La edición de la Periegesis de Barcelona de 1572

The empirical analysis uses monthly price indices and market values for the FTSE 10 industry sectors in the US, UK and Japan, for the period from December 1993 to May 2010. The whole sample has 197 observations. All of these data are collected from DataStream. The selection of FTSE sector indices is to avoid survivorship bias in the FTSE 100, with components of companies that might not always exist in indices. The currency of the price indices and market values is the US Dollar. In addition, I also collect the US one month Treasury Bill rate in the corresponding period from the Kenneth R. French Data Library. I use price indices to compute returns, and subtract the Treasury Bill rate from returns to calculate the excess return: throughout this thesis, I work with the excess returns. The market capitalization of each index is used to generate weights of all the indices in each month for the market benchmark portfolio.

Table 4.1 shows the summary statistics of excess returns for each asset from January 1994 to May 2010. The Jarque-Bera test is used to test the normality property of excess returns at 5% significance level. The null hypothesis of the Jarque-Bera test is that the sample comes from a normal distribution with unknown mean and variance, against the alternative that it does not come from a normal distribution; it is a two-sided goodness-of-fit test, suitable when a fully- specified null distribution is unknown and its parameters must be estimated. For large sample sizes, the test statistic4 has a chi-square distribution with two degrees of freedom. As can be seen from Table 4.1, the Jarque-Bera test significantly rejects the null hypothesis of normality at 5% significance level for

4 _{The test statistic is calculated by}

] 4 ) 3 ( [ 6 2 2_   n s k

tJB , where n is the sample size, s is the sample skewness, and k is the sample kurtosis.

72 each asset with p-values that are close to zero, far less than 0.05; it means that the excess return of each asset is not subject to normal distribution. In this case, the assumption of normal distribution in models actually does not apply in practice; it becomes the motivation to relax the normal distribution assumption. In the thesis, I estimate the VaR and CVaR with the normal distribution and t- distribution and compare the difference between the two different distribution assumptions with different confidence levels.

Table 4.2 reports the time series property of excess return for each asset from January 1994 to May 2010, showing the first five autocorrelation coefficients and statistic values of the Ljung-Box test for serial correlation up to 10 lags, the ARCH test of Engle (1982) and the DCC test of Engle and Sheppard (2001). Only a few excess return series display highly significant autocorrelations. In particular, the excess return series in UK Basic Materials, UK Financials, UK Telecom, USA Industrials, Japan Industrials, Japan Technology, and Japan Telecom shows virtually significant autocorrelation. The null hypothesis in the Ljung-Box Q-test is that all autocorrelations up to the tested lags are zero. This null hypothesis is significantly rejected for tests at lags from 1 to 5 and 10 lags. This seems suggest that only these excess returns series might need a conditional mean model. However, the possibilities of non-linear dependence of excess returns and low power of test still exist; there may be non-linear dependence that is picked up by momentum but not by serial correlation. I conduct Engle's ARCH test with one and two lags ARCH models to check for conditional heteroscedasticity. About 20 out of 30 excess return series reject the null hypothesis of no ARCH effects in favour of the alternative ARCH model with one and two lagged squared innovations in Engle's ARCH tests. The ARCH test suggests that there is evidence of significant volatility clustering for most of the assets excess returns. The DCC test is to test the null hypothesis of constant correlation against the alternative of dynamic conditional correlation. According to Table 4.2, the DCC test for 30 excess return series failed to reject the null of a constant correlation in favour of a dynamic structure with p-value bigger than 10%. Interestingly, the DCC test for 18 excess return series selected from 30 excess return series suggests that the data set of 18 assets exhibits significant time varying conditional correlations with p-value less than 1%. It implies that the portfolio constructed by 18 assets actually has the dynamic conditional

73 correlation, and it can be naturally concluded that the portfolio constructed by 30 assets should have the time-varying conditional correlation as well, because these 30 assets contain 18 assets with dynamic conditional correlation. In this case, it makes us doubt the power of the DCC test for 30 excess return series. The non-rejection of the null hypothesis may be due to the lower power of the test. Motivated by the results from Table 4.2, volatility models should be applied into the portfolio construction process.