The Norwegian Stock Market: - A Local Gaussian Perspective

In this thesis, using daily returns from 18 stocks, oil price, exchange rates and the main index of the Oslo Stock Exchange over a period of 5 years, we investigate how the Local Gaussian Correlation can be used to describe the change in the relationship between stocks and the market and how it can extend already established theory in finance. Topics covered in this thesis are; risk estimation by conventional risk measures and a method based on Local Gaussian Correlation, the Capital Asset Pricing Model (CAPM), copulas and GARCH as a description of volatility and as a description of the marginal distributions for copulas. Value at Risk and Expected Shortfall are well established risk measurements in finance. They are dependent on a good description for the distribution in the tail, which can be challenging. These measures only provide one single number as a description of the risk, this might be appealing, but does not really provide detailed information. By using the theory of CAPM there has been some attempt to describe the change in risk by using the so-called conditional moments of the observations. This approach might be biased, as the conditional moment fails to describe the constant correlation and variances of the Gaussian distribution. By rather using the local parameters found when calculating the Local Gaussian Correlation as a local description of the beta on our data, there seem to be higher risk in the upper tail and the lower than in the middle. However, what differs from the results found by the previously mentioned approach is that the risk in the upper tail seems to be higher than in the lower. This might be explained by very large gains for the stock market might be followed by a possible stock market downturn or even a crash (bubble), while negative values for the market is less likely to resolve in a sudden positive boost for the market