 2009 0.0640 0.5121 0.1249

Returns Feb 2009 -0.0916 0.5238 -0.1749

Returns Mar 2009 0.4481 0.4910 0.9126

Returns Apr 2009 -0.6733 0.5012 -1.3435

Returns May 2009 0.1489 0.5121 0.2907

Returns Jun 2009 -0.4388 0.4910 -0.8937

Returns Jul 2009 -0.2482 0.4910 -0.5054

Returns Aug 2009 -0.5580 0.5012 -1.1133

Returns Sep 2009 -0.4793 0.5012 -0.9563

Returns Oct 2009 -0.3468 0.4910 -0.7064

Returns Nov 2009 -0.3062 0.5121 -0.5979

Returns Dec 2009 -0.4838 0.4910 -0.9855

0.0000

0.0100

0.0200

0.0300

0.0400

0.0500

0.0600

0.0700

Forecast Volatility Realized Volatility

13

Skewness (SK) SE of SK t-test SK

Returns Jan 2010 -0.3008 0.5238 -0.5743

Returns Feb 2010 -1.1969 0.5238 -2.2853

Table 6. Yearly and Monthly Skewness of S&P 500 Returns (Own Calculation, Source: (Standard & Poor's, 2010))

The negative skewness in S&P 500 return does not appear to decline; significance test

confirms that the returns of February 2010 are significantly negatively-skewed. Therefore, we can

infer that market remains negative; expectation of sharp fall in share price persists in S&P 500

(Jokipii, 2006).

VI. CONCLUSION

By performing ACF and runs tests, the absence of serial correlations implies that the pricing

in both markets follows the random walk theory, with expected returns vary unpredictably. Testing

these markets against one of the trading rules, it is also found that there are no systematic excess

returns to be gained. Although it appears that the pricing in pre-crisis period was less efficient, we

can conclude that both markets could not be beaten consistently using this trading rule.

Further studies are necessary on the volatility forecasting method employed here; however it

can be inferred that the market shows warning signs, such as high trading volume, preceding a crash

(Jokipii, 2006; Hong & Stein, 2003). Furthermore, historical variance method actually forecast higher

volatility than that realized in the first week of October 2008. Long-horizon test on this method might

shed some more insight into stock market volatility.

Finally, by comparing skewness of daily returns, there is a high probability that realized

returns in February 2010 to be below the expected value, even higher than that in January 2010.

Therefore, it can be concluded that there is no reversal in market expectation.

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Bibliography

Blake, D. (2000). Financial Market Analysis. Chichester (UK): John Wiley & Sons Ltd.

Brock, W., Lakonishok, J., & LeBaron, B. (1992). Simple Technical Trading Rules and the Stochastic

Properties of Stock Returns. The Journal of Finance: 47(5) , 1731-1764.

Cromwell, J. B., Labys, W. C., & Terraza, M. (1994). Univariate Tests for Time Series Models. Thousand

Oaks: Sage Publications, Inc.

Cuthbertson, K. (1996). Quantitative Financial Economics: Stocks, Bonds and Foreign Exchange.

Chichester UK: John Wiley & Sons Ltd.

Elton, E. J., Gruber, M. J., Brown, S. J., & Goetzmann, W. N. (2011). Modern Portfolio Theory and

Investment Analysis. John Wiley & Sons Pte Ltd.

Hong, H., & Stein, J. C. (2003). Differences of Opinion, Short-Sales Constraints, and Market Crashes.

The Review of Financial Studies: 16(2) , 487-525.

Islam, S. M., & Watanapalachaiku, S. (2004). Empirical Finance: Modelling and Analysis of Emerging

Financial and Stock Markets. New York: Physica-Verlag HD.

Jokipii, T. (2006). Forecasting Market Crashes: Further International Evidence. Bank of Finland

Research.

Liu, Y. (1999). The Statistical Properties of the Volatility of Price Fluctuations. Physical Review Es:

60(2) , 1390-1400.

Minkah, R. (2007). Forecasting Volatility. Department of Mathematic - Uppsala University.

Rachev, S. T., Mittnik, S., Fabozzi, F. J., Focardi, S. M., & Jasic, T. (2007). Financial Econometrics: From

Basic to Advanced Modelling Techniques. Hoboken, NJ (USA): John Wiley & Sons, Inc.

Sherman, M. (2009). A Short History of Financial Deregulation in the United States. Washington D.C.:

Center for Economic and Policy Research.

Siegel, A. F. (2003). Practical Business Statistics. New York: McGraw-Hill Higher Education.

Siegel, J. J. (2009, October 27). Efficient Market Theory and the Crisis. Retrieved March 17, 2010, from

http://online.wsj.com/article/SB10001424052748703573604574491261905165886.html

Siegel, S., & N. John Castellan, J. (1988). Nonparametric Statistics for the Behavioral Sciences.

Singapore: McGraw-Hill Inc.

Sorkin, A. R. (2008, September 14). Lehman Files for Bankruptcy; Merrill Is Sold. Retrieved March 19,

2010, from The New York Times:

http://www.nytimes.com/2008/09/15/business/15lehman.html?pagewanted=all

Standard & Poor's. (2010, March 12). S&P 500: Index Level Performance. Retrieved March 14, 2010,

from Standard & Poor's: http://www.standardandpoors.com/prot/spf/docs/indices/SPUSA-500-

USDUF--P-US-L--HistoricalData.xls

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Yahoo! Finance. (2010, March 10). Hang Seng Index (HSI). Retrieved March 15, 2010, from Yahoo!

Finance:

http://ichart.finance.yahoo.com/table.csv?s=%5EHSI&a=00&b=04&c=2006&d=02&e=10&f=2010&g=

d&ignore=.csv

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Appendix

1. SUMMARY OF DESCRIPTIVE STATISTICS FOR S&P 500 AND HSI:

STATISTICS S&P 500 OVERALL HSI OVERALL

Median 0.0016 0.0053

Mode -0.0002 -0.1435 (a)

Mean -0.0038% 0.2424%

Standard Error of Mean 0.0019 0.0028

t-test -0.0203 0.8580

Standard Deviation 0.0277 0.0418

Range 0.2529 0.3118

Minimum -0.1518 -0.1435

Maximum 0.1012 0.1683

Skewness Coefficient -0.8730 -0.0400

Std. Error of Skewness 0.1640 0.1640

t-test -5.3232 -0.2439

Kurtosis Coefficient 5.7590 2.4120

Std. Error of Kurtosis 0.3270 0.3270

t-test 17.6116 7.3761

Jarque-Bera Coefficient 330.4582 53.1453

STATISTICS S&P 500 PRE-CRISIS HSI PRE-CRISIS

Median 0.0009 0.0050

Mode -0.0614 (a) -0.1181 (a)

Mean -0.0399% 0.1808%


t-test -0.2694 0.6390


Range 0.1022 0.2082

Minimum -0.0614 -0.1181

Maximum 0.0408 0.0900

Skewness Coefficient -0.7620 -0.6950


t-test -3.7723 -3.4406



t-test 3.8130 4.1421


STATISTICS S&P 500 CRISIS HSI CRISIS

Median 0.0039 0.0067

Mode -0.1510 (a) -0.1435 (a)

Mean 0.0655% 0.3608%


t-test 0.1395 0.5783

17


Range 0.2529 0.3118

Minimum -0.1518 -0.1435

Maximum 0.1012 0.1683

Skewness Coefficient -0.7480 0.2420


t-test -2.7004 0.8736



t-test 4.5566 2.6058


(a) Multiple modes exist. The smallest value is shown

(SPSS and Own Calculation, Source: (Standard & Poor's, 2010; Yahoo! Finance, 2010)

2. HISTOGRAM OF S&P 500 RETURNS FOR OVERALL PERIOD

(SPSS, Source: (Standard & Poor's, 2010)

0.15000.10000.05000.0000-0.0500-0.1000-0.1500-0.2000

Return S&P 500 Overall

60

40

20

0

Fre

qu

en

cy

Mean =-3.797717E-5Std. Dev. =0.0277215

N =219

Histogram

18

3. HISTOGRAM OF HSI RETURNS FOR OVERALL PERIOD

(SPSS, Source: (Yahoo! Finance, 2010)

4. AUTOCORRELATION COEFFICIENTS

4.1. S&P 500 for Overall Period

(Own Calculation, Source: (Standard & Poor's, 2010)

0.20000.0000-0.2000

Return HSI Overall

50

40

30

20

10

0

Fre

qu

en

cy

Mean =0.002424Std. Dev. =0.0418085

N =219

Histogram

-0.15

-0.10

-0.05

-

0.05

0.10

0.15

1 2 3 4 5 6

Correlation

Upper Limit

Lower Limit

19

4.2. S&P 500 for Pre-Crisis Period


4.3. S&P 500 for Crisis Period


4.4. HSI for Overall Period

(Own Calculation, Source: (Yahoo! Finance, 2010)

-0.20

-0.15

-0.10

-0.05

-

0.05

0.10

0.15

0.20

1 2 3 4 5 6

Correlation

Upper Limit

Lower Limit

-0.30

-0.20

-0.10

-

0.10

0.20

0.30

1 2 3 4 5 6

Correlation

Upper Limit

Lower Limit

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

1 2 3 4 5 6

Correlation

Upper Limit

Lower Limit

20

4.5. HSI for Pre-Crisis Period


4.6. HSI for Crisis Period


5. VARIABLE MOVING AVERAGE 1-200 RULE FOR S&P 500


-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

1 2 3 4 5 6

Correlation

Upper Limit

Lower Limit

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

1 2 3 4 5 6

Correlation

Upper Limit

Lower Limit

600.00 700.00 800.00 900.00

1,000.00 1,100.00 1,200.00 1,300.00 1,400.00 1,500.00 1,600.00

SMA SHORT SMA LONG

21

6. VARIABLE MOVING AVERAGE 1-200 RULE FOR HSI


7. SKEWNESS REGRESSION

Model Summary(b)

Model R R

Square

Adjusted R

Square

Std. Error of the

Estimate Durbin-Watson

1 .790(a) 0.624 0.550 1.2238899 2.001

ANOVA(b)

Model Sum of

Squares df Mean

Square F Sig.

1 Regression 440.004 35 12.572 8.393 .000(a)

Residual 265.129 177 1.498

Total 705.133 212

(SPSS, Source: (Standard & Poor's, 2010)

10,000

15,000

20,000

25,000

30,000

SMA SHORT SMA LONG

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