Analyzing the effect of the announcement by the Swiss
National Bank to unpeg the Swiss franc on the Swiss stock
market
Mats Heybroek Student number: 10002857
Deparment of International Economics University of Amsterdam BSc. Thesis
I.Introduction
After the great recession investors considered the Swiss franc to be a “Safe Haven” asset1, which could be a riskless investment when the US stock market were in turmoil. This led to an appreciative force on the Swiss franc.2 Because 72.3% of the GDP of Switzerland was made up of export of goods and services, the Swiss Nation Bank (“SNB”) considered the appreciation of the Swiss franc to be bad for the economic growth.In 2011 the SNB stated that there was a massive overvaluation of the Swiss Franc that posed a threat to the Swiss economy. They declared to aim for a sustained weakening of the Swiss franc, which meant a peg to the Euro. They would enforce this peg “with the utmost determination” and were prepared to “buy foreign currency in unlimited quantities.” 3
To maintain this policy, the SNB had to increase their official reserve accounts with Dollars and Euro’s by supplying Swiss francs. When they started their policy in 2011 they had approximately 250 billion foreign currencies in Swiss francs in their foreign currency reserves. No later than 2014, the SNB had already amassed $480 billion of foreign currency, which could effectively be translated to approximately 70% of the GDP.4 Economists like Peter Bernholz5 were convinced that the increase in foreign reserves and printing more Swiss francs could eventually lead to a Swiss hyperinflation. Therefore the Switzerland’s right-wing People’s Party (“SVP”) collected enough signatures to start a referendum into pressuring the SNB to change their exchange rate policy. This political pressure in combination with the upcoming Quantitative Easing (QE) program of the ECB, are assumed to have forced the SNB into ending their policy on the 15th of January 2015 (hereinafter referred to as “the announcement”).
Although the consequences of the shock from the day of the announcement may seem unnecessary, the SNB only had two options at that point: To keep the peg and increase their reserves, while hoping that at some point the demand for the Swiss franc would decline, or
1
Ranaldo & Söderlind, 2010 2
The economist explains (18-01-2015). Why the Swiss unpegged the franc Retrieved from: http://www.economist.com/blogs/economist-explains/2015/01/economist-explains-13
3
SNB: Press release, Zurich, 6 September 2011 4
See Footnote 1. 5
Peter Bernholz is Professor Emeritus at the Center for Economics and Business at the University of Basel.
too leave the peg and let the markets decide the exchange rate. While the first option could probably be hold for some time, the appreciation risk of the reserves would keep increasing if the demand for Swiss francs did not decline. Whereas the latter would only incur the losses it generated till that point, but will not have generated more. The SNB deemed the current policy unsustainable and choose the latter. The goal of this thesis is to answer the next research question:
Does the announcement from the SNB to unpeg the Swiss franc has an effect on stock returns and their volatility?
The Swiss franc revaluated after the announcement, which is generally considered to have a negative effect on the export sector. This is due to the fact that the international product demand is expected to be elastic, which leads to a decline in product demand when the price for foreigners in domestic products increase (Pillbeam, 2013). One way companies counter this, if possible, is by lowering the prices for their products to keep the same product demand. This decision will, however, decrease their earnings if the marginal costs are not reduced, which in term decrease the expected future earnings. Hence, the revaluation is generally expected to decrease the stock prices of companies that rely heavily on export. Although this is the general assumption, it does not always have to hold.6 Reasons for a deviation from the general assumption may be; an increase in domestic consumption of products because of an increase in purchasing power of the Swiss population, which could substitute the possible loss of the decline in product export. Secondly, the increase of purchasing power also applies to the Swiss listed companies, so the import of products becomes cheaper. Companies which use a lot of import-products for their production will see a reduction of their marginal costs which could lead to only a minimal decline in future earnings. Thirdly, the Swiss products are differentiated products that have unique qualities which makes them inelastic, in this case the price would not have to be adjusted (as much) to keep their demand at the same level. The revaluation effect on the financial companies in the Swiss market index ( Henceforth “SMI”) is different from production firms, because they depend mostly on the value of their assets and liabilities, instead of the production of
6
The Dornbusch model and Mundell-Fleming model both have a decline of export after an appreciation included (Pillbeam, 2013) and most articles expect the same.
products. The effect of the revaluation in this case can only be measured by examining their assets (Choi et al, 1992).
Besides an expected change in the average stock return, a change in the volatility is also expected. If the exchange rate becomes more volatile, the exchange risk will increase (Dumas and Solnik 1995; Adler and Dumas, 1984; Stulz 1981), and if the companies do not hedge this exchange risk, the volatility of the stock returns could also increase due to the volatility spill-over effect.
The outline will be as followed: In section II. the literature review about the possible channels will be discussed. The data will be introduced in section III., while the data will be discussed in section IV. The analysis will be done in section V., and Section VI. will contain the conclusion and discuss some remarks about the models used.
II. Literature review
II.1 Theoretical framework
Stock prices of firms are considered to depend on the real value of its assets and its expected future earnings. Indirectly, these assets seem to be influenced by macroeconomic news because they affect the value of its assets or decrease their expected future earnings (Andersen et al, 2002). ). The efficient market hypothesis suggests that the stock prices holds all information (Fama, 1981), which implies that a policy change is also incorporated in the stock prices. As the increase in demand for Swiss francs drove the price of the currency, the revaluation pressure grew. When the SNB decided to stop their unsustainable expansionary policy, a (temporary) revaluation was expected till the demand for the Swiss franc would decline. The policy change was sudden and unexpected,7 and according to Chen et al, are unanticipated events considered to have a greater effect on the stock prices than anticipated events, because they imply a sudden overload of information (Chen et al, 1986). The results of former studies will be analysed to discuss the effects of the announcement information on the stock return.
One of the effects of the unanticipated event is the increase in state risk. The state-risk comes from the rational expectations equilibrium approach (Veronesi, 1999), where investors are assumed to see a two-state economy with a possible high and low state. The economy can switch between these states. For instance, when the economy is in the low (high) state and there is good (bad) news, it will result in an increase (decrease) of the expected future asset value. Additionally , it will also increase the risk of changing between states, which results in a higher volatility. Although this study was done on the exchange rate, it can be argued that this state-risk has the same effect on stock prices since it involves the preference of investors and the uncertainty of the economy. The state risk is expected decay after a “state” switch.
Adler and Dumas researched the exchange risk. In their research they concluded that the exchange risk is the deviation from the purchasing power parity. The purchasing power parity is an equilibrium where the price of a bag of goods should be equal in two countries
7
Multiple newspapers suggested it was unexpected: BBC: “unexpected announcement as "carnage”” . Independent.co.uk.: “unexpectedly scrapping its cap on the value of the Swiss franc. Financial times: “SNB unexpectedly abandoned the cap”
with regard to the exchange rate. When this parity is not in equilibrium, the exchange risk grows. The further the exchange rate is from its parity, the higher the risk of a sudden change in value. (Adler & Dumas, 1984). Subsequently, when the central bank suddenly revaluates their currency, the exchange risk will materialize which results in asset pricing effects, according to Patro et al (2014). What the effect will be, depends on the amount of the company’s foreign debts and assets. This exchange risk is given by the deviation of the purchasing power parity, according to Stulz (1981).
This exchange risk materialization in combination with the state-risk causes uncertainty for investors in time of a policy change. This is due to the lack of information and understanding about the consequences of the exchange risks of the foreign assets, that are in possession of the particular firms and the current state of the economy. The research done by Amihud and Mendelson (1986) suggests that an increased uncertainty at times of (re) devaluations causes the stock return to overshoot as a result of the risk aversion of the investors. This implies that the studied materialization of the exchange risk and the increased state-risk will negatively affect the mean of the stock return at the time of the announcement – thereby increasing the risk premium and lowering the return – but is expected to recover when the full scale of the materialization is known and the state-risk has diminished. This overshooting effect is shown in graph. 7 (Appendix 1.) where the return on the Swiss market index (“SMI”) is depicted. Patro et al (2013), research these (de)revaluation events by using the event study methodology, which will be described in in the methodology section. The next hypothesis is composed to examine the overshooting effect:
Hypothesis 1.1
The null hypothesis for the return on the stock market is that the coefficients of all the announcement dummies equals zero. The alternative hypothesis is that the coefficient of the announcement dummy is different from zero, and the coefficients of the pre and post announcement dummies equals zero. This alternative hypothesis suggest there is a temporary effect on the mean of the abnormal stock return in the month of the announcement, which is mathematically expressed as:
Where 𝛽𝛽 represents the coefficient of the announcement dummy variable, which is one in the month of the time of the announcement, and zero otherwise, and 𝛾𝛾𝑖𝑖 the coefficient of the other dummy variables.
In addition to the expected temporary change in the mean of the return as a result of the increase in uncertainty, there is also a second revaluation effect predicted. A revaluation is besides the effect of the exchange risk on assets, also expected to influence export. Freund and Pierola analyse the effect of appreciation on export in their paper for the World Bank, they state that: “an undervaluation of the real exchange rate precedes export surges” and that the undervaluation can be seen as an effective export subsidy and import tariff. Reversely, a overvaluation can be considered an export tariff and an import subsidy (Freund and Pierola, 2008). This export “tariff” will diminish the earnings from exported products. As the majority of the firms in the Swiss market index are production firms that sell a part of their product stocks abroad, positive relationship between the exchange rate and the stock returns is expected. This will be measured using the exchange rate variable
Hypothesis 1.2
The null hypothesis for the longer-term effect of the revaluation on the stock returns, is that the coefficient of the exchange rate variable equals zero, and the alternative hypothesis states that the coefficient of the exchange rate variable is different from zero. This alternative hypothesis suggests that a change in the exchange rate affects the mean of the stock return, which is mathematically expressed as:
H0: 𝜇𝜇 = 0 , H1: 𝜇𝜇 ≠ 0
Where 𝜇𝜇 represents the coefficient of the exchange rate variable.
The last effect that is researched on the mean of the stock returns is the effect of a change in policy on the stock return. Westerfield analysed the difference between a risk premium of a pegged currency and the risk premium of a floating currency. His main findings were that a floating currency has a higher risk premium, because the exchange rate is more volatile (this may seem obvious, because a peg is not supposed to be volatile at all). So, while the
currency, the exchange risk is proved to be priced higher in the event of a floating exchange rate (Westerfield, 1977). Therefore a negative effect of the policy change on the mean of the return is expected. To exhibit the difference in the mean of the returns in the period prior and after the policy change, a post announcement dummy will be adopted
Hypothesis 1.3
The null hypothesis for the longer-term effect of the policy change on the stock returns, is that the coefficient of the post announcement dummy equals zero, and the alternative hypothesis states that the coefficient of the post announcement dummy is different from zero. This alternative hypothesis suggests there is a permanent effect on the mean of the stock return after the policy change, which is mathematically expressed as:
H0: 𝛿𝛿 = 0 , H1: 𝛿𝛿 ≠ 0
Where 𝛿𝛿 represents the coefficient of the post announcement dummy variable which is one from the time of the announcement and forth, and zero otherwise.
Besides the expected effects on the mean of the stock returns, there is also expected to be a volatility effect of the announcement. The announcement was not just a one-time revaluation, but a change in foreign exchange policy. The SNB changed from a peg on the Euro to a floating exchange rate. Lastrapes (1989) showed that volatility of exchange rate – and therefore the exchange risk - depend on the policy of the central bank (Lastrapes, 1989). Although the exchange risk can be limited by using hedge contracts, which is considered to be one of the easiest hedgeable risks (Adler & Dumas, (1984), Dumas & Solnik proved in their study that exchange risk is still very common among firms (Dumas & Solnik, 1995).
The fore mentioned increase in the volatility of the exchange rate is also expected to permanently increase the stock returns volatility (or at least for the time period where the exchange rate is floating). The adaptation of the variance of the exchange rate on the stock return is called volatility spill-over, and will be analysed by using an GARCH-model (Bollerslev 1990). This will be further explained in the methodology section.
There seems to be some controversy about the way the volatility spill-over works. Kanas concluded that there are some significant volatility spill-over effects when the stock return is used as an independent variable and the exchange rate as a dependent, but not vice versa (Kanas, 2000) Yang and Doong came to a similar conclusion that the movement of
exchange rate has less direct impact on the volatility of stock prices than the other way around (Yang & Doong, 2004). These studies did not, however, investigate the policy change from a peg to a floating exchange rate, but solely a general volatility change. Therefore it is interesting to examine an increase in volatility for the stock prices.
It is expected that a change from a fixed to a floating exchange rate will increase the volatility of the stock return on the longer term. Therefore a persistent volatility is needed with a unit root in the conditional variance.
Hypothesis 2.1
The null hypothesis for the volatility of the stock returns is that the coefficients of the GARCH (1.1) parameters are 1, while the alternative hypothesis states that the coefficient of the GARCH (1.1) parameters are zero. The alternative hypothesis indicates that the volatility returns to a unconditional variance mean, while the null hypothesis indicates a conditional variance unit root. Mathematically can this be expressed as:
H0: : α + β ≥ 1 H1: 𝛼𝛼 + 𝛽𝛽 < 1
Where 𝛼𝛼 + 𝛽𝛽 represents the coefficient of the ARCH (𝛼𝛼) and the GARCH(𝛽𝛽) term and 𝜔𝜔 the unconditional variance, in the GARCH(1,1) model (see methodology).
Additionally, an increase in the volatility of the exchange rate is expected to increase the volatility of the stock return. Therefore a positive relationship between the volatility of the exchange rate and the volatility of stock returns is expected. For the estimations the volatility spill-over effect, the next hypothesis can be made:
Hypothesis 2.2
The null hypothesis for the volatility of the stock returns is that the coefficient of the exchange rate variable in the GARCH (1.1)-model equals zero, while the alternative hypothesis states that the coefficient of the exchange rate variable in the GARCH (1.1)-model is bigger than zero. The alternative hypothesis indicates that the exchange rate volatility has a spill-over effect on the SMI return. Mathematically can this be expressed as:
H0: 𝜇𝜇 = 0 H1: 𝜇𝜇 > 0
II.2 Macroeconomic control variables
For the Ordinary least squares regression (further referred to as: “OLS-regression”) to give a precise estimation, it is necessary to include as many macroeconomic variables – that influence the stock return – as possible. The selection of the macroeconomic variables is considered arbitrary in nature, which makes the selection of the explanatory variables subjective. Unfortunately, this is an unavoidable problem according to Fama (1991). However, prior research suggests that a number of factors may be relevant with regard to stock returns. These variables are the money supply, exchange rates, interest rates on bonds and inflation. Although the relationship between macroeconomic variables and the stock returns are not considered to be entirely one direction, it is generally assumed that the stock prices depend more on the macro economy than the other way around (Chen et al, 1986). For the approach used in this thesis – which is to investigate the effect of the macroeconomic variables and the announcement variables on the stock return – it is required to make the assumption that the stock prices are endogenous, relative to the macroeconomic variables (Perron, 1986). The shock from the unpegging is also considered exogenous and not a result of underlying market variations.
The reason for implementing delay variables is the lag in the production of information concerning the macroeconomic variables. This information about the macroeconomic variable is not always instantaneously incorporated into the stock market prices and is especially important for variables that are composed on a monthly basis. (Cheung et al, 1997). Hence the money supply variable and the inflation rate variable are lagged by 1 month, in accordance with Bilson et al (2001).
All the variables are in percentage change form as done by Bilson et al (2001), to exclude possible stationarity problems. Hereafter, the justification for the macroeconomic variables: The world return index (further referred to as: “world return”) is generally assumed to affect the SMI return because of the global connection between stock markets. A change in the world return is expected to have a major positive effect on the SMI stock return. The changes in the money supply are thought to change the equilibrium of the money market. This is assumed to have an effect on the prices of assets of both companies and investors. According to the Monetary Portfolio Theory; a change in the money supply has a positive relationship with the stock returns (Cooper, 1974).
Inflation is commonly thought to be hedged when investing in stocks instead of money, because the real value of the company is expected to be revised with the amount of the inflation, consequently keeping the real rate of return unaffected (Day, 1984). However,
this is only when the monetary assets of the companies are not taken into consideration. Most companies do hold money to cover liquidity problems, thus creating a form of inflation-risk to the stock prices. The precise relationship between the inflation rate and stock returns is not very clear, because some studies were done in times of very high inflation which was deemed problematic. Then again, the current deflationary pressure is also not considered to be a stimulant for the stock returns (Gallagher & Taylor, 1986). Although the effect of the inflation rate on stock return is controversial, it should be implemented as a control variable to diminish the risk of omitted variable bias.
As the exchange risk has been explicitly discussed in the paragraphs above, the
exchange rate variable does not need an extensive clarification. The exchange rate is expected to have a positive effect on the stock return because an increase in the exchange rate is
expected to increase the competitiveness of the listed companies and increase their possible future earnings (Bilson et al, 2001).
The interest rate is used because 5 out of the 20 companies in the SMI are financial institutions, which depend on the interest rate for a part of their future earnings. A change in this interest rate has therefore an expected effect on the returns of these five companies. Choi et al found a positive relationship between change interest rate and stock returns for financial companies. (Choi et al, 1992),
Finally, the oil price variable is included because it is used in a lot of production processes and cannot be omitted, according to Sadorsky (1999): ‘‘Oil is so significant in the international economy that forecasts of economic growth are routinely qualified with the caveat: ‘provided there is no oil shock.’” The earnings will be lower as production costs increase when the oil prices rise. Thus, the oil price is assumed to have a negative effect on the stock returns.
III. Data
All the variables are collected from the DataStream database; are based on the Swiss economy; and are expressed in compounded form. In addition, they are monthly configured where the sample period spans from January 2012 till April 2016. Where possible are variables also daily configured in the same period. The announcement happened in January 2015 at approximately 4/5th of the whole sample period. All the return and percentage change variables are based on the formula:
𝑅𝑅𝑡𝑡 = (𝑋𝑋𝑡𝑡− 𝑋𝑋𝑋𝑋𝑡𝑡−1𝑡𝑡−1)
where 𝑋𝑋𝑡𝑡 is the unadjusted value. This is due to the fact that you cannot extract the percentage change form of the variables from the Datastream database.
The return on the Swiss market index consists of 20 major companies on the Swiss stock exchange market, 5 of which are financial institutions while the rest are mostly production companies, the choice for the use of this index needs no further explanation. The return of the world market index variable (𝑅𝑅𝑤𝑤,𝑡𝑡) is the MSCI World Index. The reason for this choice is because it is used in numerous articles (Patro et al, 2013; Bilson et al, 2001; etc.) and is configured of the stock exchange markets of 23 developed markets countries.8 The exchange rate variable used is the real price of 1 Euro in Swiss francs. The reason why this exchange rate was used and not the traded-weighted index is because of the previous peg to the Euro and the possible information this could give with regard to the event. The Swiss money supply is measured in M2 because the financial institutions in the SMI depend on more than only the tangible money supply in M1. Therefore the savings deposits and other time deposits are also included in the variable. The interest rate variable is measured in the return of a 3 month government bond and the inflation rate variable is the Swiss consumer price index. The oil price variable is the CMCI Brent crude oil price on a 1 year price index from UBS Bloomberg.9 All the variables have been plotted and can be found in Appendix 1.
8
According to the website: https://www.msci.com/world 9
constant maturity commodity indices: “CMCI Brent Crude Oil measures the collateralised returns from a basket of Brent Crude Oil futures contracts. It is designed to be representative of the entire liquid forward curve of each commodity in the Index.” – UBS Bloomberg (2010)
The conditional variance, that is expected to be described by the GARCH (1.1) – model, depends linearly on the past behaviour of the error terms. Therefore the residuals need to be implemented as a dataset, which will be done by using the previous stated variables.
IV. Methodology
To extract most of the microeconomic explanatory power on the variation in the stock returns from the model, the dependent variable will need to be diversified. The use of the return on the SMI as the stock return variable will do precisely this, because of the diversification argument in capital market theory (Chen et al, 1986). Chen et al, state that only the general macroeconomic and systematic variables will remain as explanatory variables when the market index is chosen instead of the separate stock returns. The next models will not hold any forecasting value in modelling the expected returns, but are introduced to examine the effects of the macroeconomic variables in the period around the unpegging of the Swiss franc. All variables will be tested for correlation and stationarity. Additionally, the Breusch-Pagan / Cook-Weisberg heteroskedasticity test will be used for heteroskedasticity testing.
For the first hypothesis (1.1) to be tested, it is important to use a time series model that can determine the effect of the announcement on the stock price and the change in the trend, while keeping attention for the regular noise of (Chatfield 2000). Therefore the event study methodology used by Patro et al (2013) is used, which uses an abnormal return variable to distinguish the effect of the researched announcement from global market deviations. In order to compose the abnormal return variable it is first needed to do an OLS-regression of the SMI return on the world return.
𝑅𝑅𝑡𝑡= 𝛼𝛼 + 𝛽𝛽 ∗ 𝑅𝑅𝑤𝑤,𝑡𝑡+ 𝜀𝜀𝑡𝑡 (1)
Where variable 𝑹𝑹𝒕𝒕 is the Swiss market index return and variable 𝑹𝑹𝒘𝒘,𝒕𝒕 is return on the MSCI world Index. 𝛼𝛼 is a constant and 𝜀𝜀𝑡𝑡 the error term. The abnormal return is constructed by
including the estimation parameters for 𝜶𝜶 and 𝜷𝜷 in eq. 1 and the indices. By making this abnormal return variable, the effect of the world market on the real return rate is excluded.
𝐴𝐴𝑅𝑅𝑡𝑡= (𝑅𝑅𝑡𝑡− 𝛼𝛼� − 𝛽𝛽̌ ∗ 𝑅𝑅𝑤𝑤,𝑡𝑡) (2)
By regressing the abnormal return to the announcement day dummies and the control variables (i.e.: exchange rate change: 𝐸𝐸𝑥𝑥𝑡𝑡; interest rate change: 𝐼𝐼𝑡𝑡; Oil prices change: 𝑂𝑂𝑂𝑂𝑙𝑙𝑡𝑡; inflation rate change: 𝐼𝐼𝐹𝐹𝑡𝑡−1; money supply change: 𝑀𝑀𝑆𝑆𝑡𝑡−1) it is possible to test the hypothesis that there is a significant overshooting effect on the Swiss market index in the month of the announcement. For the abnormal returns to be tested, the event date has to be specified. In this case the date of event is specified as TA, which indicates the month of the announcement. Therefore the announcement dummy should be the only dummy variable that is significant. The following model will be used with a monthly return interval:
𝐴𝐴𝑅𝑅𝑡𝑡 = 𝛼𝛼1+ 𝛽𝛽 ∗ 𝐴𝐴𝐷𝐷𝑡𝑡+ 𝛾𝛾1∗ 𝐵𝐵𝐴𝐴𝐷𝐷𝑡𝑡+ 𝛾𝛾2∗ 𝑃𝑃𝐴𝐴𝐷𝐷1𝑡𝑡+ 𝛾𝛾3∗ 𝑃𝑃𝐴𝐴𝐷𝐷2𝑡𝑡+ 𝜃𝜃 ∗ 𝑀𝑀𝑆𝑆𝑡𝑡−1+ 𝜗𝜗 ∗ 𝐼𝐼𝐹𝐹𝑡𝑡−1+ 𝜇𝜇 ∗ 𝐸𝐸𝑥𝑥𝑡𝑡+ 𝜋𝜋 ∗ 𝐼𝐼𝑟𝑟𝑡𝑡+ 𝜌𝜌 ∗ 𝑂𝑂𝑂𝑂𝑙𝑙𝑡𝑡+ 𝜀𝜀𝑡𝑡 (3)
Where 𝐴𝐴𝑅𝑅𝑡𝑡 is the abnormal return on the SMI at time 𝑡𝑡, 𝐴𝐴𝐷𝐷𝑡𝑡 is the announcement dummy, where 𝐴𝐴𝐷𝐷𝑡𝑡=1 if t = TA and zero otherwise, 𝐵𝐵𝐴𝐴𝐷𝐷𝑡𝑡 is the pre announcement month dummy, where 𝐴𝐴𝐷𝐷𝑡𝑡=1 if t = TA-1 and zero otherwise, 𝑃𝑃𝐴𝐴𝐷𝐷𝑂𝑂𝑡𝑡 are the post announcement month dummies, where 𝐴𝐴𝐷𝐷𝑡𝑡=1 if t = TA+𝑂𝑂 and zero otherwise, 𝑀𝑀𝑆𝑆𝑡𝑡−1 is the percentage change in a money supply variable at time 𝑡𝑡 − 1, 𝐼𝐼𝐹𝐹𝑡𝑡−1 is the inflation rate change at time 𝑡𝑡 − 1, 𝐸𝐸𝑥𝑥𝑡𝑡 is the percentage change in a exchange rate variable at time 𝑡𝑡, 𝐼𝐼𝑟𝑟𝑡𝑡 is the percentage change in an interest rate variable in time 𝑡𝑡, 𝑂𝑂𝑂𝑂𝑙𝑙𝑡𝑡 is the percentage change in an oil price variable.
To analyse the effect of the explanatory variables on the longer term (from the announcement and forth) and to test the second and third hypotheses (1.2 and 1.3), the real return of the SMI will be used. The abnormal return methodology is essentially made for a shock effect around the period of the event, and is not necessary toward longer-term effects as the longer-term level effect does not have to be “abnormal” to still have an effect on the real return. Therefore, the 𝑅𝑅𝑤𝑤,𝑡𝑡 will be reinstalled as an explanatory variable in the model to exclude omitted variable bias, like the model made by Bilson et al (2001). To examine if the policy change has a significant effect on the mean of SMI return, a post announcement dummy variable will be used. The model is given as:
𝑅𝑅𝑡𝑡 = 𝛼𝛼1+ 𝛽𝛽 ∗ 𝑅𝑅𝑤𝑤,𝑡𝑡+ 𝛿𝛿 ∗ 𝐴𝐴𝑃𝑃𝑡𝑡+ 𝜃𝜃 ∗ 𝑀𝑀𝑆𝑆𝑡𝑡−1+ 𝜗𝜗 ∗ 𝐼𝐼𝐹𝐹𝑡𝑡−1+ 𝜇𝜇 ∗ 𝐸𝐸𝑥𝑥𝑡𝑡+ 𝜋𝜋 ∗ 𝐼𝐼𝑟𝑟𝑡𝑡+ 𝜌𝜌 ∗ 𝑂𝑂𝑂𝑂𝑙𝑙𝑡𝑡+ 𝜀𝜀𝑡𝑡 𝑡𝑡 (4)
Where 𝑅𝑅𝑡𝑡 is the real return of the SMI at time 𝑡𝑡, 𝑅𝑅𝑤𝑤,𝑡𝑡 is the return of the world index at time 𝑡𝑡, 𝐴𝐴𝑃𝑃𝑡𝑡 is the post announcement dummy, where 𝐴𝐴𝑃𝑃𝑡𝑡=1 if t > TA and zero otherwise, the other variables are the macroeconomic control variables as stated in equation 3.
Regarding the effects of the announcement on the volatility of the stock return, a GARCH model is used. Before introducing the GARCH model it is important to analyse and conclude that there is indeed a change in the volatility among the whole period. Therefore the Breusch-Pagan / Cook-Weisberg heteroskedasticity test will be used to confirm the basic assumption of heteroskedasticity that is expected. If the homoskedasticity is not rejected for the abnormal return, the same test will be done on the real return of SMI. Readjusting the model to the real return of the SMI makes it possible for the change in volatility to still be examined. Besides, it also gives the opportunity to see to which extend the SMI return volatility reacts to the volatility of the world index return as an explanatory variable.
The purpose of the GARCH(1.1) model is to establish the fact that there is a spill-over effect from the volatility of the exchange rate to the volatility of the return rate and to establish if there is persistence in the volatility shift, i.e. a variance unit root (Lamoureux & Lastrapes, 1990). The GARCH(1.1) model is a derivative of the ARCH model and can explain a difference in volatility between time periods, and additionally estimate the effect of the variance of a exogenous variable to the conditional variance of the dependent variable. The degree to which conditional variance is permanent is particularly important for this thesis.
For the GARCH(1.1) model too be admissible, two conditions must be satisfied. First, the unconditional variance needs to be stationary according to Lastrapes & Lamoureux (1990). This means that there is proof of auto and serial correlation between the lagged variances of the dependent variable. This will be tested by doing a autocorrelation test and an Lagrange-Multiplier ARCH test, for the serial correlation. Secondly, the coefficients of the general variance model (eq. 5.5) are not allowed to be negative, which means that: 𝛼𝛼 > 0, 𝜔𝜔 > 0, 𝛽𝛽 > 0. Otherwise the GARCH(1.1) test makes no sense, according to Engle (2001).
It should be noted that for variance effects to be estimated, the volatility of the explanatory variables will be researched. Since the announcement dummy variables have no unconditional volatility, the dummy variables do not hold any descriptive meaning in the use of the GARCH(1.1)-model and will be omitted. This does not create a problem for the hypothesis testing, since the coefficients of the ARCH and GARCH terms are the descriptive terms for the persistence in the volatility hypothesis (2.2), and the volatility of the exchange rate variable – as an indicator of the exchange risk – is the variable of interest for the spillover hypothesis (2.1).
The model consists of a mean equation, and a variance equation that is derived from the mean equation. The mean equation to test the hypothesis is represented by:
𝐴𝐴𝑅𝑅𝑡𝑡 = 𝛼𝛼 + 𝜇𝜇 ∗ (𝑒𝑒𝑥𝑥𝑒𝑒𝑙𝑙𝑒𝑒𝑒𝑒𝑒𝑒𝑡𝑡𝑒𝑒𝑟𝑟𝑒𝑒 𝑣𝑣𝑒𝑒𝑟𝑟𝑂𝑂𝑒𝑒𝑣𝑣𝑙𝑙𝑒𝑒𝑠𝑠)𝑡𝑡+ 𝜀𝜀𝑡𝑡 (5.1) And if 𝐴𝐴𝑅𝑅𝑡𝑡 is not heteroskedastic:
𝑅𝑅𝑡𝑡 = 𝛼𝛼 + 𝜇𝜇 ∗ (𝑒𝑒𝑥𝑥𝑒𝑒𝑙𝑙𝑒𝑒𝑒𝑒𝑒𝑒𝑡𝑡𝑒𝑒𝑟𝑟𝑒𝑒 𝑣𝑣𝑒𝑒𝑟𝑟𝑂𝑂𝑒𝑒𝑣𝑣𝑙𝑙𝑒𝑒𝑠𝑠)𝑡𝑡+ 𝜀𝜀𝑡𝑡 (5.2)
Where 𝐴𝐴𝑅𝑅𝑡𝑡(𝑅𝑅𝑡𝑡) is the abnormal (real) return at time t, 𝛼𝛼 is a constant, (𝑒𝑒𝑥𝑥𝑒𝑒𝑙𝑙𝑒𝑒𝑒𝑒𝑒𝑒𝑡𝑡𝑒𝑒𝑟𝑟𝑒𝑒 𝑣𝑣𝑒𝑒𝑟𝑟𝑂𝑂𝑒𝑒𝑣𝑣𝑙𝑙𝑒𝑒𝑠𝑠)𝑡𝑡 are the explanatory variables and 𝜀𝜀𝑡𝑡 is the error term at time t which follows a normal distribution.
For the use of this model is the distribution of the error term (𝜀𝜀𝑡𝑡) very important. The conditional variance that is expected to be described by the GARCH (1.1) – model depends linearly on the past behaviour of the error terms. Therefore a residuals variable needs to be implemented to examine the autocorrelation (as mentioned above), in accordance with the next model:
𝜀𝜀𝑡𝑡 = 𝐴𝐴𝑅𝑅𝑡𝑡− (𝛼𝛼� + 𝜃𝜃� ∗ 𝑀𝑀𝑆𝑆𝑡𝑡−1+ 𝜗𝜗̌ ∗ 𝐼𝐼𝐹𝐹𝑡𝑡−1+ 𝜇𝜇� ∗ 𝐸𝐸𝑥𝑥𝑡𝑡+ 𝜋𝜋� ∗ 𝐼𝐼𝑟𝑟𝑡𝑡+ 𝜌𝜌� ∗ 𝑂𝑂𝑂𝑂𝑙𝑙𝑡𝑡) (5.3) Or, if the abnormal return is not considered heteroskedastic;
𝜀𝜀𝑡𝑡 = 𝑅𝑅𝑡𝑡− �𝛼𝛼� + 𝜎𝜎� ∗ 𝑅𝑅𝑤𝑤,𝑡𝑡+ 𝜃𝜃� ∗ 𝑀𝑀𝑆𝑆𝑡𝑡−1+ 𝜗𝜗̌ ∗ 𝐼𝐼𝐹𝐹𝑡𝑡−1+ 𝜇𝜇� ∗ 𝐸𝐸𝑥𝑥𝑡𝑡+ 𝜋𝜋� ∗ 𝐼𝐼𝑟𝑟𝑡𝑡+ 𝜌𝜌� ∗ 𝑂𝑂𝑂𝑂𝑙𝑙𝑡𝑡� (5.4)
Where 𝐴𝐴𝑅𝑅𝑡𝑡(𝑅𝑅𝑡𝑡) is the abnormal (real) return on the SMI at time 𝑡𝑡,and the other variables are the estimated coefficients of equation 3 and 4. Respectively.
If the error terms are considered to be auto correlated and give signs of an ARCH effect, the general variance model can be made. This general variance model of the GARCH(1.1) model can be notated as:
𝜎𝜎𝑡𝑡2 = 𝜔𝜔 + 𝜇𝜇 ∗ (𝑒𝑒𝑥𝑥𝑒𝑒𝑙𝑙𝑒𝑒𝑒𝑒𝑒𝑒𝑡𝑡𝑒𝑒𝑟𝑟𝑒𝑒 𝑣𝑣𝑒𝑒𝑟𝑟𝑂𝑂𝑒𝑒𝑣𝑣𝑙𝑙𝑒𝑒𝑠𝑠)𝑡𝑡+ 𝛼𝛼 ∗ 𝜎𝜎𝑡𝑡−12 ∗ 𝜀𝜀𝑡𝑡−12 + 𝛽𝛽 ∗ 𝜎𝜎𝑡𝑡−12 (5.5)
Where 𝜔𝜔 expresses the unconditional variance, 𝜇𝜇𝑖𝑖 expresses the effects of explanatory variable 𝑂𝑂 on the variance of the dependent variable, 𝛼𝛼 the past variance times the squared residuals, and 𝛽𝛽 the past variances of the dependent variable. (Engle, 2001). The 𝜎𝜎𝑡𝑡−12 ∗ 𝜀𝜀𝑡𝑡−12 term depicts the ARCH term and the 𝜎𝜎𝑡𝑡−12 depicts the GARCH term. The ARCH term presents the effect of the previous return on the current variance, and the GARCH term presents the effect of the previous variance on the current variance
This general variance equation can be rewritten for the SMI return variance by implementing the explanatory variables of equation 3 (with the exemption of the dummy variables) in equation 5.5. The GARCH (1.1) – variance model of abnormal SMI return is expressed as:
𝜎𝜎𝑡𝑡2 = 𝜔𝜔 + 𝜃𝜃 ∗ 𝑀𝑀𝑆𝑆𝑡𝑡−1+ 𝜗𝜗 ∗ 𝐼𝐼𝐹𝐹𝑡𝑡−1+ 𝜇𝜇 ∗ 𝐸𝐸𝑥𝑥𝑡𝑡+ 𝜋𝜋 ∗ 𝐼𝐼𝑟𝑟𝑡𝑡+ 𝜌𝜌 ∗ 𝑂𝑂𝑂𝑂𝑙𝑙𝑡𝑡+ 𝛼𝛼 ∗ 𝜎𝜎𝑡𝑡−12 ∗ 𝜀𝜀𝑡𝑡−12 + 𝛽𝛽 ∗ 𝜎𝜎𝑡𝑡−12 (5.6)
Or, if the abnormal return is not considered heteroskedastic: The GARCH (1.1) – variance model of real SMI return:
𝜎𝜎𝑡𝑡2 = 𝜔𝜔 + 𝜎𝜎 ∗ 𝑅𝑅𝑤𝑤,𝑡𝑡 + 𝜃𝜃 ∗ 𝑀𝑀𝑆𝑆𝑡𝑡−1+ 𝜗𝜗 ∗ 𝐼𝐼𝐹𝐹𝑡𝑡−1+ 𝜇𝜇 ∗ 𝐸𝐸𝑥𝑥𝑡𝑡+ 𝜋𝜋 ∗ 𝐼𝐼𝑟𝑟𝑡𝑡+ 𝜌𝜌 ∗ 𝑂𝑂𝑂𝑂𝑙𝑙𝑡𝑡+ 𝛼𝛼 ∗ 𝜎𝜎𝑡𝑡−12 ∗ 𝜀𝜀𝑡𝑡−12 + 𝛽𝛽 ∗ 𝜎𝜎𝑡𝑡−12 (5.7)
The GARCH (1.1) model will estimate if the regression has a mean returning volatility and if there is a spill-over effect of the volatility of the explanatory variables. These will be examined to estimate the effects on the variance of the SMI return.
V.Results
V.1 Results on average returns
Time series are usually not considered to have a complete random walk because they may be dependent through time, i.e. they tend to be affected by their former values (Chatfield 2000). Therefore, it is important to investigate if there is a possible relationship between the value of a variable in time t and the value in time: t-1. This relationship can come from the value itself, which indicates an autoregressive movement, or the relationship between the residuals of the variable in time t and time t-1, which indicates a moving average. If they would be non-stationary the results of an OLS-regression may result in invalid estimates and these regressions are called spurious regressions, which have high t –values and R2 values but their conclusions hold no economic meaning (Philips 1986). To counter this problem, the original variables have been transmitted into percentage change, and return variables to make them stationary. All the explanatory variables in the model with the exception of the dummy variables, have been tested for a unit root by using the augmented dickey fuller test. The results are depicted in Table 1 and are compared to the critical values in table 2. These result lead to an overall rejection of a unit root for any of the variables, which creates the necessary possibility to use the OLS regression. If, however, the SMI returns are heteroskedastic, the Dickey-Fuller test might not give the right significance because the ADF test is computed using non robust standard errors. This implies that the standard errors in the ADF test are homoskedastic-only.
Table 1 Augmented Dickey-Fuller test Table 2. ADF critical values
Variable t- statistic 𝑨𝑨𝑹𝑹𝒕𝒕 - 4.761** 𝑹𝑹𝒕𝒕 - 5.614** 𝑹𝑹𝒘𝒘,𝒕𝒕 - 6.465** 𝑴𝑴𝑺𝑺𝒕𝒕−𝟏𝟏 - 4.654** 𝑬𝑬𝒙𝒙𝒕𝒕 - 4.610** 𝑰𝑰𝒓𝒓𝒕𝒕 - 3.279* 𝑰𝑰𝑭𝑭𝒕𝒕−𝟏𝟏 - 4.574** 𝑶𝑶𝑶𝑶𝒍𝒍𝒕𝒕 - 2.994* Crit value 1% 5% 10% - 3.587 - 2.933 - 2.601
Note: *indicates significant at the 5% level; **indicates significant at the 1% level
The heteroskedasticity of the abnormal return variable is tested by doing the Breusch-Pagan / Cook-Weisberg test for heteroskedasticity and is depicted in table 3. Since the
heteroskedasticity test does not reject the null hypothesis of the abnormal return variable to be homoskedastic, the aforementioned assumption that the results of the ADF-test give the right significance can be made.
Table 3. Heteroskedasticity test Type Monthly DF 9 Chi2 statistic 6.86 P- value 0.3341
The second test to exclude possible estimation problems with the model is the correlation test. With this test the possibility of multicollinearity can be measured. In case the model contains variables with perfect multicollinearity, it will be impossible to compute the correct OLS estimator (Stock & Watson 2015). From the values of table B. (included in Appendix 3) can be concluded that there is no indication of perfect multicollinearity, but there is a form of imperfect multicollinearity among the explanatory variables, namely, between the announcement dummy and the exchange rate variable. This does not make the whole model biased, but can give an imprecise t-statistic of the coefficient of the announcement dummy or the exchange rate variable because of an increase in the standard error of the variable. With the addition of the abnormal return variable in table B (Appendix 3), it is possible to examine the vector of the relationship between the dependent and independent variables, and to assess if these correspond with the assumption in the literature review.
Both the announcement dummy and the post announcement dummy have, as assumed, a negative correlation with the abnormal and real SMI returns. For the macroeconomic variables it is different. As expected, the exchange rate change does have a positive correlation and the oil prices a negative relation with the abnormal returns. The money supply and the interest have a very small, but unexpected correlation. The effects of the interest rate change and the money supply change were expected to be positive, because of the financial institutions in the stock market index. Instead, the correlations are tested to
have a negative effect on the abnormal returns. This may be due to an insignificant correlation between the interest rate and money supply change, and the abnormal return.
The results for the OLS regression with regard to the first hypothesis are shown in table 4.1. The objective of this regression is to reject the null hypothesis that the announcement day has no significant effect on the stock return. Equation 3. is tested using the OLS regression.
Table 4.1
OLS regression on the monthly abnormal return, from January 2012 to April 2016. This table reports the results of the model in equation (3). Standard error are used because the homoscedasticity was not rejected. The T-statistic test the null hypothesis that the coefficient is equal to zero.
Coefficient St. Error T – stat. P- value 95% confidence interval 𝐴𝐴𝐷𝐷𝑡𝑡 -0.06294 0.0065 -2.43 0.020 -0.1147 -0.0105 𝐵𝐵𝐴𝐴𝐷𝐷1𝑡𝑡 -0.0155 0.0269 -0.57 0.569 -0.0699 0.0389 𝑃𝑃𝐴𝐴𝐷𝐷𝑡𝑡 0.0350 0.0248 1.41 0.166 -0.0151 0.0850 𝑃𝑃𝐴𝐴𝐷𝐷2𝑡𝑡 0.0197 0.0258 0.76 0.449 -0.0323 0.0718 𝑀𝑀𝑆𝑆𝑡𝑡−1 0.06256 0.4239 0.15 0.883 -0.8841 0.8470 𝐼𝐼𝐹𝐹𝑡𝑡−1 0.0001 0.0006 0.10 0.924 -0.0011 0.0013 𝐼𝐼𝑟𝑟𝑡𝑡 0.0005 0.0009 0.56 0.697 -0.0015 0.0022 𝑂𝑂𝑂𝑂𝑙𝑙𝑡𝑡 -0.1519 0.1200 -1.27 0.212 -0.4756 0.0897 𝑐𝑐𝑒𝑒𝑒𝑒𝑠𝑠𝑡𝑡𝑒𝑒𝑒𝑒𝑡𝑡 -0.0002 0.0033 0.88 0.932 -0.0070 0.0065 Note: As stated above, there was some evidence of imperfectly multicollinearity between the announcement day dummy and the exchange rate variable. To test the announcement day variable without the multicollinearity, the exchange rate variable was omitted.
Table 4.2 Overall statistics of the model. General summary
observations 52 F(6, 45) 4.09 Prob > F 0.024* R-squared 0.1963
In the results shown in table 4.1, the announcement dummy is significant, while the other dummy variables are not. With the estimated t-value of -2.43 is the null hypothesises rejected by a 5% level that there is no significant abnormal return in the month of the
announcement, opposed to the announcement dummies surrounding the announcement which cannot be rejected. Therefore it can be concluded that the announcement had a significant negative overshooting effect on the Swiss market index. None of the control variables - that are not omitted - had an effect on the stock return in this particular timeframe. Unfortunately, the exchange rate variable had to be omitted because of high correlation with the
announcement dummy. This could indicate that the announcement had a similar effect on the exchange rate as on the dummy variable (a significant spike at the time of the
announcement). Regressing the announcement day dummy to the exchange rate variable seems to acknowledge this statement by rejecting the null hypothesis that the announcement day has no effect on the exchange rate variable, with a t-statistic of -13.69 and a p-value that is lower than 1%.
For the second hypothesis test with regard to the permanent effect of the announcement, it is not necessary to exclude a variable, because there are no multicollinearity problems. Hence, the exchange rate variable is no longer omitted. The results for the OLS regression with regard to the longer-term hypotheses (1.2 & 1.3) are shown in table 5.1. The objective of this regression is to reject the null hypothesis that the announcement has no significant effect on the mean of the SMI return. Equation 4. is tested using the OLS regression.
Table 5.1
OLS regression on the monthly real return of the SMI, from January 2012 to April 2016. This table reports the results of the model in equation (4). Robust Standard error is used for heteroskedasticity. The T-statistic test the null hypothesis that the coefficient is equal to zero.
Coefficient St. Error T – stat. P- value 95% confidence interval
𝑅𝑅𝑤𝑤,𝑡𝑡 0.7539 0.1108 6.72 0.000 0.5307 0.9772 𝐴𝐴𝑃𝑃𝑡𝑡 -0.0094 .0073 -1.29 0.204 -0.0241 0.0053 𝑀𝑀𝑆𝑆𝑡𝑡−1 -0.0178 0.5568 -0.07 0.975 -1.140 1.105 𝐼𝐼𝐹𝐹𝑡𝑡−1 0.0000 .0011 0.04 0.980 -.0021 0.0014 𝐸𝐸𝑥𝑥𝑡𝑡 0.4218 0.1620 2.60 0.013 .0978 0.6550 𝐼𝐼𝑟𝑟𝑡𝑡 0.0004 0.0016 0.34 0.737 -0.0014 0.0020 𝑂𝑂𝑂𝑂𝑙𝑙𝑡𝑡 -0.1718 0.1148 -1.21 0.142 -0.3989 0.0994 𝑐𝑐𝑒𝑒𝑒𝑒𝑠𝑠𝑡𝑡𝑒𝑒𝑒𝑒𝑡𝑡 0.0035 0.0050 0.70 0.485 -0.0042 0.0095
Table 5.2 Overall statistics of the model. General summary
observations 51 F(6, 44) 10.90 Prob > F 0.0000*** R-squared 0.5982
After assessing table 5.1, the post announcement dummy does not seem to have a significant effect on the mean of the abnormal return. Although the coefficient is indeed negative, the t-statistic is not significant for a 5% or 10% rejection of the null hypothesis. Therefore the expected permanent effect of the policy change on the mean of the SMI return cannot be concluded. It is possible that this is due to the small amount of observations (51) in the regression, which makes the test less reliable. As expected does the world index return have a significant effect on the SMI return.
The exchange rate has a significant effect on the abnormal returns with a t- statistic of 2.60. The null hypothesis of it not a having an effect, can be rejected with 95% certainty. The exchange rate variable has a positive coefficient, thus a revaluation (decline in the exchange rate) will lead to a decline in the SMI returns, because it decreases the expected future earnings. The oil price tstatistic is the second closest to being significant with a tvalue of
-1.21. which gives a p-value of 0.232. Although the negative coefficient was expected, no conclusions can be made from this value because of the significance.
The other macroeconomic variables seem to have no effect on the SMI returns at all. This conclusion may be a bit biased because these macroeconomic variables had no significant reaction to the announcement. It is possible (and generally assumed) that these variables have dp an effect on the SMI return when a longer time frame is taken.
V.2 Results on return volatility
The next regression will involve the GARCH (1.1) model to analyse the possible increase in variance after the change. Although the abnormal return is the best fit to test an event, table 3 in the previous paragraph has shown that the abnormal return was significantly proven to be homoscedastic. Therefore the hypothesis of the GARCH-model relating to the abnormal return cannot give the satisfactory results with regard to the volatility. The real return is better suitable for testing if there is proof of an increased volatility in the Swiss market index. As the homoskedasticity is significantly rejected for both the monthly and daily configured real SMI return in Table 6. The real return of the SMI is preferred model and the equations 5.2; 5.4 and 5.7 will be used to test hypotheses 2.1 and 2.2.
Table 6. Heteroskedasticity test on real returns of SMI Heteroskedasticity test
Type Monthly Daily
DF 6 3
Chi2 statistic 22.91 12.65
P- value 0.0008 0.0055
For the usability of the GARCH model it is necessary to test for autocorrelation. The tested squared residuals come from the equation 5.4. whereas the autocorrelations of the squared residuals can be found in Table A.1 in Appendix 2. If there would be no autocorrelation, there could not be an ARCH effect and the GARCH model could not be tested (Engle, 2001). The autocorrelation in Table A.1 shows significant statistical evidence to reject the null hypothesis of no ARCH effect for both the daily and monthly configured real return models. To further test the serial correlation, an ARCH LM test has to be done. This ARCH LM test
is included as table A.2 in Appendix 2.From table A.2 can be significantly concluded that the null hypothesis of no arch effects can be rejected for the daily configured model, but not for the monthly configured model. It is expected that the monthly configured GARCH (1.1) model holds no meaning because of a lack of serial correlation.
Table 7. Results of the GARCH (1.1) model in equation 5.7 for both monthly and daily real return. In the daily configured model the money supply change, inflation rate change and oil price change are omitted, because of the lack of daily information.
Variance Monthly: 𝑅𝑅𝑡𝑡 Daily: 𝑅𝑅𝑡𝑡
𝑅𝑅𝑤𝑤,𝑡𝑡 0.6752668* (0.1033741) 0.5957945*** (.0324505) 𝐸𝐸𝑥𝑥𝑡𝑡 0.4181163 (.2109223) 0.3189094*** (0.0167624) 𝐼𝐼𝑟𝑟𝑡𝑡 0.0003651 (.0022774) -0.0005671 (.0010889) 𝑀𝑀𝑆𝑆𝑡𝑡−1 0.0006751 (0.00329) 𝐼𝐼𝐹𝐹𝑡𝑡−1 -0.0004712 0.0011995 𝑂𝑂𝑂𝑂𝑙𝑙𝑡𝑡 -0.0708744 (0.0938618) 𝛼𝛼 0.4732803 (0.4402013) 0.4221834*** (0.0832671) 𝛽𝛽 -0.4406056 (0.6015004) 0.2818941** (0.1324265) 𝜔𝜔 0.0004693 (0.0002776) 0.0000288*** (8.84e-06) Observations: 51 490
Note: The coefficient is the first number in the cell and the standard error is stated between brackets. Besides:* = p < 10%, ** = p < 5%,*** = p =< 1%.
As expected after the results of the ARCH LM test, is the monthly configured GARCH (1.1) model unusable. This can be concluded from the GARCH (1.1) model by examining the variance coefficients of the model. 𝛼𝛼, 𝛽𝛽 and 𝜔𝜔 all need to be higher than zero in order for the GARCH (1.1) model to be admissible. As table 7 shows, the 𝛽𝛽 is negative, which makes the monthly configured model unusable. A lager sample size is suggested to
benefit the usability of the model. For the daily configured model are both conditions met. Namely, the auto and serial correlation are validated and 𝛼𝛼, 𝛽𝛽 and 𝜔𝜔 are all positive.
Regarding the hypothesis 2.1, can be concluded that 𝛼𝛼 and 𝛽𝛽 are 0.4221834, respectively 0.2818941. The sum of these coefficients is 0.4221834 + 0.2818941 = 0.7040775. As the parameters are both significant (by the 1% and 5% critical value), the probability of the sum being less than one is also significant. Therefore, the null hypothesis can be rejected. This means there is significant evidence to conclude that the SMI return holds no persistent
variance. Therefore the variance will decay after the variance shock and the effect of previous variances on the current variance diminishes. Although the model forced this hypothesis, the rejection of the null hypothesis was not expected as it does not imply a permanent increase in the volatility because of the policy change.
On hypothesis 2.2. is the null also rejected, because the volatility spill-over effect of exchange rate on the volatility of the SMI is proved to be significant. These results suggests that an increase in the volatility of the exchange rate will increase the volatility of the SMI return with approximately 32%. As there is formerly proved that the volatility is higher in a floating exchange rate policy than a fixed exchange rate policy, the SMI return should have a higher volatility since the change in policy. These two effects seem to contradict themselves. It is possible that the uncertainty of the materialization of the exchange risk and the increase in state risk overshoot the volatility at the moment of the announcement, after which it will decay to its new higher variance mean. This assumption would proof both expectations (for a higher permanent variance mean and a spill-over effect from the exchange rate) to be true. Testing this assumption is not possible with the GARCH(1.1) model
VI. Conclusion
The focus of this thesis was to determine the effects of the announcement and the policy change on the stock return in the SMI. Both the effect on the mean stock return, as on the volatility of the stock return were researched. In order to explain the effect of the announcement on the mean return an OLS regression was used. Additionally, for the description of the effect of the announcement on the volatility of the return, the GARCH(1.1) model was used.
All the used variables were tested beforehand for a unit root to exclude the possibility of spurious regressions and the abnormal and real returns were tested for heteroskedasticity.
By using the abnormal returns model of Patro et al (2013) it was possible to conclude that there was indeed a significant negative effect from the announcement on the mean return of the Swiss market index in the month of the announcement. The effect of an unexpected revaluation was found to overshoot the abnormal stock returns.
The real return model was used for the longer-term hypotheses where the world return was reinstalled as a explanatory variable. The expected negative longer-term effect of the policy change on the mean of the SMI return could not be significantly concluded, although the coefficient suggests this result. It is possible that the number of observations creates this insignificance, and a larger sample for future studies is advised.
Unlike the post announcement dummy, the exchange rate variable did show significance. This finding indicates that there is a positive effect of exchange rate changes on SMI returns, and that a revaluation can be considered bad for the Swiss companies, when the assumption holds that exchange rate changes are exogenous and the stock returns endogenous. The other macroeconomic control variables do not seem to have any effect on the mean of the stock returns in the observed period.
Aside from the mean of the stock returns, is the volatility effect of the announcement harder to measure. A GARCH(1.1) model was used to examine the effects of the policy change and the increase in exchange risk as a result of an exchange rate volatility increase, on the volatility of the stock return. Although the spill-over effect of the volatility of the exchange rate on the volatility of the SMI return is shown to be significant, the increase in the mean of the variance of the stock return by examining a persistence in the variance could not be concluded. The statement that there is a permanent increase in volatility because of the
announcement can therefore not be made. Further studies should show that there is indeed an increase in the volatility of the stock return as a result of the policy change.
Literature
• Adler, M., & Dumas, B. (1983). International portfolio choice and corporation finance: A synthesis. The Journal of Finance, 38(3), 925-984.
• Adler, M., & Dumas, B. (1984). Exposure to currency risk: definition and measurement. Financial management, 41-50
• Andersen, T. G., Bollerslev, T., Diebold, F. X., & Vega, C. (2002). Micro effects of macro announcements: Real-time price discovery in foreign exchange (No. w8959). National bureau of economic research.
• Bilson, C. M., Brailsford, T. J., & Hooper, V. J. (2001). Selecting macroeconomic variables as explanatory factors of emerging stock market returns. Pacific-Basin Finance Journal, 9(4), 401-426.
• Bollerslev, T. (1990). Modelling the coherence in short-run nominal exchange rates: a multivariate generalized ARCH model. The review of economics and statistics, 498-505. • Chatfield, C. (2000). Time-series forecasting. CRC Press.
• Chen, N. F., Roll, R., & Ross, S. A. (1986). Economic forces and the stock market. Journal of business, 383-403.
• Cheung, Y. W., He, J., & Ng, L. K. (1997). What are the global sources of rational variation in international equity returns? Journal of International Money and Finance, 16(6), 821-836.
• Choi, J. J., Elyasiani, E., & Kopecky, K. J. (1992). The sensitivity of bank stock returns to market, interest and exchange rate risks. Journal of banking & finance, 16(5), 983-1004. • Cooper, R. V. (1974). Efficient capital markets and the quantity theory of money. The
Journal of Finance, 29(3), 887-908.
• Day, T. E. (1984). Real stock returns and inflation. The journal of finance, 39(2), 493-502 • Dumas, B., & Solnik, B. (1995). The world price of foreign exchange risk. The journal of
finance, 50(2), 445-479.
• Engle, R. (2001). GARCH 101: The use of ARCH/GARCH models in applied econometrics. The Journal of Economic Perspectives, 15(4), 157-168.
• Fama, E. F. (1981). Stock returns, real activity, inflation, and money. The American Economic Review, 71(4), 545-565.
• Fama, E. F. (1991). Efficient capital markets: II. The journal of finance, 46(5), 1575-1617.
• Freund, C. L., & Pierola, M. D. (2008). Export surges: the power of a competitive currency. World Bank Policy Research Working Paper Series, Vol. 2008
• Gallagher, L. A., & Taylor, M. P. (2002). The stock return–inflation puzzle revisited. Economics Letters, 75(2), 147-156.
• Kanas, A. (2000). Volatility spillovers between stock returns and exchange rate changes: International evidence. Journal of Business Finance & Accounting, 27(3-4), 447-467. • Lamoureux, C. G., & Lastrapes, W. D. (1990). Persistence in variance, structural change,
and the GARCH model. Journal of Business & Economic Statistics, 8(2), 225-234.
• Lastrapes, W. D. (1989). Exchange rate volatility and US monetary policy: an ARCH application. journal of Money, Credit and Banking, 21(1), 66-77.
• Patro, D. K., Wald, J. K., & Wu, Y. (2013). Currency devaluation and stock market response: an empirical analysis. Journal of International Money and Finance, 40, 79-94. • Perron, P. (1989). The great crash, the oil price shock, and the unit root hypothesis.
Econometrica: Journal of the Econometric Society, 1361-1401
• Phillips, P. C. (1986). Understanding spurious regressions in econometrics. Journal of econometrics, 33(3), 311-340.
• Pilbeam, K. (2013). International Finance, 4rd Edition. New York, NY: Palgrave Macmillan. ISBN 978-1-137-34657-5.
• Press release Swiss National Bank (2014) Swiss Balance of Payments and International Investment Position.
• Ranaldo, A., & Söderlind, P. (2010). Safe haven currencies. Review of Finance, rfq007. • Sadorsky, P. (1999). Oil price shocks and stock market activity. Energy Economics,
21(5), 449-469.
• Stock, J. H., & Watson, M. W. (2015). Introduction to econometrics. Boston: Pearson/Addison Wesley, updated 3d version, ISBN: 978-1- 292-07131
• UBS Bloomberg (2010), London Stock Exchange Commodities UBS ETC on UBS Bloomberg CMCI Brent Crude Oil Index,
• Veronesi, P. (1999). Stock market overreactions to bad news in good times: a rational expectations equilibrium model. Review of Financial Studies, 12(5), 975-1007. • Westerfield, J. M. (1977). An examination of foreign exchange risk under fixed and
• Yang, S. Y., & Doong, S. C. (2004). Price and volatility spillovers between stock prices and exchange rates: empirical evidence from the G-7 countries. International Journal of Business and Economics, 3(2), 139.
• Statement of Originality
This document is written by Student Mats Heybroek who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Appendix 1. Variable time plots
1. Abnormal return 2. SMI return
3. world index return 4. Change in inflation rate (in %)
5. change in exchange rate (in %) 6. Change in interest rate (in %)
-.
05
0
.05
AR
Jan 2012 Jan 2013 Jan 2014 Jan 2015 Jan 2016 Date3 -. 1 -. 05 0 .05 .1 MR sw iss
Jan 2012 Jan 2013 Jan 2014 Jan 2015 Jan 2016 Date3 -. 1 -. 05 0 .05 .1 R wo rld
Jan 2012 Jan 2013 Jan 2014 Jan 2015 Jan 2016 Date3 -2 0 -1 0 0 10 Inf Ch an ge
Jan 2012 Jan 2013 Jan 2014 Jan 2015 Jan 2016 Date3 -. 15 -. 1 -. 05 0 .05 X R c ha ng e
Jan 2012 Jan 2013 Jan 2014 Jan 2015 Jan 2016
Date3 -5 0 5 10 15 Ir c ha ng e
Jan 2012 Jan 2013 Jan 2014 Jan 2015 Jan 2016
7. Change in oil prices (in %)
8. SMI overshooting, 50 days prior and 50 days after the announcement
-. 1 -. 05 0 .05 O ilc ha ng e
Jan 2012 Jan 2013 Jan 2014 Jan 2015 Jan 2016
Date3 80 00 85 00 90 00 95 00 SMI 01/11/2014 01/12/2014 01/01/2015 01/02/2015 01/03/2015 01/04/2015 Date2
Appendix 2
Table A.1 Autocorrelation of the squared residuals
Daily Monthly
AC Q-stat P-value AC Q-stat P-value
1 -0.1665 13.659 0.0002 0.7329 29.036 0.0000 2 -0.0154 13.777 0.0010 0.7113 56.944 0.0000 3 -0.1070 19.444 0.0002 0.5963 76.968 0.0000 4 -0.0412 20.286 0.0004 0.5863 96.74 0.0000 5 0.0921 24.505 0.0002 0.5336 113.47 0.0000 6 0.0261 24.844 0.0004 0.4476 125.51 0.0000 7 -0.0486 26.025 0.0005 0.3263 132.05 0.0000 8 -0.0169 26.025 0.0010 0.3009 137.74 0.0000
Table A.2 LM test for Arch effects on 𝑅𝑅𝑡𝑡
Daily Monthly
Lags Chi2 DF P-value Lags Chi2 DF P-value
1 52.148 1 0.0000 1 4.891 1 0.0270
2 44.904 2 0.0000 2 5.584 2 0.0613
3 31.093 3 0.0000 3 6.616 3 0.0852
4 74.543 4 0.0000 4 6.531 4 0.1629
It can be significantly concluded that the null hypothesis of no arch effects can be rejected for the daily configured model, but not for the monthly configured model. Therefore the
Appendix 3.
Table. B Correlation matrices
variables 𝑨𝑨𝑹𝑹𝒕𝒕 𝑹𝑹𝒕𝒕 𝑹𝑹𝒘𝒘,𝒕𝒕 𝑴𝑴𝑺𝑺𝒕𝒕−𝟏𝟏 𝑬𝑬𝒙𝒙𝒕𝒕 𝑰𝑰𝑭𝑭𝒕𝒕−𝟏𝟏 𝑨𝑨𝑫𝑫𝒕𝒕 𝑨𝑨𝑷𝑷𝒕𝒕 𝑰𝑰𝒓𝒓𝒕𝒕 𝑶𝑶𝑶𝑶𝒍𝒍𝒕𝒕 𝑨𝑨𝑹𝑹𝑡𝑡 1.000 𝑹𝑹𝒕𝒕 0.7085 1.000 𝑹𝑹𝒘𝒘,𝒕𝒕 0.0000 0.7058 1.000 𝑴𝑴𝑺𝑺𝒕𝒕−𝟏𝟏 -0.0013 0.0244 0.0359 1.000 𝑬𝑬𝒙𝒙𝒕𝒕 0.3465 0.2842 0.0549 0.0131 1.000 𝑰𝑰𝑭𝑭𝒕𝒕−𝟏𝟏 0.0066 -0.0972 0.1444 -0.0271 0.0883 1.000 𝑨𝑨𝑫𝑫𝒕𝒕 -0.3247 -0.3050 -0.1062 -0.0510 -0.8890 -0.0226 1.000 𝑨𝑨𝑷𝑷𝒕𝒕 -0.2184 -0.2548 -0.1418 -0.1996 -0.1133 0.0455 0.2092 1.000 𝑰𝑰𝒓𝒓𝒕𝒕 -0.0112 0.0297 0.0533 -0.1195 0.0365 0.0853 -0.0235 -0.0565 1.000 𝑶𝑶𝑶𝑶𝒍𝒍𝒕𝒕 -0.1348 0.2224 0.4505 0.1390 0.1765 0.0573 -0.1917 -0.0635 0.2831 1.000 Note:𝐴𝐴𝑅𝑅𝑡𝑡= abnormal return on SMI, 𝑅𝑅𝑡𝑡 = return on SMI; 𝑅𝑅𝑤𝑤,𝑡𝑡= return on MSCI; 𝑀𝑀𝑆𝑆𝑡𝑡−1 = monthly growth in money supply; 𝐸𝐸𝑥𝑥𝑡𝑡 = monthly growth in exchange rate; 𝐼𝐼𝐹𝐹𝑡𝑡−1 = monthly growth in inflation rate; 𝐴𝐴𝐷𝐷𝑡𝑡 = Announcement day dummy; 𝐴𝐴𝐷𝐷2𝑡𝑡 = post announcement dummy; 𝐼𝐼𝑟𝑟𝑡𝑡 = growth in interest rate on government bonds; 𝑂𝑂𝑂𝑂𝑙𝑙𝑡𝑡 = monthly growth in oil price
