Solutions Shreve Chapter 3

Topics: Statistical hypothesis testing, Statistics, Regression analysis Pages: 6 (1783 words) Published: January 7, 2013
Empirical Finance 4.2 – Case 3

Julinda Kllapi, 2514073,
Valkana Lesseva, 1836994,

The recent financial crisis saw CDS spreads soaring across the Euro area as the full picture behind the public finances of many European countries became apparent. As a result many countries, such as Portugal and Ireland lined up for a bailout from the rest of the Eurozone as they found it harder and prohibitively expensive to borrow from the international markets. We take into consideration the development of CDS spreads of one such country, Greece, and of a Greek financial institution, the Alpha Bank, and use an ARMA-GARCH design to model the heteroskedasticity in both of these series. The input from a range of some important auxiliary tests is also taken into account.

The report has the following structure. Section two describes the data. On the other hand, the empirical analysis and interpretation of the results is conducted in section three. Finally, the last section concludes.

In our analysis, we employ data collected from Thompson Reuters’ Datastream on 5-year CDS spreads of Greece and Alpha Bank, an important Greek financial institution. The data we gathered cover the period from 1 January 2008 until 31 December 2010, and obviously the frequency of the data is daily. Table 1 provides a multitude of informative key descriptive statistics.

Table 1. Descriptive statistics of the 5 Year CDS spreads of (i) a sovereign, Greece, and (ii) a financial institution, Alpha Bank. All numbers are in basis points. | Spread_Greece| Spread_AlphaBank|

Mean| 298.419| 468.322|
Median| 162.36| 445.32|
Maximum| 979.72| 998.29|
Minimum| 21.9| 142.5|
Standard Deviation| 291.152| 270.977|
Skewness| 1.066| 0.372|
Kurtosis| 2.631| 1.709|
Observations| 784| 663|

The maximum spread during the period under consideration is reached at approx. 980 basis points for the sovereign and 200 basis points for Alpha Bank. Figure 1, which depicts the movement in time of both series, confirms the whooping several-hundred fold increase in the borrowing costs in just two years! Jarque-Bera tests on the normality of the distribution indicates that both series are not normal, although for Spread_Greece the test statistic is just barely over the critical value at a 5% significance level. A significantly lower kurtosis than 3 for Spread_AlphaBank points to a more rounded peaked and lighter tails than what is predicted under normality.

Figure 1. Daily 5-Year CDS spreads for Greece and Alpha Bank from 1 January 2008 until 31 December 2010.

Moreover, Figure 1 also suggests a high correlation between both spreads if one analyses the close co-movement of both series over time. The reason here might be that as the economic, financial and social crisis deteriorated in Greece, it also spilled over to the private financial sector, in the form of more toxic assets held by the banks, lower deposits resulting from bank runs etc. It can also be observed that the correlation has increased as the situation with the public finances has become more dire.

Empirical Analysis
We start our empirical analysis by checking the stationarity of both of our CDS spread series. In order to do just that, we employ an Augmented Dickey Fuller and a Phillips-Perron unit root test for both series. No matter the test we use, under the null hypothesis, the series are not stationary or contain a unit root. The test statistics that result out of these tests are provided in Table 2. For Spread_Greece, for example, the ADF test statistic (a linear trend is included here) the extremely high p-value indicates that we fail to reject the null hypothesis of the presence of a unit root. The same fate befalls on the CDS spread for our financial institution as well.

Given the presence of unit root in both of our series in their normal form, any regression analysis where...
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