We have collected the daily closing price of three benchmark indexes from different countries, specifically US (S&P500), UK (FTSE100) and Hong Kong (HSI). We selected the data sample from Bloomberg and the period is from January 6th 2003 to December 23rd 2010.
A portfolio comprised of equal weight in all three assets S&P500, FTSE100 and HSI are computed as we want to equally diversify our risk within these 3 securities. We tested the stationarity of data using Augmented Dickey-Fuller Test in Eviews and the test results are summarised in Table 1. t-statistics Probability (p-value) Standard & Poor’s 500 (S&P 500) -1.719708 0.4211 Financial Times Stock Exchange 100 (FTSE100) -1.734055 0.4139 Hang Seng Index (HSI) -1.529055 0.
5188 Portfolio -1.585160 0.4900 Table 1: Augmented Dickey-Fuller Test Statistics for Closing Price We are able to conclude that our data, in fact, have a unit root. The data is then transformed into log-return using the formula below and a database of 1906 observations is computed,where represents then closing price of the asset at time . We repeated the test mentioned above to measure the stationarity of the data and the results in summarised in Table 2. t-statistics Probability (p-value) Standard & Poor’s 500 (S&P 500) -35.80342 0.
0000 Financial Times Stock Exchange 100 (FTSE100) -34.18122 0.0000 Hang Seng Index (HSI) -45.74177 0.
0001 Portfolio -42.93229 0.0000 Table 2: Augmented Dickey-Fuller Test Statistics for log-return We proceed with plotting the graph of the log-return against their respective time period in Figure 3. It can be seen that under the time period being studied, there are clear periods of volatility clustering around the year 2008 – 2009 which is when the subprime crisis peaks. Figure 3: Log of Daily Returns against Time The figure above also shows that our series is stationary with most data being centralised around zero. We then utilise the descriptive statistics to analyse the features of our data.
S&P500 FTSE100 HSI Portfolio Mean 0.000159 0.000212 0.000453 0.000381 Median 0.000820 0.000652 0.
000745 0.000726 Maximum 0.109579 0.093843 0.134068 0.105329 Minimum -0.094697 -0.
092656 -0.146954 -0.118384 Std. Dev.
0.013716 0.013049 0.017147 0.014388 Skewness -0.262713 -0.
128083 -0.183161 -0.240604 Kurtosis 13.57033 11.62666 14.20533 13.49777 Jarque-Bera 8895.290 Prob: 0.
0000 5915.343 Prob: 0.0000 9982.161 Prob: 0.
0000 8770.366 Prob: 0.0000 Table 4: Descriptive Statistics for the Daily Log-returns The results in Table 4 shows that the most volatile is the Hang Seng index, with S&P500 and FTSE100 being less risky relatively. This is because the United States and United Kingdom’s economy are well developed compared to Hong Kong. From the Capital Asset Pricing Model (CAPM), investors would normally expect a higher return for investing in HSI index given the systemic risk of the market.
This is proven true as HSI provides the highest compensation compared to the other two equity indexes. Using the concept of CAPM, FTSE100 would be the most conservative investment out of all the indexes listed here as it has the lowest volatility and generates a relatively better return than S&P500.Looking at the skewness and kurtosis of our data, all series exhibit negative excess skewness and are asymmetrical. The skewness of a normal distribution should be zero, negative skewness means that we have a left tail that is relatively long to the right tail. In words, it means that we have observed more daily negative returns than positive returns for the time period that we’ve chosen.
The Jarque-Bera test statistics provide a more comprehensive view that all log-return series are not normally distributed at a statistically high significance level of 0.5%.