Welcome,

1.1 Background and Motivation

Traditionally, financial theory assumes that systematic risk remains constant over time. The Capital Asset Pricing Model aims to explain the expected return of an asset through a linear dependence on systematic risk, measured by beta, implying that sensitivity to market movements is stable across both downturns and upturns (Sharpe, 1964; Lintner, 1965). More recent research challenges this by suggesting a conditional relationship between beta and returns (Pettengill et al., 1995) and documenting downside risk and asymmetric responses to negative market returns (Ang and Chen, 2007).

The oil-dependent Norwegian stock market distinguishes Norway from many other European economies. DNB Asset Management (2020) estimates that the oil and gas sector makes up around 20% of the Norwegian equity universe, and Finanstilsynet (2022, p. 2) notes that "the Norwegian stock market is heavily exposed to the energy sector". Economies that are dependent on a commodity may be particularly susceptible to asymmetric or state-dependent systematic risk across different price regimes, and existing evidence shows that Norwegian stock returns respond positively to oil price shocks (Bjørnland, 2009; Park & Ratti, 2008).

To the best of current knowledge, there is little research that has examined whether oil price regimes affect the symmetry of systematic risk in the Norwegian stock market relative to broader European markets. This presents Norway as a natural case study for examining patterns of beta asymmetry across oil price regimes.

Understanding regime dependencies in systematic risk is important for portfolio risk management as well as for explaining past performance and behaviour in the Norwegian market. If Norwegian equities exhibit higher beta during periods of falling oil prices, this information can be used to model systematic risk more efficiently, based on oil price movements. This motivates the central research question of this thesis.

1.2 Research Questions and Hypotheses

This thesis aims to address the following question:

Does the Norwegian equity market's systematic risk relative to the European market differ across rising and falling oil price regimes?

The analysis is extended to three European equity markets, including Norway, Sweden, and France, to explore oil conditional systematic risks in markets with different energy profiles. Sweden is included as a net energy-importing economy, while France represents a European market with lower fossil-fuel dependence. The analysis also examines whether the estimated relationships are robust across data of different frequencies, namely daily, weekly, and monthly, and across two subperiods that capture major structural changes, the 2008 financial crisis and the 2014 oil price collapse.

We formulate the following testable hypotheses:

Hypothesis 1 (Existence of Oil Conditional Systematic Risk Asymmetry)
The interaction term between European market returns and the oil price direction dummy is statistically different from zero, implying that the systematic risk in the Norwegian equity market with respect to the European market differs across oil price regimes.

Hypothesis 2 (Direction of the Effect)
The conditional beta in regimes with falling or flat oil prices exceeds the conditional beta in rising regimes, reflecting an increase in the economic vulnerability of the Norwegian equity market when oil revenues decline.

Hypothesis 3 (Cross-Country Heterogeneity)
Oil conditional beta effects are significantly weaker for Sweden and France compared to Norway, providing evidence that the oil-dependent economy exhibits higher risk asymmetries.

Hypothesis 4 (Robustness)
The main oil conditional beta patterns for Norway are robust to (a) alternative data frequencies (weekly, monthly), (b) major structural periods (pre/post-2008, pre/post-2014), (c) alternative oil benchmarks (WTI versus Brent), and (d) oil volatility regimes rather than price directional regimes.

1.3 Main Findings and Contributions

The analysis shows clear statistical evidence that Norwegian equity market systematic risk is asymmetric across oil price regimes, while Sweden and France do not show similar patterns, indicating that oil dependence, not general European market dynamics, drives the asymmetry. The results are robust to alternative model specifications, data frequencies, oil benchmarks, and structural break periods, suggesting that they reflect genuine economic patterns rather than being the result of coincidences or noise in the data or model.

The thesis connects conditional beta models with the literature on oil dependence by including oil price direction in the risk modelling. Empirically, it shows clear evidence that systematic risk changes across oil price regimes in an oil-exporting economy, and that standard CAPM implementations can therefore misestimate Norwegian equity exposure during oil downturns (downside β = 1.0339 versus upside β = 0.8778), precisely when accurate risk assessment matters most.

1.4 Structure of the Thesis

The thesis is structured as follows. Chapter 2 provides an overview of relevant theoretical literature on the Capital Asset Pricing Model, conditional beta models, and the relationship between oil prices and equity returns. Chapter 3 explains the methodology used in the analysis, including data sources, model specifications, and empirical strategy. Chapter 4 presents descriptive statistics and preliminary analysis of the data, including summary statistics, correlation analysis, and stationarity tests. Chapter 5 presents the main empirical results from the conditional CAPM estimation, testing all four hypotheses. Chapter 6 extends the main results by conducting robustness checks across alternative model specifications, data frequencies, oil benchmarks, and structural break periods. Chapter 7 concludes, discusses the findings, limitations, and directions for future research.

The following literature review follows the progression from the traditional static Capital Asset Pricing Model to conditional beta frameworks, and then reviews the literature on the relationship between oil price shocks and stock markets in oil-exporting versus oil-importing economies. Together, these perspectives form the theoretical basis for the empirical analysis and motivate the conditional CAPM specifications and country choices used later in the thesis.

2.1 Foundations of the CAPM and the Stability of Beta

The Capital Asset Pricing Model is a foundational equation showing the linear relationship between the systematic risk of an asset and its expected return (Sharpe, 1964; Lintner, 1965). The systematic risk is measured by beta, which is the asset's covariance with the market portfolio divided by the variance of the market. Beta gives the fraction of the market risk premium that is added to the risk-free rate. The linear relationship implies that a higher beta gives a higher expected return for bearing more market risk. The model assumes that beta is constant and fully captures the systematic risk exposure of the asset.

Fama and MacBeth (1973) created a two-pass regression to test the relation between risk and return and found that higher betas generated higher average returns. In this thesis, this static CAPM provides the baseline specification against which conditional extensions are compared. Later research has extended the CAPM to include risk premia and betas that vary with information variables such as human capital, dividend yields, and default and term spreads, with evidence showing that systematic risk explains stock returns better when it is allowed to vary over time (Ferson & Harvey, 1991; Jagannathan & Wang, 1996). This idea of a beta that changes over time is developed further in later sections, where beta is allowed to vary across oil price regimes, but as a starting point, the standard CAPM can be written as:

where E[r_i,t − r_f,t] is the expected excess return on asset i, r_f,t is the risk-free rate, β_i is asset i's beta, and E[r_m,t − r_f,t] is the market risk premium.

The empirical models in Chapter 3 adopt this excess-return formulation and then relax the assumption of a single, constant beta. These assumptions were challenged when Fabozzi and Francis (1978) investigated the consistency of the single-index model parameters. They employed a random coefficients specification to the standard OLS model and found that changes to beta parameters generate heteroskedasticity and give unstable, sample-dependent intercepts, implying that the usual Ordinary Least Squares (OLS) estimates of systematic risk are inefficient, and that alpha takes on a different economic meaning. The study highlights the possibility that systematic risk changes over time or with structural changes, and motivates the use of models that allow for shifting coefficients. This provides a direct motivation for testing whether Norwegian systematic risk differs across oil price regimes, rather than assuming a single, stable beta.

2.2 Conditional Beta Models

A key study by Bollerslev, Engle, and Wooldridge (1988) shows that variation in the conditional covariance structure in asset returns implies variation in systematic risk as well. The study integrates a multivariate Generalized Autoregressive Conditional Heteroskedasticity framework with the CAPM model. Their model includes a conditional beta, defined as the ratio of conditional covariance to market variance. Their main finding is that the data strongly reject the CAPM with a constant beta. The conditional beta varies, especially during periods of market stress. They argue that investors form expectations from current market conditions, rather than historical averages, and that systematic relationships fluctuate with market states. Although this thesis does not estimate a full multivariate GARCH model, the conditional CAPM specifications build on the same idea that systematic risk should be allowed to depend on prevailing conditions, here captured by oil price regimes.

In a related study, Jagannathan and Wang (1996) propose a conditional CAPM where both the risk premium and beta vary over time and depend on human capital and business-cycle variables. The study shows that adding these conditional specifications in the CAPM explains returns across assets better than a static model with a single beta estimate. This provides theoretical support for testing oil-conditional beta patterns, as there is an apparent reason to allow for time-varying relationships when modelling systematic risk. The conditional CAPM used in this thesis follows the same logic, but uses oil price direction as the conditioning variable instead of macroeconomic state variables.

Feder-Sempach, Szczepocki, and Dębski (2023) examined the systematic risk of 239 U.S. blue-chip companies over 31 years, from 1990 to 2021. They compared the linear Sharpe model with several dynamic versions of the CAPM, estimated using the Kalman filter, which allows beta to be time-varying, for example through mean reversion. The Kalman filter models produced the smallest forecast errors, and they concluded that beta is not constant over long horizons, and that allowing for beta variation in models leads to more accurate risk calculations. This provides further support that static models might fail to capture the structural changes in systematic risk that occur during different market regimes. In the empirical analysis that follows, a simpler dummy-based conditional CAPM is used instead of a full Kalman filter approach, but with the same objective of capturing systematic risk that changes across regimes.

2.3 Asymmetric Beta and State-Dependent Risk

Unconditional testing was challenged by Pettengill, Sundaram, and Mathur (1995), who argue that weak beta–return correlations can arise when studies pool observations across different market states. By separating observations into periods with positive versus negative market excess returns, they show a conditional beta–return relationship, where high-beta assets tend to outperform when market excess returns are positive and underperform when they are negative. This state-dependent pattern can be masked in unconditional models that average across market conditions and do not condition on market regimes. The conditional modelling strategy in this thesis follows the same idea but uses oil price regimes, rather than the sign of the market risk premium, as the conditioning state variable.

Related evidence on asymmetries in financial markets is provided by Longin and Solnik (2002), who study international equity market co-movements and find that correlations increase during extreme downturns using extreme value theory. Following this logic, systematic risk may also vary across economic regimes, and for an oil-exporting economy like Norway, oil price direction may be a particularly relevant state variable. This motivates the hypothesis that Norwegian beta may be higher in "bad" oil states (falling oil prices) than in "good" oil states (rising oil prices). A similar pattern for U.S. equity portfolios is documented by Ang and Chen (2002). They show how correlation is higher when both the market and portfolio are experiencing a downturn, referred to as downside correlations, compared to when both are experiencing an upturn, or upside correlation. Traditionally defensive sectors are particularly affected by this. While the energy sector is typically cyclical, its dominance in the Norwegian market creates a unique risk profile where systematic exposure is asymmetric during commodity price shocks. These studies support the idea of asymmetric movements in market states and are consistent with the oil price conditional modelling of beta used in this thesis, where the focus is on whether the Norwegian market is more exposed in downside oil regimes.

Baker and Wurgler (2006) show that investor sentiment has an asymmetric effect on stock returns. In their study, they argue that the cross-section of future returns on stocks that are difficult to value, such as small, young, and unprofitable stocks with little arbitrage opportunity, are more sensitive to shifts in investor sentiment. This leads to lower returns later when sentiment is high, and the opposite when sentiment is low, meaning they earn higher returns later. This creates a theoretical foundation for explaining oil-conditional risk with behavioural finance, as an oil price shift may trigger a sentiment shift in investors' view of the Norwegian market's risk profile, contributing to asymmetric beta patterns. While sentiment is not explicitly modelled in this thesis, these behavioural mechanisms provide one possible interpretation of any asymmetry found in Norwegian systematic risk across oil regimes.

2.4 Oil–Equity Market Relationships

A study focusing on the Norwegian economy's relationship between oil and stock prices (Bjørnland, 2009) found that an increase in oil price has a positive effect on real stock returns, with a 10% increase in oil prices leading to about a 2.5% increase in the Norwegian market index. The study argues that this is due to the net effect of two opposing mechanisms. First, higher oil prices increase national income, demand, and overall activity in the Norwegian economy, leading to higher market valuations. Second, higher oil prices can reduce the overall demand for other exports than oil, as oil-importing economies experience lower growth. Over the sample period, the positive increase in stock prices shows that the first mechanism dominates the net effect in Norway's economy. These findings motivate treating Norway as a natural case study of an oil-dependent equity market and motivate examining not only the level of returns, as in Bjørnland (2009), but also whether systematic risk is conditional on oil price regimes.

More broadly, Sadorsky (1999) documents that oil prices and volatility have significant effects on stock returns, and this is reinforced in the study where Basher and Sadorsky (2006) show that oil price risk is an important factor in explaining returns of emerging stock markets.

Degiannakis, Filis, and Arora (2018) review the oil and stock market relationships documented in the literature and conclude that studies show changes in oil price volatility are reflected in stock market volatility, and that information from equity markets can help improve forecasts of both oil prices and their volatility. These studies add to the evidence that risks related to oil are relevant for equity returns and motivate studying similar effects on systematic risk, particularly in oil-exporting economies such as Norway.

Park and Ratti's (2008) study of the U.S. and 13 European countries, including Norway, from 1986 to 2005, found that many oil-importing European countries experienced a negative reaction in the stock market to increases in oil prices, as well as to increases in oil price volatility. The negative correlation is attributed to higher production costs and higher interest rates used to combat inflation. On the other hand, Norway showed a significant positive response to oil price increases. They found some evidence of asymmetric effects of positive and negative oil price shocks on the stock market in Norway and the U.S., but little evidence elsewhere. Apergis and Miller (2009) apply a structural VAR framework to distinguish different types of oil shocks and find that the effects on stock returns are generally small in magnitude and heterogeneous across countries, suggesting that oil and equity markets remain only partially integrated. Taken together, these studies support the hypothesis that oil-exporting and oil-importing countries differ systematically in how their equity markets respond to oil shocks, which motivates the comparison between Norway, Sweden, and France in this thesis.

Kilian and Park (2009) show that how U.S. stocks respond to oil price shocks depends on the cause of the shock. They decompose the oil price shocks into three different categories. The first category, global supply shocks, is shown to be much less important than the two following, aggregate demand shocks and oil-specific demand shocks. This critically recognises that not all changes in oil prices are alike and reinforces the idea that stock markets of oil-dependent economies may exhibit behaviours based on the underlying oil price regime. Although shocks are not decomposed in this thesis, the empirical design captures regime dependence by splitting the sample into rising and falling oil price days.

Together, these studies suggest that the impact of oil price changes on stock markets depends on factors such as the direction of the price change, the underlying cause of the price shock, and whether an economy is a net oil importer or exporter. For Norway, the evidence points to oil price increases being positive for stock returns, in contrast to many oil-importing European economies. The existing studies have focused mainly on the level of stock returns, rather than on systematic risk, and this gap motivates the present thesis.

2.5 Research Gap and Theoretical Motivation

In summary, the literature reveals two key developments that have not yet been directly connected. First, systematic risk is not necessarily constant over time and can vary across economic states, as shown by conditional beta models and time-varying CAPM specifications. Second, stock returns in oil-dependent economies react asymmetrically to oil price movements, and these reactions differ between oil exporters and oil importers.

This thesis aims to address this gap by combining the conditional beta logic of Pettengill et al. (1995) with the asymmetric oil price insights from Park and Ratti (2008) and Bjørnland (2009) to test for oil-conditional systematic risk in the Norwegian market. The empirical strategy allows Norwegian beta with respect to a European market proxy to differ between rising and falling oil price regimes, and compares this pattern with Sweden and France, which are oil-importing economies. Together, these studies motivate the construction of a conditional CAPM where systematic risk is allowed to vary across oil price regimes, and provide the theoretical basis for the hypotheses and model specifications in Chapter 3.

The following chapter presents the econometric framework used to test hypotheses H1–H4, formulated in Chapter 1, using four main model specifications. The starting point, a baseline CAPM, is extended to a conditional CAPM where oil dependence motivates the inclusion of oil price direction. A two-factor model with a separate oil return factor is then used to test for direct oil effects, and subsample specifications are estimated to examine stability across major regime shifts. All empirical analyses are implemented in Python, using the pandas and statsmodels libraries to perform data cleaning, construction of variables, estimation of the regressions, and to produce results and plots. Then, diagnostic checks and robustness tests used to validate the results are described. Finally, a discussion of the use of AI in the thesis is included.

3.1 Baseline Regression Model (Static CAPM)

The empirical analysis begins with the standard CAPM. This model assumes systematic risk remains constant over time and provides the starting point for comparing the oil-conditional results. The baseline regression is:

where r_i,t − r_f,t is the realized excess return on country i's equity index at time t, and r_m,t − r_f,t is the realized market excess return, with r_m,t proxied by the European market index (STOXX Europe 600). α_i is the intercept (Jensen's alpha) and should be zero if the CAPM holds. β_i measures systematic risk relative to this market proxy and is expected to be positive for all countries tested, as they are European economies exposed to common European market conditions. ε_i,t is an error term capturing idiosyncratic shocks. In expectation, the CAPM implies E[r_i,t − r_f,t] = β_i · E[r_m,t − r_f,t] when α_i = 0.

The baseline CAPM relies on the standard OLS (Ordinary Least Squares) assumptions: linearity in parameters, exogeneity of regressors, no perfect multicollinearity, homoskedastic errors, and no serial correlation in the residuals. These assumptions may be violated in financial return data, but they still motivate the use of OLS as a starting point. In Section 4.5, the econometric challenges of heteroskedasticity and autocorrelation are addressed by applying Newey–West heteroskedasticity and autocorrelation consistent (HAC) standard errors, and a set of diagnostic tests is discussed to assess whether the remaining regression assumptions are satisfied.

3.2 Conditional CAPM

The core specification, which tests whether systematic risk varies with oil price regimes, extends the static CAPM by incorporating an oil-direction dummy and its interaction with market returns:

where:

In words, D^oil_t is a dummy variable equal to 1 if the oil price increased on day t (positive log return), and 0 otherwise (zero or negative log return). The increase or decrease is calculated using the log return of the oil spot price. The term D^oil_t · R_EU,t is the interaction term that captures the oil-conditional sensitivity of market i to the European market. This interaction term allows systematic risk to vary across different oil price regimes, creating state-dependent beta relationships. When oil prices are non-positive (flat or falling, D^oil_t = 0), the systematic risk equals β_1,i. When oil prices are rising (D^oil_t = 1), the systematic risk becomes β_1,i + β_3,i. The coefficient β_3,i measures the difference in systematic risk across oil price regimes.

For an oil-exporting economy such as Norway, rising oil prices generally signal favourable economic conditions through higher national income, increased demand, and stronger government finances, whereas falling oil prices are associated with weaker revenues, reduced economic activity, and heightened uncertainty. The dummy D^oil_t therefore captures transitions between economically “good” and “bad” oil states in a way that is consistent with the wealth and demand channels documented in the literature.

The level-shift parameter β_2,i captures the differential average returns between oil regimes, independent of European market movements. This coefficient measures the direct effect of oil regimes on domestic market performance through channels such as wealth effects, aggregate demand shifts, or changes in market sentiment. For oil-exporting countries like Norway, economic theory predicts β_2,i > 0, indicating higher average returns during rising oil price periods due to positive macroeconomic effects.

The state-dependent beta coefficients provide direct measures of systematic risk across oil regimes:

where β^DOWN_i represents systematic risk during non-positive (flat or falling) oil price periods and β^UP_i represents systematic risk during rising oil price periods.

Based on the theoretical framework established in Chapter 2, which links oil dependence to systematic risk patterns, the expected value of β_3,i varies across countries according to their oil dependence. For Norway, an oil-exporting economy, we expect β_3,i < 0, implying that β^UP_i < β^DOWN_i; that is, systematic risk is higher when oil prices fall and lower when oil prices rise, consistent with the wealth and demand mechanisms documented in Bjørnland (2009). For Sweden and France, as oil-importing economies, the expected value of β_3,i is close to zero, indicating minimal oil conditional systematic risk effects, consistent with their more diversified sector structures and less direct oil exposure in their equity indices.

3.3 Conditional Two-Factor CAPM with Direct Oil Returns

In the final model specification, a two-factor model with direct oil effects is used to separate direct oil effects from conditional systematic risk. This specification is estimated only for the Norwegian market, where direct oil exposure is most relevant:

The specification is otherwise the same as in Section 3.2, but includes the additional term γ R_OIL,t to capture the direct impact of oil returns. The coefficient γ measures the marginal effect of oil returns on Norwegian equity returns while holding European market movements constant, allowing the model to distinguish between the direct impact of oil price shocks on the Norwegian market and the conditional effect where the sensitivity to European market returns changes across oil price regimes. Including R_OIL,t therefore provides a more complete characterisation of how oil prices affect systematic risk.

3.4 Subsample Regressions

The subsample analysis uses the conditional regression model specified in Section 3.2 and splits the full sample into subsamples around major regime shifts. First, the 2008 financial crisis is examined by splitting the data into a pre-2008 period and a post-2008 period, with the split at 1 January 2009. Second, the 2014 oil price collapse is examined by splitting the data into a pre-2014 period and a post-2014 period, with the split at 1 July 2014. Third, the COVID-19 pandemic is examined by splitting the data into a pre-COVID period and a post-COVID period, with the split at 1 March 2020. All subsample regressions are estimated using daily frequency data only. This design tests the robustness of the hypotheses across major economic and health-related regime shifts.

3.5 Estimation Details

All regressions use excess log returns based on prices in EUR, where returns are calculated as log price changes minus the risk-free rate, as defined in detail in Chapter 4. Newey–West heteroskedasticity and autocorrelation consistent (HAC) standard errors are employed to provide robust standard errors that remain valid under violations of the classical OLS assumptions (Newey & West, 1987).

These statistical challenges are common in daily financial return data, as equity returns typically exhibit both conditional heteroskedasticity and serial correlation. Using HAC corrections ensures reliable statistical inference even when the residuals display volatility clustering and serial dependence, which would otherwise render standard t-tests and F-tests invalid. To confirm stationarity, Augmented Dickey–Fuller (ADF) and KPSS stationarity tests are conducted and reported in Appendix A (Dickey Fuller, 1979).

The baseline analysis uses daily return data to maximise the sample size and the statistical power for detecting oil conditional effects. To check robustness, weekly and monthly return data are included to reduce microstructure noise and show systematic risk patterns without the short-term noise found in daily returns. Multicollinearity concerns are limited due to the simple structure of the model. Variance inflation factors and correlation diagnostics will be inspected to ensure that the dummy and interaction terms do not suffer from problematic multicollinearity.

The chosen linear interaction model follows directly from the theoretical setup of a regime-dependent CAPM. By allowing systematic risk coefficients to vary across oil price regimes, the specification yields economically intuitive parameter interpretations. To ensure that this functional form is appropriate, linearity assumptions will be assessed using the Ramsey RESET test (Ramsey, 1969) and other standard diagnostic tests, including tests for omitted variables, nonlinearity, and residual misspecification.

3.6 Diagnostic Tests

The following diagnostic tests are applied to ensure that the estimated parameters are reliable and robust: unit root tests (ADF and KPSS) to confirm that all return series used in regressions are stationary, serial correlation tests (Ljung–Box, Breusch–Godfrey) to assess whether residuals exhibit autocorrelation beyond what HAC can correct for, heteroskedasticity tests (White test, Autoregressive Conditional Heteroskedasticity (ARCH) effects) to detect nonlinear volatility patterns in residuals, normality tests (Jarque–Bera) to evaluate whether residual distributions deviate from normality, and specification tests (Ramsey RESET) to identify potential omitted nonlinearities or functional form concerns. A test for structural breaks, defined in Section 3.5, is used to detect shifts around economically meaningful periods, namely the 2008 financial crisis and the 2014 oil price collapse. The results of the diagnostic tests are reported in Appendix A, while the structural break analysis is presented in Section 5.4.

3.7 Robustness Specifications

To assess stability and validate the main empirical findings, several robustness specifications are implemented:

i) Alternative oil benchmarks: Brent crude is replaced with West Texas Intermediate (WTI) to test whether the results depend on the specific oil price measure. Similar findings across Brent and WTI suggest that the patterns are not driven solely by North Sea oil pricing.

ii) Alternative return frequencies: The models are re-estimated using weekly and monthly returns. Weekly data reduces microstructure noise and very short-term trading effects while retaining sufficient observations to detect regime-dependent systematic risk.

iii) Oil volatility regimes: A volatility-based dummy is constructed using squared oil returns relative to long-run variance to test whether systematic risk varies with oil-market uncertainty rather than direction. Formally, D^vol_t = 1 if R²_oil,t > Var(R_oil), and D^vol_t = 0 otherwise.

iv) Subperiod regressions: Separate regressions are run on subsamples before and after major economic events, including the 2008 global financial crisis, the 2014 oil price collapse, and the COVID-19 pandemic. This is done using the conditional model described in Section 3.4 to examine whether the oil-conditional relationship is stable over time.

v) Alternative European market proxies: The STOXX Europe 600 is replaced with an alternative benchmark, the Euro Stoxx 50, to test whether the estimated betas depend on the specific proxy for the European market.

Collectively, these robustness checks help ensure that the main results reflect genuine oil conditional systematic risk patterns, rather than being driven by specific modelling choices such as the oil benchmark, regime definition, sample period, or return frequency.

3.8 Use of Generative AI Tools

For transparency, this section documents how generative AI tools were used throughout the work on this thesis. Claude was used to assist in writing and debugging code in Python and creating the LaTeX code for the thesis document. For clarifying concepts, checking the consistency of notations and assumptions in the paper, and improving writing, ChatGPT was used. All suggestions generated by AI have been reviewed and checked thoroughly before being implemented. AI has only been used as a complementary tool, and the final result is based on independent assessments.

This chapter describes the data used to estimate the econometric models in Chapter 3. It outlines how the data are sourced and why the specific indices are chosen, how return and regime variables are constructed, and the summary statistics of the dataset. Bloomberg tickers are noted in parentheses where needed throughout the chapter.

4.1 Data Sources and Sample Period

The sample period covers 25 years, from 1 January 1999 to 31 December 2024. All data are obtained from the Bloomberg Terminal, with prices downloaded directly in EUR. The start date is chosen based on the availability of consistent data for all indices, and the length of the period provides enough observations across several oil price cycles, including the 2008 global financial crisis and the 2014 oil price collapse, to test the persistence of the relationships during periods of market and oil market stress.

To put the analysis period in context, Figure 4.1 shows cumulative returns for the Norwegian, Swedish, and French equity indices, the European market proxy, and Brent oil prices from 1999 to 2024. Over this period, the equity indices tend to track each other closely, whereas oil prices move more sharply. Several episodes of market stress are visible.

Only days when all markets are open at the same time are kept, so that systematic risk estimates are not affected by different holiday calendars across countries, which resulted in a final sample of 6,418 daily observations. These dropped days account for fewer than 0.5% of the potential sample. Daily data use closing prices (PXLAST), weekly data are based on Friday closes, and monthly data use the last business day of each month.

Equity Indices

Sweden and France are included as comparison markets because they are oil-importing European economies with developed equity markets but much lower direct oil exposure than Norway. The national equity markets are represented by indices with wide market coverage. These indices are used as country-level market portfolios in the CAPM and conditional CAPM regressions.

• Norway: Oslo Børs All-Share Index (OSEBX Index)
• Sweden: OMX Stockholm All-Share Price Index (OMXSPI Index)
• France: Société des Bourses Françaises 120 Index (SBF 120 Index)

European Market Proxy

In practice, the "true" market portfolio that includes every available asset cannot be observed. This thesis therefore uses the STOXX Europe 600 (SXXP) as a proxy for the European equity market. The index has a fixed number of 600 components and provides broad and diversified coverage across 17 European countries and 11 industries in Europe's developed markets, representing nearly 90% of the underlying investable market (STOXX Ltd., 2025a). As a robustness check, the EURO STOXX 50 (SX5E) is also used as an alternative market proxy, focusing on the largest, most traded companies in the Eurozone across 50 European companies weighted by free-float market capitalisation (STOXX Ltd., 2025b).

Oil Prices

Brent Crude (CO1 Comdty), which reflects North Sea oil production and is the main benchmark for European crude, is the primary oil price measure. WTI Crude (CL1 Comdty) is used in a robustness analysis.

Risk-Free Rate

The risk-free rate used to compute excess returns in all regressions is the 3-month EURIBOR (EUR003M Index). This rate reflects short-term euro funding conditions and is a common choice when working with returns measured in euros.

4.2 Variable Construction

For each equity index and oil benchmark, daily log returns are computed from the price time series. All returns are downloaded and expressed in EUR. Excess returns subtract the daily risk-free rate:

The oil regime dummy variable classifies each day into a rising or falling/flat oil state based on log oil returns:

For robustness tests, an oil volatility dummy is also constructed, where D^vol_t = 1 if r²_oil,t > Var(r_oil), and 0 otherwise. The long-run variance Var(r_oil) is computed as the sample variance over the full 25-year period.

4.3 Summary Statistics

Table 4.1 reports mean excess returns, standard deviations, and higher-moment characteristics for the excess returns across all series.

Table 4.1: Summary statistics for daily excess returns (1999–2024)

Notes: Daily excess log returns in EUR. Excess returns computed as log returns minus the 3-month EURIBOR. N = number of observations. Skewness and Kurtosis are sample skewness and excess kurtosis.

The Norwegian equity index (OSEBX) exhibits a daily mean excess return of 0.0238% (approximately 6.0% annualized) with a daily volatility of 1.567% (24.9% annualized). The Swedish index (OMXSPI) shows a slightly lower daily mean of 0.0210% (about 5.3% annualized) and volatility of 1.500% (24.0% annualized). The French index (SBF120) displays the lowest mean among the three, at 0.0099% (around 2.5% annualized) with a volatility of 1.329% (21.1% annualized).

The broad European market proxy (STOXX Europe 600) has the lowest mean excess return at 0.0083% daily (about 2.1% annualized) and the lowest volatility at 1.170% (18.6% annualized), consistent with a diversified benchmark. Brent crude has a mean daily return of 0.0288% with a volatility of 2.300%, while WTI has a mean of 0.0509% and a volatility of 2.574%. Both series are substantially more volatile than the equity indices.

All equity return series are negatively skewed (from about −0.19 for Sweden to −0.76 for Norway), meaning large negative moves are more common than large positive moves. Excess kurtosis is high for all equity indices (around 4.5–7.3), and even higher for oil (about 11 for Brent and 17 for WTI), indicating fat tails and a higher probability of extreme returns.

For the oil regime variable, the sample includes 3,446 days with positive oil returns and 3,176 days with flat or negative oil returns. Figure 4.2 visualizes this distribution.

4.4 Correlation Analysis

Figure 4.3 presents the correlation matrix of all variables. The key finding is that Norwegian equity returns show higher correlation with Brent oil (0.375) compared to Sweden (0.206), France (0.217), and the European index (0.240). This provides evidence that oil prices affect Norwegian equities differently than other European economies.

4.5 Stationarity and Normality of Key Return Series

This section reports basic time series tests for the main return series used in the analysis. It is important to check that the data are suitable for regression, especially that they are stationary and that their distributional features are understood.

Table 4.2: Stationarity and Normality Tests for Key Return Series

Note: ADF null: unit root (reject if p < 0.05). JB null: normality (reject if p < 0.05).

The Augmented Dickey–Fuller (ADF) test strongly rejects the null hypothesis of a unit root for all series (p = 0.0000), confirming that the daily log return series are stationary and can be used directly in the regressions. The Jarque–Bera test rejects normality for all series, reflecting the well-known fact that financial returns have heavy tails and more extreme observations than a normal distribution would predict. These departures from normality, combined with the likelihood of heteroskedasticity and autocorrelation in daily returns, motivate the use of Newey–West HAC standard errors throughout.

This section presents the main empirical findings from the conditional CAPM estimation. The analysis tests whether systematic risk in the Norwegian equity market varies across oil price regimes.

5.1 Baseline CAPM: Systematic Risk Across Countries

The standard Capital Asset Pricing Model is first estimated for Norway, Sweden, and France by regressing each country's excess equity returns on the STOXX Europe 600 excess return to isolate systematic risk. Results in Table 5.1 show that the market beta for Norway is 0.9904 (SE: 0.0295), meaning it moves very close to the European market. For Sweden, the market beta is higher at 1.1108 (SE: 0.0165), suggesting greater sensitivity to European market swings. France has a beta of 1.0890 (SE: 0.0066), which lies between Norway and Sweden, but with the smallest standard error, reflecting very strong links to the European market.

Table 5.1: Baseline CAPM for Norway, Sweden and France

Notes: Dependent variable is daily excess log return on each country's equity index in EUR. Explanatory variable is daily excess log return on STOXX Europe 600 (SXXP). Newey–West HAC standard errors (10 lags) in parentheses. *** significant at the 1% level.

R-squared values show clear differences in how strongly each national market is linked to the broad European market. For France, an R² of 0.922 means that about 92.2% of its return variation is explained by European market movements, compared with 75.4% for Sweden and 55.2% for Norway. The lower R² for Norway suggests that Norwegian equities are more influenced by other, possibly oil-related, factors beyond the European market. All estimated alphas are close to zero, indicating that the CAPM captures most of the systematic return variation.

5.2 Conditional CAPM: Oil-Driven Asymmetric Beta

Before interpreting the conditional CAPM results, Figure 5.1 presents four diagnostic plots for the conditional CAPM for Norway. The residuals over time are centred around zero with no clear trend, although periods of higher volatility appear around major shocks. The Q–Q plot shows that residuals are close to the normal line in the middle but deviate in the tails, meaning there are more extreme values than a normal distribution would predict, which is typical for daily financial returns. The Residuals vs Fitted Values plot shows two clusters for the two oil regimes, with residuals scattered around zero and no clear cone shape, suggesting that heteroskedasticity is not severe. Overall, these diagnostics indicate that the model is reasonably well specified.

Table 5.2 reports the results from the conditional CAPM, and Table 5.3 and Figure 5.2 show the betas for each oil regime.

Table 5.2: Conditional CAPM — r_i = α + β₁r_EU + β₂D^oil + β₃(D^oil · r_EU) + ε

Notes: Dependent variable is daily excess log return on each country's equity index in EUR. Newey–West HAC standard errors (10 lags) in parentheses. *** significant at the 1% level.

Table 5.3: Regime-Specific Betas from Conditional CAPM

Notes: β^DOWN is systematic risk when oil prices are falling or flat; β^UP is systematic risk when oil prices are rising. Newey–West HAC standard errors (10 lags) in parentheses.

For Norway, β₃ = −0.1561 (SE: 0.0398, t = −3.92, p < 0.001) is statistically significant. When oil declines, Norwegian market beta is β^DOWN = 1.0339 (SE: 0.0380), and when oil rises, it falls to β^UP = 0.8778 (SE: 0.0298). The difference of 0.1561 represents roughly a 15% reduction in systematic risk during periods of rising oil prices. Figure 5.3 provides visual confirmation through a scatter plot of Norwegian versus European returns, with regression lines fitted to each regime illustrating the asymmetric beta pattern.

For Sweden and France, there is no meaningful oil conditional change in systematic risk. For Sweden, β₃ = −0.0159 (SE: 0.0218, t = −0.73, p = 0.47), and for France, β₃ = 0.0142 (SE: 0.0115, t = 1.24, p = 0.22); both are statistically insignificant. The regime-specific betas are almost the same for Sweden [β^DOWN = 1.1199 and β^UP = 1.1040], and for France [β^DOWN = 1.0835 and β^UP = 1.0976].

For Norway, there is a slight improvement in fit with the conditional CAPM compared with the static CAPM (R² increases from 0.5516 to 0.5711), suggesting that oil price direction adds useful information. For Sweden and France, R² changes very little, consistent with oil being much less important for these markets. Overall, the results show that oil price direction matters for systematic risk in Norway, but not in Sweden or France, supporting the idea that oil dependence drives a special beta pattern.

5.2.1 Residual Diagnostics for the Norwegian Conditional CAPM

The Ljung–Box test (lag 10) strongly rejects the null of no serial correlation, and the White test rejects the null of homoskedasticity. This means that the residuals show both autocorrelation and heteroskedasticity, which is common in daily financial return data. The Jarque–Bera test also rejects normality, consistent with the fat tails and extreme observations seen in the summary statistics.

Because of these features, the model is estimated with Newey–West HAC standard errors, which correct for autocorrelation and heteroskedasticity and make inference more reliable. The RESET test rejects the null of correct functional form, suggesting that there may be some nonlinearity or omitted variables not captured by the conditional CAPM. However, the combination of Newey–West HAC standard errors, robustness checks, and subsample analyses indicates that the main conclusions about oil-conditional systematic risk for Norway are not driven by these residual patterns.

5.3 Conditional Two-Factor CAPM with Direct Oil Returns

Table 5.4 reports the two-factor model estimates for Norway. The direct oil coefficient is γ = 0.1423 (SE: 0.0096, p < 0.001). This means that, after controlling for the European market and the oil interaction term, higher oil returns are positively associated with Norwegian equity returns. The important point is that the conditional coefficient β₃ = −0.1313 remains highly significant. The R² of 0.5956 confirms that the main source of explanatory power comes from the regime-dependent beta rather than the direct oil factor.

Table 5.4: Two-Factor Conditional Model (Norway)

Notes: Dependent variable is daily excess log return on OSEBX in EUR. Explanatory variables are excess return on STOXX Europe 600, excess return on Brent crude oil, and an interaction term between the oil-regime dummy and European market return. Newey–West HAC standard errors (10 lags) in parentheses.

When comparing the Conditional Two-Factor CAPM results across the three countries, Table 5.5 shows that Norway is distinctly different from Sweden and France. Norway's β₃ = −0.1488 is statistically significant, while Sweden (β₃ = −0.0141) and France (β₃ = 0.0162) show no significant β₃. Additionally, Norway's direct oil coefficient β_oil = 0.0987 (SE: 0.0195, p < 0.001) is notably stronger than Sweden (0.0108) and France (0.0254), confirming that the asymmetric beta pattern is specific to Norway and not a general European phenomenon.

Table 5.5: Conditional Two-Factor Model — All Countries

Notes: Newey–West HAC standard errors (10 lags) in parentheses. *** significant at the 1% level.

5.4 Subsample Stability

The conditional CAPM is re-estimated across six subsamples: pre- and post-2008, pre- and post-2014, and pre- and post-COVID-19. Tables 5.6, 5.7, and 5.8 report the results from the separate regressions.

Table 5.6: Subsample Analysis — Pre/Post 2008 Financial Crisis

Notes: Conditional CAPM for Norway split around the 2008 financial crisis (split at 1 January 2009). Newey–West HAC standard errors (10 lags) in parentheses.

Table 5.7: Subsample Analysis — Pre/Post Oil Price Collapse (2014)

Notes: Conditional CAPM for Norway split around the 2014 oil price collapse (split at 1 July 2014). Newey–West HAC standard errors (10 lags) in parentheses.

Table 5.8: Subsample Analysis — Pre/Post COVID-19 Pandemic

Notes: Conditional CAPM for Norway split around the COVID-19 pandemic (split at 1 March 2020). Newey–West HAC standard errors (10 lags) in parentheses.

Table 5.9: Subsample Regime Betas

Notes: β^DOWN is systematic risk when oil prices are falling or flat; β^UP is systematic risk when oil prices are rising. Newey–West HAC standard errors (10 lags) in parentheses.

Figure 5.4 shows these estimates. The narrow range (−0.1918 to −0.1140) around the full-sample estimate of −0.1561 demonstrates remarkable consistency across diverse market conditions. This temporal stability strongly supports Hypothesis 4, confirming robustness across structural break periods.

5.5 Hypothesis Evaluation

The empirical results support all four hypotheses. Hypothesis 1 is confirmed, as Norway's interaction term β₃ is statistically significant, indicating that systematic risk varies with oil price direction. Hypothesis 2 is supported because Norwegian systematic risk is higher during oil declines than during oil rises. Hypothesis 3 is strongly supported through the cross-country comparison, where Sweden and France exhibit statistically insignificant β₃, confirming that oil conditional systematic risk is unique to Norway. Specifically, for these control markets, we fail to reject the null hypothesis of systematic risk symmetry, indicating that their market beta remains statistically constant regardless of oil price direction. Hypothesis 4 is supported by subsample regressions where β₃ remains negative and significant, and further by the robustness checks in Chapter 6, showing that the main results hold across alternative specifications.

Several robustness checks are conducted to evaluate whether the main results remain stable across alternative modelling choices, as defined in Chapter 3.

Table 6.1: Robustness — Oil-Conditional Coefficient Across Specifications

Notes: Each row reports β₃ under an alternative choice of oil benchmark, data frequency, or market proxy. P-values refer to the test of β₃ = 0.

6.1 Alternative Oil Benchmark: WTI vs. Brent

Brent crude is the primary global oil benchmark, but we verify that results are not driven by this choice, using West Texas Intermediate (WTI) for the oil direction dummy. Table 6.2 shows β₃ = −0.1209 (SE: 0.0410), compared to baseline Brent β₃ = −0.1561. While the WTI estimate is about 23% smaller — likely because WTI is more volatile and represents a different type of crude oil than Brent — it is still clearly significant.

Table 6.2: Robustness — WTI vs. Brent Oil

Notes: β₃ measures how the sensitivity to the European market changes between rising and falling oil price days. Baseline uses Brent front-month futures (CO1); alternative uses WTI front-month futures (CL1). P-values refer to the test of β₃ = 0.

6.2 Frequency Robustness: Weekly and Monthly Returns

To check whether the pattern is present at other data frequencies, the conditional CAPM is re-estimated using weekly and monthly returns. Weekly returns show a smaller oil-conditional coefficient, β₃ = −0.0836, which remains negative but is only borderline significant (p = 0.051). Monthly returns yield a larger estimate in magnitude, β₃ = −0.2040, which is statistically significant at the 5% level (p = 0.018).

With fewer observations (1,281 weekly and 299 monthly versus 6,418 daily), standard errors naturally widen. The key result is that β₃ is negative at all frequencies, with the clearest evidence for oil-conditional systematic risk in the daily and monthly specifications.

Table 6.3: Robustness — Weekly and Monthly Data

Notes: β₃ for Norway when the conditional CAPM is estimated at daily, weekly, and monthly frequencies. N is the number of observations. P-values refer to the test of β₃ = 0.

6.3 Market Proxy: Euro STOXX 50 vs. STOXX 600

Table 6.4 reports results using the narrow Euro STOXX 50 as the market proxy instead of the broad STOXX Europe 600. The β₃ estimate is very close to the baseline (β₃ = −0.1462, SE: 0.0368, t = −3.97, p < 0.001). The result is robust to the alternative market index, confirming that oil conditional systematic risk is not driven by the choice of European benchmark.

Table 6.4: Robustness — Alternative Market Proxies

Notes: β₃ for Norway estimated with two different European market proxies. R² is the coefficient of determination for each specification.

6.4 Joint Direction and Volatility Model

To assess whether oil-price direction and oil-price volatility act as competing or distinct mechanisms, we extend the conditional CAPM by including both regime indicators simultaneously:

Table 6.5: Joint Test — Direction and Volatility Dummies (Norway, Daily)

Notes: Conditional CAPM with both oil-direction and oil-volatility dummies for Norway. Dependent variable is daily excess log return on OSEBX in EUR. SE denotes Newey–West HAC standard errors (10 lags). *** significant at the 1% level.

Both interaction terms are significant and have opposite signs. The direction interaction β^dir₃ = −0.1360 (p = 0.0005) implies a lower market beta when oil returns are positive, falling from 0.9658 to about 0.8298 (roughly 14%). The volatility interaction β^vol₃ = 0.1362 (p = 0.0028) implies a higher market beta on high-volatility days, rising from 0.9658 to about 1.1020.

Compared to the single-dummy models, both effects shrink slightly in the joint regression — the direction effect from −0.1561 to −0.1360 (about 13%) and the volatility effect from 0.1637 to 0.1362 (about 17%) — suggesting the two dummies capture mostly different variation in systematic risk. When both dummies are active simultaneously (11.62% of trading days), the two effects almost cancel out. The joint model fits better than the unconditional CAPM (R² = 0.5738 versus 0.5516), confirming that both direction and volatility contribute independently to conditional systematic risk.

6.5 Robustness Summary

The robustness tests show that the negative asymmetric beta in oil-dependent Norway is not driven by any single model choice. All main specifications produce negative β₃ estimates, except the volatility dummy, which tests a different mechanism. The figure below summarises β₃ across all specifications.

7.1 Summary of Main Findings

This thesis tested whether oil price changes affect the systematic risk of the Norwegian equity market relative to Europe. The analysis reveals that Norwegian systematic risk exhibits significant asymmetry: β = 1.0339 during oil declines versus β = 0.878 during oil rises, representing a 0.15 reduction in systematic risk during oil price rises. The oil conditional systematic risk is unique to the oil-dependent economy, compared to the control countries Sweden (β₃ = −0.0159, p = 0.47) and France (β₃ = 0.0142, p = 0.22), which showed statistically insignificant effects. β₃ remains negative and significant across alternative specifications, providing evidence that this conditional risk is a structural characteristic of the Norwegian equity market rather than a product of general European market dynamics.

7.2 Theoretical & Practical Implications

This work has three main theoretical contributions.

First, the finding that Norwegian systematic risk changes across oil regimes supports the conditional CAPM framework suggested by Pettengill et al. (1995), where beta is not constant but depends on economic conditions. It adds to the work of Bollerslev et al. (1988) by showing that beta not only varies over time, but also in response to oil price direction.

Second, it extends the literature on oil and equities by Bjørnland (2009) and Park & Ratti (2008), showing that oil affects not just stock returns but also systematic risk. When oil prices are rising, Norwegian equities require less European market exposure to achieve given returns, indicating that oil dependence shapes both return and risk levels in a way consistent with sentiment-based models (Baker & Wurgler, 2006).

Third, it shows that oil conditional systematic risk patterns are specific to oil-dependent economies. The stark contrast between Norway and the oil-importing economies of Sweden and France suggests that the mechanism reflects economic structure rather than general European market dynamics.

7.3 Practical Implications for Risk Management

Norwegian equity risk models should include an oil conditional beta, as it could improve risk management accuracy. The standard CAPM estimates a single beta of approximately 0.99, but the true beta is 1.0339 during oil downturns and 0.8778 during oil upturns. This 15% swing means the standard CAPM misestimates Norwegian equity exposure during oil price declines — precisely when accurate risk assessment matters most.

The framework could extend beyond Norway to other oil-exporting countries, which may exhibit similar patterns, consistent with the global role of oil price shocks documented by Kilian & Park (2009). In summary, this thesis combines earlier work on conditional beta and oil–equity relationships with new evidence for Norway, showing that a conditional CAPM is both theoretically supported and practically useful for understanding and managing risk in oil-dependent equity markets.

7.4 Limitations and Directions for Future Research

This analysis has some limitations that should be discussed and suggest directions for future work.

First, the analysis relies on oil futures contracts (CO1, CL1) rather than spot prices. Futures may diverge from physical oil, though they are standard in finance research and provide the only reliable daily data source for the full sample period.

Second, the composition and weights of the equity indices change over the 25 years. These shifts may affect how systematic risk is measured over time, although the subsample analysis in Section 5.4, around major events seen in Figure 7.1 below, helps reduce this concern.

Third, the analysis only includes three countries, so testing the same framework on other oil-exporting countries would reveal whether the findings apply beyond Norway and whether the degree of oil dependence changes how the oil conditional beta varies.

Fourth, all estimated models are linear, so they capture average relationships but cannot identify more complex patterns — for example, whether very large oil price movements have disproportionately strong effects on systematic risk.

Fifth, in the two-factor model for Norway, the direct oil return and the interaction term are both influenced by oil market conditions, so their effects are not completely independent and could be separated more clearly in alternative modelling frameworks.

Finally, the oil regimes are defined using realised oil price movements and do not use forward-looking information such as option-implied volatility. Very large or expected future shifts in oil prices could change how markets price risk, but this is not modelled here.

7.5 Final Remarks

This thesis shows that oil prices create an asymmetric pattern in Norwegian systematic risk. The equity market is more sensitive to European movements when oil prices fall than when they rise. The comparison with Sweden and France confirms this pattern is specific to oil-dependent economies. For investors and risk managers, this finding is critical: standard risk models that ignore oil conditional beta will underestimate exposure during oil downturns, when accurate assessment matters most. The consistency of findings across time periods, data frequencies, and model specifications demonstrates that these results represent genuine economic patterns. The framework is simple enough to apply in practice yet captures important risk dynamics that standard models miss. Future research extending this approach to other oil-exporting countries and commodities could deepen understanding of how commodity dependence shapes financial markets globally.

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Appendix A: Diagnostic Tests and Robustness Checks

Tables report results for the primary daily return series used in the main regressions.

Table A.1: Augmented Dickey–Fuller Test for Unit Roots

Null: unit root. Series are stationary if p < 0.05.

Table A.2: KPSS Stationarity Test (Complementary to ADF)

Null: stationarity. Series are stationary if p > 0.05.

Table A.3: Ljung–Box Test for Serial Correlation (Lag 10)

Null: no serial correlation. Rejection if p < 0.05.

Table A.4: Breusch–Godfrey Test for Serial Correlation (Lag 10)

Null: no serial correlation. More robust than Ljung–Box.

Table A.5: Jarque–Bera Normality Test

Null: normality. Financial returns typically exhibit non-normality.

Table A.6: White Heteroskedasticity Test

Null: homoskedasticity. Rejection motivates HAC standard errors.

Table A.7: ARCH–LM Test for ARCH Effects

Null: no ARCH effects. Positive results indicate volatility clustering.

Table A.8: Ramsey RESET Test for Specification

Null: correct specification. Failure to reject (p > 0.05) supports the model.

Table A.9: Chow Test for Structural Breaks (50% Breakpoint)

Null: no structural break. Rejection suggests regime change.