1
Thesis MSc Economic Development and Globalization
Haijo Schipper s2467801
The volatility of stocks across monetary eras
Abstract
2 1. Introduction
In this section, I start with the discussion of the relevance of the research in section 1.1. Thereafter, in section 1.2 I summarize the findings. Lastly, in section 1.3 I introduce the approach.
1.1 Discussion of relevance
Volatility of stocks fluctuates over time. In the Capital Asset Pricing Model (CAPM) risk is considered the main reason for volatility to fluctuate. Empirically, Schwert (1989) finds that volatility increases during recessions, which is likely to be caused by a higher degree of risk. For stock markets, risk is partially caused by macroeconomic factors, next to the individual risk of companies. A recent example is the volatility caused by the trade war between the United States and China. In the past couple of decades, monetary policy has been one of the macroeconomic factors that is likely to influence risk for companies. In this thesis, I distinguish three events that change monetary policy in such a way that I argue a new monetary era has started. I test the difference in volatility during these monetary eras and test whether the difference is caused by differences in leverage and/or inflation rates. The aim of this thesis is to give insight in why stock volatility varies over time.
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1.2 Summary of findings
Based on a T-test (Table 4), this thesis finds that Bretton Woods is the least volatile period of the past decades in the United States. Table 1 shows the 12-month moving average of stock volatility of the S&P index in the United States:
Table 1. Stock market volatility in the United States
This thesis tests two explanations for this increased volatility: 1. Debt levels have risen since the Bretton Woods periods, increasing bankruptcy risk for listed firms, and 2. Inflation rates have decreased in the most recent decades, leading to higher deflation risk if inflation is close to zero. Deflation risk is the increased chance deflation occurs. Deflation can have harmful effects on the economy, because investment and consumption are delayed as prices decrease. This phenomenon can trigger a crisis. Higher deflation risk is associated with recessions and recessions are found to increase volatility (Schwert, 1989).
4 firms on the indexes shows a significant positive effect of the debt-to-equity ratio on the volatility of the stock prices for France, Japan and Germany. This effect is not found for the other countries, except when outliers are excluded.
1.3 Summary of approach
This thesis uses a dual approach. Firstly, the thesis analyzes in an EGARCH model the volatility of companies for structural breaks. Furthermore, this thesis uses the EGARCH model to test whether there is asymmetry in volatility. Theoretically, downward shocks should be stronger than upward shocks. A structural break shows a sudden increase or decrease in volatility. Secondly, I use a fixed effects model to see whether the periods differ significantly in volatility, or whether differences can be explained by the control variables in the least squares model. The control variables the thesis uses are debt-to-equity ratios and inflation rate. The approach of the least squares analysis is at the individual stocks at the country level. The motivation behind individual stocks is that at the individual firm level this thesis excludes financial firms with extreme values for leverage from the analysis. The reason for the country level is that some countries have many more listed firms than others on the indexes, which would lead to a bias if indexes are pooled. Moreover, separate regressions yield more detailed information than a clustered regression with dummies. The remaining structure of this thesis is as follows: section 2 describes the theoretical framework of the thesis, section 3 describes the methodology, section 4 describes the empirical findings and section 5 offers the conclusion, implications, limitations, and further recommendations.
2. Theoretical framework
5 2.1 Literature on stock volatility
In finance, the volatility of stocks is traditionally divided in two parts: systematic risk and unsystematic risk. Systematic risk cannot be diversified and therefore requires a risk premium on the expected return of stocks. Unsystematic risk can be diversified away by investors and therefore requires no risk premium. The risk premium is included in the standard CAPM as introduced by Sharpe (1964) and Black and Scholes (1974).
Volatility risk is an important factor that covariates with asset pricing (Bansal, Kiku and Shaliastovich, 2014). They include two other factors of risk as well, namely cash flow risk and discount rate risk. Discount rate risk is the risk that the present value of future cash flows of a firm decreases, when the discount rate of future cash flows increases. Generally, the risk-free rate is used as the discount rate. Therefore, when the risk-free rate increases, the present value of the firm decreases. In asset pricing, expected return depends on the risk an investor is willing to take and the risk-free rate.
6 Figure 2. Annualized standard deviations of U.S. monthly stock returns
Based on the updated data from Schwert (1989), high volatility during crises and during system changes can be observed. The Bretton Woods era seems relatively stable at first glance, as well as the period before 1835. Interesting to see is whether this pattern only holds for the United States or can be generalized for other countries as well. Furthermore, Schwert (1989) and Cortes and Weidenmier (2019) do not provide the answer to the question of why volatility is higher during crises. Has bankruptcy risk increased due to higher leverage ratios? This thesis tests whether leverage has a role in the increase in volatility during crises.
2.1.1 Why would stock volatility be influenced by monetary eras?
7 (1981): ‘Exchange rate risk is the variability of nominal and real effective exchange rates.’ When you invest with e.g. dollars in Mexico and a year later the peso has depreciated by 10%, the dollar value of your investments has also dropped by 10%. The exchange rate risk is higher for firms in a flexible exchange rate system, than for firms in a fixed exchange rate system. Generally, in a fixed exchange rate system, currencies do not depreciate, unless the fixed exchange rate is no longer sustainable. This is where the monetary eras come in, during Bretton Woods there were fixed exchange rates, during the periods after Bretton Woods there were flexible exchange rates. European countries created a monetary union mitigating exchange rate risk within the EMU. Through exchange rate risk, monetary eras can influence stock volatility. A second reason why monetary eras can influence volatility of stocks is inflation targeting. Central banks influence the inflation rate by expansionary or contractionary policy. The more effective monetary policy is, the lower the difference between the target inflation rate and the realized inflation rate. The inflation rate influences the required return for investors. When inflation is higher, required returns increase. Investors want to be compensated for the loss of purchasing power of their investment. According to Jaffe (1985), this compensation effect is less than a one-on-one relation. Thus, investors take part of the loss in purchasing power as a downside risk. Therefore, part of the loss in purchasing power caused by inflation for investor’s needs to be compensated. Inflation rate volatility and stock market volatility are thus likely to be correlated.
8 2.2 Literature on monetary eras
Benati (2008) investigates inflation under different monetary regimes. He finds significant differences across countries and regimes with the current Post-Bretton Woods system having the lowest inflation rates since the Second World War. He includes the Classical Gold standard, Interwar period, Gold exchange standard with a central bank, Bretton Woods, March 1951-August 1971, Great Inflation and Post-Volcker Stabilization. Volcker was Chairman of the Federal Reserve Board when the high inflation rates were countered with some stabilization measures. In the analysis, this thesis focuses on the periods after the second world war. Most notably, the Great Inflation is an interesting period to analyze volatility. This thesis approaches the different monetary regimes across countries in a similar way as Benati (2008).
Bretton Woods era
9 Rancière, Tornell and Westermann (2008) find that more systemic risk tends to increase long-term GDP when the number of crises is limited. The rationale behind the higher systemic risk is that systemic risk stimulates financial development and financial development boosts growth. Since the economy is the aggregate of individual firms, higher GDP growth is caused by output growth in firms. This reasoning is consistent with the CAPM, where investors who take more risk are rewarded with a higher expected return. Volatility therefore in itself is not necessarily undesirable. Based on the relative stability of Bretton Woods, I would expect lower volatility in this period. Lower risk is associated in the CAPM with a lower expected return.
The Great Inflation
I take 1971 as the start of the Great Inflation period, because this was when the Bretton Woods system was abolished. In 1971, President Nixon declared the dollar was no longer convertible into gold ending the Bretton Woods system. The Bretton Woods system was succeeded by a period of flexible exchange rates. After years of current account deficits, the U.S. started to print more dollars. Since the gold reserves did not increase significantly, the dollar and gold drifted apart. Shortly after, other currencies became free floating currencies and fixed exchange rates were abolished by some countries. Inflation rates in the U.S. increased tremendously to more than 10%. A time of high exchange rate volatility started (Wasserfallen, 1989). There are two opposing views on why the 1970’s saw a tremendous increase in inflation. The first is the informed decision: policy opportunism where central bankers thought of inflation as collateral damage to prevent a recession. The second view is more accidental: in this case mistakes were made causing bad monetary policy (Collard and Dallas, 2007). Schwert (1989) finds evidence that inflation influences stock returns and volatility, where more inflation leads to more volatility. Based on these results, this thesis argues that the Great Inflation period would be one with relatively high stock volatility in the United States. There were both more banking crises than the previous Bretton Woods period and higher inflation which would theoretically result in a higher stock volatility (Buch and Heinrich, 1999).
Great Moderation
10 Woods, but this is confusing since the Great Inflation is also Post-Bretton Woods. Due to the strong volatility impact of the 2007-2009 global financial crisis, the period Great Moderation is from the end of the Great Inflation in 1982 to the start of the global financial crisis in 2008. The period of free-floating exchange rates continues, although some countries choose a peg and others formed the European Economic and Monetary Union. The period after the Great Inflation is characterized by both relatively low inflation and relatively regular crisis periods, of which some banking crises. Therefore, from a theoretical point of view, the Great Moderation period would be an in-between period with lower volatility than the Great Inflation, but also more volatility due to more crises, than in the Bretton Woods period.
2007-2009 Global Financial Crisis
The crisis of 2007 to 2009 started with the burst of the US housing bubble in 2007. The banking crisis started with the fall of Lehmann Brothers, which made the Western world to fall into recession, as well as parts of the developing world. The banking crisis caused governments to react; new laws and agreements were introduced as a result, such as Basel III.
The global financial crisis of 2007 to 2009 is argued to be the first major global crisis since the Great Depression in the late twenties and early thirties of the 20th century (Bekaert et al., 2014). Bekaert et al. (2014) find contagion of equity market recession from the United States to other countries. Jung and Maderitch (2014) find structural breaks in volatility spillovers during the global financial crisis. This suggests there is a difference in volatility between pre- and post-crisis years. Was the global financial post-crisis the end of an economic era? To analyze this question, this thesis uses autoregressive models. If there is a clear cut off point in 2008, it makes sense to take a sample split in 2008 for a new era of volatility. Furthermore, Schwert (2011) finds the crisis period of 2008 was a period with relatively high stock volatility. He finds that during recessions in general, volatility rises. Therefore, this thesis includes the crisis period of 2007 to 2009 as a period in which there potentially is a structural break in the data.
Is the economy destabilizing?
11 higher volatility due to the increasing debt levels globally (Lund et al., 2018). Notably, the debt burden of China is increasing quickly. Furthermore, some corporations suffer from the ‘original sin’, which is issuing debt denominated in foreign currencies. This poses a greater risk, due to the currency risk that emerges when the national currency depreciates vis-à-vis the debt denominated currency. This depreciation can cause steep increases in leverage of companies. There are nevertheless disciplining forces as well, such as the banks taking measures to be safer and reduced correlation between capital flows, decreasing the intensity of boom and bust cycles (Renata, Asta and Otilija, 2019; Lund et al., 2018). The risk of local crises contaminating other countries reduces when the interconnectedness is lower. Bank crises are less likely with banks taken measures to be safer. Regulatory changes since the global financial crisis include Basel III in the European Union which include increased requirements for tier I capital as a percentage of debt, a maximum on leverage, requirements for liquidity ratios and counter-cyclical reserves. Furthermore, the European Banking Authority (EBA), the European Securities and Market Authority (ESMA) and the European Insurance and Occupational Pensions Authority (EIOPA) were established. The main goal of these supervising authorities is to supervise the financial sector.
2.3 Other variables potentially influencing stock volatility
In previous research, several factors significantly influence the level of volatility of firms. In this section, this thesis summarizes the most important ones, which are included as control variables.
Size
12 in order to prevent multicollinearity, this thesis excludes size as a control variable in the analysis and includes leverage.
Leverage and taxes
Guo, Wang and Wu (2011) find that leverage has a positive effect on stock volatility when unanticipated negative shocks occur. More generally, Schwert (1989) finds that more leverage generally leads to an increase in stock volatility. Based on these studies, in testing volatility over periods of time, this thesis includes a variable on the leverage of the firms included in the sample. In finance, undiversifiable risk of a stock is calculated as the equity beta. The equity beta can be calculated in the following way:
𝛽𝑒 = 𝛽𝑎((1 +𝐷
𝐸(1 − 𝑇𝐶)) (1)
where 𝛽𝑒 is the equity beta, 𝛽𝑎 is the asset beta, D/E is the debt-to-equity-ratio, and 𝑇𝐶 is the tax rate. The debt level of companies thus influences the riskiness of equity. More risk means more volatility. This means that leverage of companies influences the level of volatility for equity stocks. Therefore, both theoretically and empirically leverage has a positive relationship with the volatility of stocks. The tax rate influences the decision for desired debt-to-equity ratios for companies but does not likely influences stock volatility directly. Companies have tax deductibility for interest payments but need to pay taxes over profits. Thereby making debt more attractive over equity. However, equity is less risky, and companies seek the optimal balance. By including leverage in the model and running separate regressions for each country, this thesis indirectly includes the potential effect taxes might have. I calculate leverage as the debt-to-equity ratio.
Inflation
13 can be caused by lack of trust in a currency. To see whether the finding of Davis and Kutan (2003) is valid and to prevent omitted variable bias, this thesis controls for inflation.
Interest rates
Mascaro and Meltzer (1983) find that short- and long-term interest rates affect the demand for financial assets. With a higher interest rate, demand for other assets on the financial market decreases. Changes in demand lead to changes in prices ceteris paribus. Price changes lead to increases in volatility. Interest rate changes therefore increase the volatility of demand for assets by the general public. However, it is likely that there is a high correlation between the level of interest rates and the level of inflation. Therefore, although there is some evidence on the effect of interest rates, this paper includes inflation in the main model and exclude interest rates as a control variable.
2.4 Hypotheses
Based on the literature, this thesis has several expectations on the effects of monetary eras on the volatility of stock prices. Bretton Woods had fewer banking crises and banking crises correlate to other crises, such as currency crises (Kaminsky and Reinhart, 1999). Furthermore, the overall stock market volatility for the United States was lower (Cortes and Weidenmier, 2019). Crises could cause more volatile periods to stock prices. For Bretton Woods at the index level as unit of analysis, this paper only has data for Germany, the United States, and Japan. Therefore,
Hypothesis 1:
Bretton Woods system has the least volatile stock prices of the four post-war periods for Germany, the United States, and Japan.
14 Hypothesis 2:
There is a structural break in 2008 for company-level stock price volatility as well as index-level volatility.
Negative shocks are stronger than positive shocks in volatility according to literature (David, 1997). Therefore,
Hypothesis 3:
There are asymmetric shocks in volatility, where negative shocks are stronger than positive shocks.
Thirdly, the post-crisis period of after 2008 shows an increase in conservatism, regulation, and alternative investments and speculative assets (Lund et al., 2018). Based on risk-premium increases immediately after a crisis, this thesis has the following hypothesis:
Hypothesis 4:
Stock price volatility is lower after the 2008 financial crisis than during the Great Moderation. In hypothesis 2, this thesis uses a structural break test to test whether there is a structural break at the point of the crisis. In hypothesis 4, this thesis tests whether two prolonged periods have different dummy variables. Those are two different tests.
The other two periods are the Great Inflation and Great Moderation. In the literature, Davis and Kuwan (2003) find significant negative effects of inflation on volatility in low-inflationary countries. When inflation is included as a control variable in the equation, there is no reason to expect the dummy for the period immediately after the Great Inflation to be different than the dummy for the Great Inflation. Therefore,
Hypothesis 5:
Stock price volatility during the Great Inflation (1971-1982) is not significantly different from stock price volatility during the period Great Moderation (1982-2008).
Furthermore, bankruptcy risk is higher for more leveraged firms. The risk of bankruptcy can cause more volatility due to potential liquidity problems, therefore:
Hypothesis 6:
15 Lastly,
Hypothesis 7:
The inflation rate has a negative effect on stock volatility for countries with low inflation rates (Germany and Japan).
Previous findings from Kutan (2003) suggest a negative effect and the destabilizing deflation risk is lower with a higher inflation rate.
3. Methodology and data
This section discusses the methodology of the analysis more thoroughly. Section 3.1 discusses the volatility analysis. Section 3.2 explains the least squares analysis more thoroughly, section 3.3 discusses some validity tests, and finally section 3.4 gives an overview of the data.
3.1 Volatility analysis
The unit of analysis for the volatility analysis is the stock level. For stock volatility, this thesis uses the following added definition based on Zhang (2010): ‘Stock volatility is the standard deviation of monthly stock returns.’ In asset pricing, volatility is measured in different ways. The standard deviation of a specific stock returns and of stock market returns is most intuitive. Therefore, this thesis measures stock volatility as the standard deviation of stock prices as in Pinches and Kinney (1971):
√∑ (𝑃𝑖−𝑃̅)2
𝑛 𝑛
𝑖=1 (2)
16 Betas
Investors measure the volatility of a stock by its standard deviation. Of the standard deviation there is a diversifiable part and an undiversifiable part. The last part is measured by a stock’s beta. A stock’s beta (the equity beta) is calculated by:
𝛽𝑒 =𝑐𝑜𝑣(𝑅𝑒,𝑅𝑚)
𝑣𝑎𝑟(𝑅𝑚) (3)
where 𝛽𝑒 is the equity beta, 𝑐𝑜𝑣(𝑅𝑒, 𝑅𝑚)is the covariance between the return of the equity and the return in the market, and 𝑣𝑎𝑟(𝑅𝑚) is the variance in the returns of the market. In this beta, the effect of leverage is excluded.
3.1.1 Included periods
The sample period in this thesis is 1963-2019. The reason to start in 1963 is that this is the year the S&P 500 was established. The periods this thesis includes are 1963-1971 Bretton Woods, 1971-1982 The Great Inflation, 1982-2008, Great Moderation, and 2008-2019 Post-global financial crisis. For these periods this thesis includes a dummy in the OLS and fixed effects regressions. For the EGARCH volatility analysis this thesis takes monthly data for the entire period of 1963-2019. The reason to pick monthly data is that it includes more observations than yearly data and the comparability with previous research such as Schwert (1989) and Cortes and Weidenmier (2019) is higher.
3.1.2 Included countries
17 3.1.3 Econometrics
For the volatility analysis, this thesis uses an EGARCH approach to test for potential breaks in the data, indicating there would be a structural break. Furthermore, the thesis tests whether there is a significant difference in upward and downward volatility in the data:
EGARCH
Finance and economics use generalized autoregressive conditional heteroskedasticity (GARCH), introduced by Engle (1982) to analyze the volatility of stocks and to find structural breaks in the analyzed period. Later, exponential GARCH (EGARCH) was introduced by Nelson (1991). For the volatility analysis, this thesis uses EGARCH in order to test for autocorrelation. Furthermore, this thesis tests whether is a structural break in volatility during the start of the global financial crisis of 2008, the start of the Great Inflation, the end of the Great Inflation and during the end of the Bretton Woods era. The aim of this test is to find whether these events cause a structural change in stock volatility. Formula 4 describes the volatility measure behind the standard EGARCH approach from Dahlvid and Granberg (2017):
ln(𝜎𝑡2) = 𝜔 + 𝛽ln(𝜎𝑡−12 ) + γ 𝑢𝑡−1 √𝜎𝑡−12 + 𝛼 [|𝑢𝑡−1| √𝜎𝑡−12 − √2 𝜋] (4)
Where σ2 is the volatility measured as the variance of returns, ω is the constant, γ, β, and α are the coefficients. ln(𝜎𝑡−12 )is the lagged GARCH term, 𝑢𝑡−1
√𝜎𝑡−12
is the asymmetric shock of last
period, and [|𝑢𝑡−1|
√𝜎𝑡−12 − √2
18 market and/or indexes? If that is the case, there is likely some event causing a structural break in the volatility of stocks.
3.2 Ordinary least squares and fixed effects analysis
The unit of this analysis for the ordinary least squares (OLS) and fixed effects is the company level. The equation for the ordinary least squares analysis is:
𝜎𝑡 𝑃𝑡 ̅̅̅= 𝛼0 + 𝛼1𝐷1,𝑡+ 𝛼2𝐷2,𝑡+ 𝛼3𝐷3,𝑡+ 𝛼4 𝐷 𝐸𝑡+ 𝛼5𝜋𝑡+ 𝜀𝑡 (5) 𝜎𝑖𝑡 𝑃𝑖𝑡 ̅̅̅̅ = 𝛽0+ 𝛽1𝐷1,𝑡+ 𝛽2𝐷2,𝑡+ 𝛽3𝐷3,𝑡+ 𝛽4 𝐷 𝐸𝑖,𝑡+ 𝛽5𝜋𝑡+ 𝛿𝑖+ 𝜀𝑖𝑡 (6)
where t is the monetary era included, i refers to each firm, 𝛼0 and 𝛽0 are the constants, the other α’s and𝛽’s are the coefficients of the dummy variables 𝐷1−3 for the monetary eras included, the debt-to-equity ratio, and the inflation rate 𝜋. 𝜀𝑡 is the error at time t. 𝛿𝑖 is the fixed effect for firm i. By using all companies (except for financial firms) from multiple indexes, this thesis tests whether the findings are robust across monetary eras and countries. Furthermore, you can see the impact of the control variables by including the companies.
3.2.1 Included variables
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3.2.2 Dummies for periods
For the periods included in the timeframe, this thesis uses dummy variables to test whether volatility was generally higher during that era. The dummies this thesis uses are D1 (Late Bretton Woods, 1964-1971), D2 (Great Inflation, 1971-1982), D3 (Post Great Inflation, 1982-2008). In this thesis, D1 and D2 are combined into one dummy because otherwise there is a multicollinearity problem. The multicollinearity problem and solution are mentioned later in this thesis. The reference period in this case is the current post-Global Financial Crisis period.
3.2.3 Econometrics
The econometrics program this thesis uses for the OLS and fixed effects tests and the volatility analysis is STATA.
3.3 Validity and reliability tests
One of the ways this thesis tests the reliability of the outcomes of my research, is by testing whether the findings are robust across countries. This thesis measures reliability across time by including multiple samples in different time-horizons.
3.4 Data
In this section the thesis presents the data collection and a description of the data:
3.4.1 Data collection and description
20 tax rates. This analysis uses the S&P and TOPIX because these indexes are more diversified (S&P over Dow Jones) and a more appropriate representation of the market (TOPIX over Nikkei) than the main index of their countries (Kenton, 2019). The data is monthly stock prices for 1963 to 2019 and reported normal debt-to-equity ratio, which is yearly data. Therefore, I have collected time-series data for both stock prices and debt-to-equity ratios.
For the indexes, the data of the TOPIX start at 1-1-1963, for the S&P 500 at 1-1-1964, for the DAX at 1-1-1965, the FTSE 100 at 1-1-1984, the CAC40 at 1-8-1987 and the Borsa Italiana at 1-1-1998. Most of the individual stock data start at 1-1-1973 for the companies already listed in that year. Below this thesis presents an overview of the observations. Most outliers for the debt-to-equity ratio are in the financial services industry. Therefore, this thesis excludes companies active in the financial services industry. The sample of companies consists of 1169 companies when financial services industries are excluded. Figure 3 and 4 presents the 12-month moving averages representing the volatility of the indexes:
21 Figure 4. Volatility of the indexes
In figure 3 and 4, you can see that the 12-month average positive returns’ peaks are not as high as the negative returns’ valleys (except for the TOPIX). This signals negative skewness, which is consistent with common literature on stock volatility (David, 1997). Therefore, in the analysis part, the thesis tests for deviations from normality. Moreover, stock returns are characterized by excess kurtosis or fat tails. Another characteristic of stock markets is the asymmetric feedback of excess returns on volatility. Negative excess returns have a strong increasing effect on future volatility, whereas positive excess returns have weaker effects on decreasing future volatility (David, 1997).
22 Table 1. Summary statistics for listed firms
Italy Observations Mean St. deviation Minimum Maximum
Volatility 33,819 0.0764 0.1098 0 9.5697
Leverage 31,632 169.60 1449.61 -48,082 43,587
Inflation 62,744 5.9689 5.7066 -0.6000 28.68
France Observations Mean St. deviation Minimum Maximum
Volatility 16,152 0.0679 0.0787 0 5.5455
Leverage 15,108 132.68 628.04 -17,352 5,793
Inflation 21,356 4.1179 4.1323 -0.7300 15.16
Germany Observations Mean St. deviation Minimum Maximum
Volatility 10,826 0.0628 0.0613 0 1.3431
Leverage 10,836 100.12 155.29 -1,348.53 1,596.08
Inflation 19,778 2.5933 1.7692 -0.9274 7.8378
U.K. Observations Mean St. deviation Minimum Maximum
Volatility 37,772 0.0660 0.0672 0 1.8867
Leverage 32,508 74.71 904.96 -25,131 24,867
Inflation 62,744 5.6490 4.9072 -1.5700 26.88
U.S. Observations Mean St. deviation Minimum Maximum
Volatility 165,681 0.0717 0.2228 0 85.15
Leverage 155,893 70.01 1,431.22 -77,922 45,539
Inflation 300,762 3.8584 2.8494 -2.1000 14.76
Japan Observations Mean St. deviation Minimum Maximum
Volatility 169,096 0.0720 0.0707 0 2.5000
Leverage 174,879 106.93 148.29 0 988.17
23 As you can see in Table 1, the extreme values for leverage are very high and low. Since all low equity companies are excluded when all outliers are excluded, this thesis includes the outliers. However, in order to test robustness of the results, this thesis includes a test where outliers are excluded.
4. Analysis
In this part, the thesis starts with the volatility analysis including the EGARCH model, thereafter the thesis continues with the findings and discussion of the findings, then the thesis summarizes the findings of the least squares and the fixed effects analysis and discuss them, and the analyzes ends with some validity tests for both the volatility analysis and the least squares analysis. The EGARCH model is included to test whether there is asymmetry in the volatility of the indexes, as well as to test if there are structural breaks in the data. The thesis presents tests for differences in upside and downside shocks in an EGARCH model, because the theory suggests that downside shocks have a stronger effect than upside shocks. The thesis includes an OLS and fixed effects model to see whether there are significant effects of leverage and inflation rate on the volatility of stocks. Furthermore, the thesis presents tests on whether there is a significant difference in volatility across monetary eras by including dummies. Davis and Kutan (2003) find that inflation has a negative relation with volatility when inflation rates are low. It is interesting to see whether this research yields the same results or finds other links.
4.1 Volatility analysis
24 Table 2. Observations at the index level for different monetary eras
Observations Bretton Woods The Great Inflation Great Moderation Post-Global Financial Crisis S&P 500 Composite 103 112 334 130 FTSE 100 0 0 299 130 DAX 30 Performance 91 112 334 130 France CAC 40 0 0 256 130
FTSE MIB Index 0 0 131 130
TOPIX 115 112 334 130
Table 3. Volatility of returns of stock indexes of the G6-countries Volatility standard deviation of returns Bretton Woods The Great Inflation Great Moderation Post-Global Financial Crisis S&P 500 Composite 3.462% 4.661% 4.384% 4.613%
FTSE 100 N.A. N.A. 4.950% 3.925%
DAX 30 Performance 4.857% 4.325% 6.220% 5.422%
France CAC 40 N.A. N.A. 6.274% 4.850%
FTSE MIB Index N.A. N.A. 6.599% 6.370%
TOPIX 4.704% 3.714% 5.713% 5.261%
25 However, a formal T-test can confirm whether the difference in volatility during the different eras is significant. In Table 4 you can see the level of significance of the differences in means. For this analysis, I used a single-sided heterogeneity robust uncoupled T-test:
Table 4. Significance of T-tests T-tests of significance of difference Bretton Woods - Great Inflation Bretton Woods - Great Moderation Bretton Woods - Post-Global Financial Crisis S&P 500 Composite -1.899% *** (0.0088) -0.922% ** (0.0158) -1.151% ** (0.0134) DAX 30 Performance 0.532% (0.1450) -1.363% *** (0.0034) -0.565% (0.1721) TOPIX 0.990% ** (0.0326) -1.009% ** (0.0219) -0.557% (0.1477) *, **, ***= significance at the 10%, 5% and 1% level
(0.0088) = P-value of the T-test
The T-test shows the significance of the differences in volatility between Bretton Woods and the other three periods. Table 4 shows that Bretton Woods is indeed significantly the least volatile period of the four periods for the United States at the 5% level, since minus indicates lower volatility during Bretton Woods. For Germany, Table 4 shows Bretton Woods was significantly less volatile than the Great Moderation, but not significantly more volatile than the other periods. For Japan, Table 4 shows Bretton Woods is significantly more volatile than the Great Inflation and significantly less volatile than the Great Moderation. Hypothesis 1 states that Bretton Woods is the least volatile period for the United States, Germany and Japan. Therefore, hypothesis 1 that Bretton Woods is the least volatile period is rejected for Japan, confirmed for the United States, and neither confirmed nor rejected for Germany.
4.1.1 Findings on the stock market level
26 Therefore, in this section the unit of analysis is the index level. For monthly returns all variables except the FTSE100 and the Borsa Italiana have a significant autoregression variable, meaning significant autocorrelation. All variables have a significant ARCH lag 1 variables, thus have significant autocorrelation in the error terms. However, an ARCH (1,1) model is not as reliable as the EGARCH model, thus this thesis continues with the GARCH (1,1) to move towards the EGARCH model. The results of the ARCH and GARCH models are discussed in appendix A and B.
In the GARCH (1,1) model, I start with the S&P 500 composite. For both the ARCH and the GARCH variable it is significant at the 1% level. When checking for autocorrelation in the residuals, the model finds no significant autocorrelation in the residuals. For the other models, the results show that in the GARCH model the ARCH variables are significant for all models, whereas for the GARCH variables, they are significant for all models except the FTSE index. The correlograms for correlation in the error terms in the model, which is undesirable, shows no significant error for the S&P, the FTSE100, the CAC40 and the FTSE MIB. However, the DAX shows significance autocorrelation at the 5% level, whereas the TOPIX shows significance at the 1% level.
27 Table 5. EGARCH models results for aggregate indexes
EGARCH results
Auto-correlation constant
Gamma Alpha Beta
Market (Standard error) (Standard error) (Standard error) (Standard error) S&P 500 -3.7503*** (0.0517) -0.0030 (0.0770) -0.5752*** (0.1206) -0.7853*** (0.1223) FTSE 100 -3.8451*** (0.0886) -0.0295 (0.0704) 0.4926*** (0.1248) 0.7925* (0.4640) DAX 30 -3.5817*** (0.0684) 0.0717 (0.1064) 0.0993 (0.1392) 1.0328*** (0.2182) CAC 40 -3.4477*** (0.0755) 0.0389 (0.0495) 0.0705 (0.0766) 3.0787* (1.8114) FTSE MIB -3.4648*** (0.0857) 0.2579 (0.3009) -0.7045 (0.5009) -0.8104 (0.5070) TOPIX -0.4493*** (0.1360) -0.0284 (0.0254) 0.2319*** (0.0468) 0.9237 (0.0224)
where *=significant at the 10% level, **= significant at the 5% level and *** significant at the 1% level.
Most indexes have β parameters which are significant at the 1% or 10% level. Therefore, the natural logarithmic values of the equations are significant, implying there is significant autocorrelation in the volatility of the indexes. Interesting to see is that autocorrelation for some indexes is positive whereas for other indexes is negative. There is little evidence of asymmetric shocks in the volatility at index-level. The EGARCH term (beta) is significant for most indexes, implying past volatility can be used to predict future volatility. A positive sign shows for the FTSE, DAX and CAC higher past volatility leads to higher future volatility. For the S&P the opposite is found, higher volatility in the past leads to lower volatility in the future.
4.1.1a Structural breaks
28 there is significance at the 10% level, the estimated month is October 2002, the year the euro currency was introduced. The measured effect for Italy is bigger than for Germany and France, which were economically more stable countries already before the euro was introduced. There is no significant structural break during the crisis of 2007-2009 for any of the stock indexes. Thus, hypothesis 2 on structural breaks is not confirmed.
4.2 Least squares’ and fixed effects analysis
The least squares’ analysis provides data on all the individual stocks composing the index listed in the end of the period. Thus, in contrast to the volatility analysis, in this section, the unit of analysis is individual stocks. The OLS regression of the DAX thus consists of the 30 companies comprising the DAX for the analysis of the stock volatility. The analysis includes all listed companies except for the companies in the financial sector of the stock indexes. It shows patterns on the stock level, it allows to exclude the banking sector, and it increases significance of the results relative to the stock index level.
4.2.1 Findings
29 Table 6. OLS models for all the indexes
Index Debt-to-Equity coefficient*100 % (SE) Inflation rate Dummy BW & GI Dummy Great Moderation Adjusted R2 Number of observations S&P 500 -0.0000 (0.0000) -0.0038*** (0.0002) 0.0502*** (0.0020) 0.0176*** (0.0005) 0.0105 146,370 FTSE 100 0.0000 (0.0000) -0.0015*** (0.0002) 0.0309*** (0.0032) 0.0088*** (0.0008) 0.0057 29,679 DAX 30 0.0013*** (0.0004) -0.0079*** (0.0006) 0.0182*** (0.0046) 0.0136*** (0.0014) 0.0281 9,510 CAC 40 0.0020*** (0.0002) 0.0002 (0.0003) 0.0085* (0.0048) 0.0123*** (0.0012) 0.0150 14,053 FTSE MIB -0.0000 (0.0000) 0.0000 (0.0003) 0.0296*** (0.0113) -0.0007 (0.0016) 0.0003 29,534 TOPIX 0.0007*** (0.0001) -0.0014*** (0.0001) -0.0007 (0.0012) 0.0085*** (0.0004) 0.0052 169,096
Dependent variable: stock volatility. No fixed effects applied. * significant at the 10% level.
** significant at the 5% level. *** significant at the 1% level.
30 Table 7. Fixed effects models for all the indexes
Index Debt-to-Equity coefficient*100% (st. error) Inflation rate Dummy BW & GI Dummy Great Moderation within R2 Number of observations S&P 500 0.0000 (0.000) -0.0029*** (0.0002) 0.0517*** (0.0019) 0.0201*** (0.0005) 0.0142 146370 FTSE 100 0.0000 (0.0000) -0.0013*** (0.0002) 0.0365*** (0.0032) 0.0122*** (0.0008) 0.0100 29679 DAX 30 0.0017*** (0.0005) -0.0077*** (0.0006) 0.0208*** (0.0046) 0.0148*** (0.0014) 0.0290 9510 CAC 40 0.0017*** (0.0003) 0.0007** (0.0003) 0.0077 (0.0047) 0.0136*** (0.0012) 0.0148 14053 FTSE MIB -0.0000 (0.0000) -0.0001 (0.0004) 0.0323*** (0.0113) -0.0012 (0.0016) 0.0005 29534 TOPIX 0.0021*** (0.0002) -0.0011*** (0.0001) 0.0001 (0.0012) 0.0096*** (0.0004) 0.0068 169096 Dependent variable: stock volatility. Including company fixed effects.
* significant at the 10% level. ** significant at the 5% level. *** significant at the 1% level.
BW & GI = Bretton Woods and Great Inflation combined.
31 The economic interpretation is interesting: when controlling for leverage and inflation rate, the current period is the period with the lowest volatility for the United States, United Kingdom, Italy and France. The hypothesis that the inflation rates for Germany and Japan have a significant negative effect on volatility is confirmed by the data. Furthermore, interestingly inflation rates also have a significant negative effect on volatility in the United States and the United Kingdom. The fixed effects model has one significant difference compared to the OLS model, which is that inflation has a positive effect on volatility in listed companies in France. This significant effect is not found in the OLS model. France is a country with prolonged periods of over 10% inflation, which is high. Volatility is higher for periods with very low inflation but might well be higher with high levels of inflation as well, due to increased uncertainty. This would explain why the other country with high inflation (Italy) does not show a significant negative relationship between inflation and volatility either.
The economic significance of inflation rate is quite low for France, Japan and the United Kingdom. When inflation rate increases with 1 percentage point, the volatility decreases for Japan and the United Kingdom with only 0.11 and 0.13% and increases in France with only 0.07%. Compared to the mean volatility in countries of 6 to 8%, the changes are relatively small, hence the economic significance is limited. For Germany the economic significance is much higher, where a 1 percentage point increase in inflation leads to a decrease in volatility of 0.77%. The United States is in between with a decrease of 0.29% for every percentage point increase in the inflation rate. For leverage a 1 percentage point increase in debt-to-equity leads to a 0.0017% increase in volatility for Germany and France and 0.0021% for Japan. This yields relatively low economic significance. However, with big changes in leverage there is an effect, e.g. when moving from a full equity company to a one-third equity company the increase in leverage is 200%, leading to a 0.42% increase in monthly volatility in Japan. Therefore, only with big changes the leverage effect on volatility is economically significant.
In order to test for robustness, this thesis reports fixed effects models where outliers of >500% debt-to-equity ratio and negative debt-to-equity ratios are excluded. The Table is reported in Appendix D. The main result from this robustness test is that the results for all variables are robust. All countries have significant and positive values for leverage when outliers are excluded. Therefore, there is some evidence that high leverage, if the company has a significant amount of equity, leads to higher volatility.
32 for GM. In the models of Table 6 and 7 Bretton Woods and the Great Moderation are clustered, which is undesirable for this test. Therefore, the T-test uses a different model with a cluster of Bretton Woods and the Post-Global Financial Crisis as the reference period in order to exclude the effect of Bretton Woods. Below you can find the T-test results of this dummy difference:
Table 8. T-tests differences Great Inflation and Great Moderation
Country Difference in
volatility
p-value mean
(difference) = 0
Hypothesis 5
Italy GI>GM 0.0000 Rejected
France GI>GM 0.0000 Rejected
Germany GI>GM 0.0000 Rejected
United Kingdom GI>GM 0.0000 Rejected
United States GI>GM 0.0000 Rejected
Japan GI<GM 0.0000 Rejected
4.3 Overview of the hypotheses
Below you can find an overview of the hypotheses:
Table 9. Overview of the hypotheses and conclusions
Hypothesis Rejected/not rejected Comments
1. Bretton Woods system has the least volatile stock prices of the four post-war periods for Germany, the United States, and Japan.
Not rejected for the United States, rejected for Japan and not confirmed for the other countries.
Bretton Woods is
significantly the least volatile period for the United States. Hypothesis 1 is not rejected for the United States. For Germany the difference is not significant and for Japan
Bretton Woods is
33 Therefore, Hypothesis 1 is rejected for Japan. Tested with a T-test in Table 4. 2. There is a structural break
in 2008 for company-level stock price volatility as well as index-level volatility.
Not confirmed The structural breaks in the data are not during the Global Financial Crisis. Tested in Appendix C.
3. There are asymmetric shocks in volatility, where negative shocks are stronger than positive shocks.
Not confirmed The results of the EGARCH model are not consistent and mostly insignificant. Tested in Table 5.
4. Stock price volatility is
lower after the 2008
financial crisis than during the Great Moderation.
Confirmed for all countries except the United Kingdom.
The dummy for the Great Moderation is significant and positive for all countries except the U.K. The reference period was the Post-Global Financial Crisis. Derived from Table 6 and 7. 5. Stock price volatility
during the Great Inflation
(1971-1982) is not
significantly different from stock price volatility during the period Great Moderation (1982-2008).
Rejected for all countries All countries have a significant difference between both periods, when comparing the Great Inflation to the Great Moderation. Tested with a T-test in Table 8.
6. More leveraged firms have higher stock price volatility.
Confirmed for Germany, France and Japan. For the other countries the values were not significantly different from zero.
The coefficients of leverage are either significant and positive, or not significantly different from zero in the model. Derived from Table 6 and 7.
7. The inflation rate has a negative effect on stock
Fully confirmed, additionally inflation rates also have a
34 volatility for countries with
low inflation rates (Germany and Japan).
significant negative effect for the United States and the United Kingdom. In France the fixed effects model shows a significant positive relation between inflation rates and stock volatility.
negative for 4 countries, positive and significant for France and not significant for Italy. Derived from Table 6 and 7.
5. Conclusion, implications and limitations 5.1 Conclusion
Leveraged firms are more volatile in Germany, Japan and France. Furthermore, higher inflation rates lead to lower volatility in Germany, Japan, the United States and the United Kingdom. This thesis tests whether there is a significant difference in volatility across time during different monetary eras and whether leverage and inflation rates influence volatility. The results show significant but weak differences in volatility across time with lower volatility during the Bretton Woods era for European countries and Japan, whereas the United States experienced higher volatility during the Bretton Woods era. However, when correcting for interest rates and leverage, the current period since the Global Financial Crisis is significantly the least volatile period for all countries except Japan and Italy. The hypothesis that companies with higher debt-to-equity ratios experience higher volatility cannot be rejected. Furthermore, the hypothesis that there is no significant difference in the dummy variables of the Great Inflation and the period after the Great Inflation until the Global Financial Crisis is rejected at the 5% level for all countries.
5.2 Implications and recommendations for future research
35 This research finds a negative correlation between the US stock market volatility and the volatility of the European and Japanese G6 countries. This suggests that international stock markets serve as a tool for investors to ameliorate the effects of higher volatility in U.S. markets. Furthermore, this research finds a link between inflation rates and stock volatility for the United States and United Kingdom. These are interesting fields for further research.
5.3 Limitations of this research
One of the limitations of this research is that although this research includes six different countries, it does not fully represent companies in those countries. The companies included in the sample are listed companies and have considerable size. This research cannot be generalized to small and medium sized enterprises. Furthermore, for e.g. the United States and Japan not all large cap firms are included in the sample. Therefore, it is a, arguably not representative, sample of the population rather than the entire population of large cap firms. One should be cautious in generalizing the results of the regressions for these countries.
This paper uses the volatility of stock returns, but the literature also suggests alternative measures of volatility. One of them is option-implied volatility, derived from the Black-Scholes model. Further research could include other measures of volatility in order to test the robustness of the results.
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39 7. Appendices
Appendix A: ARCH (1,1) models
Index
Autocorrelation coefficient
(st. error) ARCH coefficient (st. error)
S&P 500 .0059*** (.0018) .1834*** (.0365)
FTSE 100 .0033 (.0022) .3703*** (.0946)
DAX 30 .0054** (.0023) .1975*** (.0487)
CAC 40 .0067** (.0030) .3877*** (.0848)
FTSE MIB INDEX -.0007 (.0041) .3115*** (.1091)
TOPIX .0042 ** (.0020) .1726*** (.0301)
**= significant at the 5% level. *** significant at the 1% level.
Appendix B: GARCH (1,1) models
Index autocorrelation coefficient (st. error) ARCH coefficient (st. error) GARCH coefficient (st. error) S&P 500 .0049*** (.0016) .1355*** (.0240) .8260*** (.0212) FTSE 100 .0037* (.0022) .3664*** (.0940) .1638 (.1476) DAX 30 .0044** (.0022) .1366*** (.0305) .7796*** (.0415) CAC 40 .0069** (.0030) .3297*** (.0784) .3969** (.1541) FTSE MIB INDEX .0004 (.0042) .2746** (.1086) .4708*** (.1735) TOPIX .0043** (.0018) .1061*** (.0177) .8538*** (.0273) * significant at the 10% level.
40 Appendix C: Structural breaks on aggregate level
Structural breaks Swald statistic Breakpoint month 1
Market (P-value)
S&P 500 9.2317 (0.1283) No
FTSE 100 5.5800 (0.4704) No
DAX 30 7.7943 (0.2213) No
CAC 40 8.1975 (0.1906) No
FTSE MIB 10.0706 (0.0920) October 2002
TOPIX 13.5271 (0.0216) January 1990
Appendix D: Robustness checks when leverage outliers are excluded
Index Debt-to-Equity coefficient*100% (st. error) Inflation rate Dummy BW & GI Dummy Great Moderation within R2 Number of observations S&P 500 0.0011*** (0.0003) -0.0026*** (0.0002) 0.0491*** (0.0019) 0.0188*** (0.0005) 0.0129 140,499 FTSE 100 0.0042*** (0.0007) -0.0011*** (0.0002) 0.0365*** (0.0031) 0.0128*** (0.0008) 0.0120 28,324 DAX 30 0.0064*** (0.0011) -0.0071*** (0.0006) 0.0208*** (0.0045) 0.0154*** (0.0014) 0.0307 9,282 CAC 40 0.0047*** (0.0009) 0.0006** (0.0003) 0.0086* (0.0045) 0.0131*** (0.0012) 0.0151 13,653 FTSE MIB 0.0058*** (0.0008) 0.0002 (0.0004) 0.0308*** (0.0114) 0.0013 (0.0016) 0.0023 27,035 TOPIX 0.0036*** (0.0003) -0.0011*** (0.0001) 0.0009 (0.0012) 0.0097*** (0.0004) 0.0074 163,907 Dependent variable: stock volatility. Including company fixed effects.
* significant at the 10% level. ** significant at the 5% level. *** significant at the 1% level.
