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Prague University of Economics and Business Faculty of International Relations
International Business
BACHELOR THESIS
Gold price determinants during selected economic crises
AUTHOR: ANDREJ CHEPELAU
THESIS SUPERVISOR: JAKUB JEDLINSKÝ
YEAR: 2021
2 Declaration of Authorship
The author hereby declares that he compiled this thesis independently, using only the listed resources and literature, and the thesis has not been used to obtain a different or the same degree.
The author grants to University of Economics in Prague permission to reproduce and to distribute copies of this thesis document in whole or in part.
Prague, April 2021 Signature: __________________¨
3 Acknowledgement
I would like to express my sincerest gratitude to my supervisor Mgr. Ing. Jakub Jedlinský, Ph.D.
for the continuous support, for his patience, motivation, and immense knowledge. His guidance was helpful at all times of writing of this thesis.
4 Abstract
The goal of this thesis is to find out which factors that are believed to be strong determinants of the price of gold in the long-run still determine the price of gold in the short-run of economic crises. The theoretical part firstly goes through the various aspects of gold. Then, through literature review, the determinants that are often believed to be determinants of the price of gold in the long-run are found. Then I describe the various methodological approaches in particular literature sources and follow with a description of my approach. The practical part consists of the analysis of chosen determinants and their effect on the price of gold. The findings indicate that the determinants that are generally believed to be important factors of the pricing of gold, in the long run, do not necessarily hold the same relationship during economic crises.
Keywords: gold, economic crises, regression, OLS
JEL classification: G01, C3, C52, C80
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T ABLE OF CONTENTS
Introduction ... 1
1 Gold ... 2
1.1 Characteristics ... 2
1.1.1 Physical aspect of gold ... 2
1.1.2 Economic aspect ... 3
1.2 Determinants found in literature ... 3
2 Methods ... 5
2.1 Research problem ... 5
2.1.1 Problem ... 5
2.1.2 Objectives ... 5
2.2 Research designs ... 6
2.2.1 Levin, Montagnoli, Wright ... 6
2.2.2 Susan Sharma ... 7
2.2.3 Lili, Chengmei ... 7
2.2.4 Elfakhani, Baalbaki, Rizk ... 8
2.2.5 Fan, Fang, Lu ... 9
2.3 My research design ... 9
2.3.1 Data ... 10
2.3.2 Analysis ... 12
3 Analysis ... 14
3.1 Selection of Crises ... 14
3.2 Selection of variables ... 14
3.2.1 Dependent variable ... 14
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3.2.2 Independent variables ... 15
3.3 Analyzing gold price during selected crises ... 18
3.3.1 1st crisis ... 19
3.3.2 2nd crisis ... 25
3.3.3 3rd crisis ... 29
3.3.4 4th crisis ... 32
Conclusion ... 36
List of figures ... 37
Appendix A ... 40
Independent Variables Scatterplots, 1st Crisis ... 40
Independent Variables Scatterplots, 2nd Crisis... 41
Independent Variables Scatterplots, 3rd Crisis ... 42
Independent Variables Scatterplots, 4th Crisis ... 43
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I NTRODUCTION
Gold can be used in many ways in nowadays world. It is used in technology, jewelry, stomatology, and the list could probably go on for quite a while. However, there were also times when it was used as currency and a store of value. And while the former does not apply to gold today, the same can not be said about the latter. We can see that even though gold is not the best-performing asset when it comes to returns on investment, small or big investors often find a little space in their portfolio for this metal and one could even argue that the gold- allocated funds would even grow during times of global crises, which often come with uncertainty, volatility on markets and possibly even inflation. This means that there is some importance to the investing aspect of the mentioned commodity. And a very crucial part of any investment is the price and what factors may affect it. And that would be the aim of this thesis.
This thesis aims to find out which factors, and in what way, affected price during times of global crises. I will study multiple factors that are often said to determine price of gold and I will try to assess the ones that I will find to be most explanatory when it comes to the price of gold.
The theoretical part of this thesis will consist of two sub-parts. The first one will be about gold, where I will very briefly classify this metal and shortly describe its history, and provide some reasoning on why it is so valuable when it comes to times of crisis and uncertainty. The second sub-part will be the more important one, as I will be describing the methods that I will be using to achieve my goal mentioned in the second paragraph of the introduction.
The practical part, or the main content of this thesis, will start with the selection of global crises that I will include. Second to that will be the selection of factors that will go into the analysis. The last sub-part will consist of the actual analysis of the price of gold using selected factors. The method I chose to use is the Ordinary Least Squares Regression.
Finally, I will conclude this thesis by listing the factors I found to be important determinants of the price of gold during crises and I will also compare my results with long-term determinants found in other literature.
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1 G OLD
1.1 C
HARACTERISTICSWe can perceive two sides of a gold “coin”. One of them is the physical aspect, which includes its properties and uses spanning many different industries like jewelry, stomatology, electronics, and many more. The next one would be the economic aspect, which describes gold not only as currency but also as an asset, that people often find themselves investing in.
In this chapter, I will first talk about the former aspect and then I’ll move on to the latter one.
1.1.1 Physical aspect of gold
Should we look for a gold element in the periodic table, we would find it in 79th place under the symbol Au. It appears as a non-toxic soft metal with characteristic yellow color1. It occurs naturally in gold veins and alluvial deposits with China, Russia, and Australia being the three largest producers in 20192 that together accounted for approximately 30 percent (over 1000 tonnes) of total global production. However, overall, gold is rather scarce.
According to World Gold Council, estimates currently available suggest that throughout history, 197 576 tonnes have been mined (by 2019)3. And given gold's very high density, 19.3 g/cc, it is not as much when it comes to volume as one would expect. If we were to put all the available gold together, in a cube, that cube would only measure around 21 meters on each side. And US Geological Survey estimates, that the below-ground stock of gold currently is around 50 000 tonnes4. So where does it all go?
Leaving out Investment and Central bank demand, we are left with Jewelry and Technology.
Together they accounted for approximately 56 percent of global demand in 20195. However, an overwhelming majority of that (48,5 percent) is demanded by Jewelry. And that does not come as a surprise, considering its historical value as a status of power and wealth.
1 https://www.rsc.org/periodic-table/element/79/gold
2 https://www.gold.org/goldhub/data/historical-mine-production
3 https://www.gold.org/about-gold/gold-supply/gold-mining/how-much-gold
4 https://www.bbc.com/news/business-54230737
5 https://www.gold.org/goldhub/data/gold-supply-and-demand-statistics
3 1.1.2 Economic aspect
Throughout history, gold has been used not only as a currency but also as a store value. While the former does not apply today as we have other currencies we use on daily basis, such as fiat, the latter can still be said about gold. Gold is still perceived as a store of value today, by many investors, who often find themselves allocating some part of their portfolio to this metal. And one could even argue that allocation even grows during times of crises and uncertainty, meaning that while jewelry and industrial demand tend to follow business cycles, the demand for gold from investors appears to be counter-cyclical, as gold prices tend to rise during recessions. (Baur, McDermott 2009)
There could be many reasons for the price of gold to act like that, however, some would say that it is because gold can serve as a safe-haven asset for most developed countries' stock markets. (ibid.)
In 2019, Investment and Central banks' demand accounted for approximately 44 percent of global gold demand, with Investment demand taking up 29 percent and Central banks' demand reaching over 14 percent.
1.2 D
ETERMINANTS FOUND IN THE LITERATURESince gold is perceived as a good store of value, it is no surprise that plenty of literature can be found regarding its determinants. In this section, I will describe what are the determinants of gold according to the literature, so that I can compare it with my results later.
For example, Levin, Montagnoli, Wright ( 2006), state in their work that even though in short- term, price can deviate due to a number of factors, in the long-run, the price of gold is only determined by US price levels. In other words, with inflation in US consumer prices comes a rise in the gold price as well. To be more specific, one percent increase in the general price levels in the US tends to lead to one percent increase in the price of gold, in the long-run.
The same conclusion is achieved by Sharma ( 2016). In that work, the price of gold is tested against price levels of 54 countries, however, their predictability test results reveal that CPI can predict gold price returns only for 10 of them. In general, it is found that gold price returns are predictable using CPI.
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By using the statistical method FAVAR, Lili, Chengmei ( 2013). They studied the relationship between the spot price of gold and three factors, namely gold reserve and energy products, financial markets indices, and global macroeconomic indicators. They concluded that in the case of the first factor, gold reserve, and energy products, the relationship is positive, while the two latter factors share a negative relationship with the price of gold.
Elfakhani, Baalbaki, Rizk (2009) too explored the different factors that may impact gold prices.
They found out that the price of gold is primarily determined by monetary considerations such as central banks, US stock market activities, and the value of the dollar on the exchange market. On the other hand, according to their research, the price of gold is explained to a lesser extent by determinants such as production and fabrication.
Fan, Fang, Lu (2014) worked on explaining gold pricing during the financial crisis and found out, that CRB index(arithmetic average of commodity futures prices with monthly rebalancing), USDX index, and US Treasury CDS spreads are selected as the macro-factors that impact the price of gold during financial crisis. They used VAR model, which showed a significant relationship between the gold price and mentioned macro-factors.
In general, it is obvious that public consensus revolves around macro-indicators when it comes to determinants of gold price. The most mentioned factor appears to be the CPI index, namely the US one. However, the price of gold being affected by stock markets and the strength of USD also appears to be the case.
It is clear that there are many methods that can help explain the price of gold using other variables. Some are mentioned in 1.2 with all of them being quantitative methods, as this type of tools are the prevailing option when analyzing the price of gold. Methodologies of these researchers will be discussed in the following chapter.
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2 M ETHODS
2.1 R
ESEARCH PROBLEM2.1.1 Problem
When it comes to the price of any asset, it is always subject to a number of determinants and there are many sources regarding determinants of the price of gold. However, these sources usually focus on long-term determinants, and they usually do not cover times of economic crises separately.
The hole that I’m trying to fill with my research is revolving around the long-term determinants as well, but only considering their relationship with the price of gold in short term, which in this case are the economic crises. To put it more simply, I want to find out what determinants(that are often said to determine the price of gold in the long-term) actually hold the relationship with the price of gold even when considering only short-term span of economic crises. That is the problem(or question) that I will be trying to solve.
2.1.2 Objectives
The general objective of this thesis is to find the determinants of the price of gold during selected economic crises. That will be achieved through the following specific objectives:
• Through literature review, find the determinants that are generally considered to be determinants of the price of gold. (I’ve already done already this in 1.2)
• Use these determinants as variables in a model and determine whether they actually explain the price of gold during economic crises.
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2.2 R
ESEARCH DESIGNSIn this part, I will first go through the methodologies of researchers mentioned in chapter 1.2 and then I will follow with the methodology of my choice.
2.2.1 Levin, Montagnoli, Wright
In this work, researchers developed a theoretical framework based on the simple economics of “supply and demand” and then used cointegration techniques to analyze data from January 1976 to August 2005.
First, they start off by analyzing the price of gold against the US dollar and revealing that over the last few decades, gold has not always been a reliable hedge against inflation. They state that depending on the time of buying, some investors would gain relative to inflation, while others wouldn’t. But they also state that exchange rates between USD and other currencies fluctuate and different inflation rates also vary. For those reasons, they proceed with analyzing some other currencies of countries that rank high in gold production or consumption. They find that gold appears to be an excellent inflation hedge in China, India, Indonesia, and Turkey, but fails to hold the same property in Russia, UAE, UK, etc.
After discussing factors that influence short-term demand and supply they present a simple empirical model of the price of gold based on the supply and demand explanation of movements in the price of gold. This model hypothesizes that the price of gold is determined by the US and world price levels, the US and world inflation, US and world volatility, world income, US-world exchange rate, the gold lease rate, alternative investment opportunities, credit risk, and time-specific uncertainty caused by political and/or financial risk.
However, to test their hypotheses, they use statistical methods of “cointegration regression”, which can be used to isolate the factors that are correlated with movements of a variable in both the short-run and the long-run.
They start by examining the bivariate relationships between the market price of gold and each of the explanatory variables, but they also point out that this analysis may reveal specious trends and correlations. The subsequent multivariate analysis then holds other factors constant while examining the effect of each variable on the price of gold.
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Main findings of their work are already mentioned in chapter 1.2, so I won’t be going through them again.
2.2.2 Susan Sharma
This work focuses on analyzing the relationship between the price of gold and CPI indices of 54 countries. This is done through a test of predictability based on flexible generalized least squares estimator, which accommodates endogeneity and heteroscedasticity.
After describing the dataset, the researcher goes on to review some additional sources that support a relationship between the price of gold and inflation and proposes a predictive regression model where the price of gold is a function of CPI. However, to avoid any bias interference, the researcher uses a bias-adjusted GLS estimator that removes endogeneity.
Main findings of this work are discussed in chapter 1.2.
2.2.3 Lili, Chengmei
In this paper, researchers focus on the influence of macro-economic factors on the price of gold.
Firstly, they review various sources that use different methods of determining the factors that influence the price of gold and then discuss their cons and pros. However, for this paper, researchers present a new method, the FAVAR model(Factor-augmented vector autoregression), which is based on a large number of variables.
They describe the structure of the model, which is based on the assumption that the futures price for one maturity is driven both by prices of other maturities and by macroeconomic shocks. After that, they move on to the empirical analysis, which starts of by describing the dataset and the analysis method.
In the first step of the analysis method, they extract three common factors from the dataset and find, that these factors account for approximately 90% of variability within the dataset.
They break down the contribution to the loadings of each factor by three groups of series, which are mentioned in chapter 1.2.
Then they proceed with an ADF test(which is used to test the null hypothesis that a unit root is present in a time series sample) and determine that the variables used do indeed have unit root(meaning that the time series are not stationary). The factors are then used in a causality
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test that concludes that energy prices, financial data, and macro data all have a causal relationship with the gold price, which proves that the factors which have been thought to influence gold price have a scientific foundation.
Taking all of the information gathered up to that point into consideration, researchers then proceed with constructing the final model, which presents the determinants of the price of gold, mentioned in chapter 1.2.
2.2.4 Elfakhani, Baalbaki, Rizk
The next work to be reviewed in more detail is that of Elfakhani, Baalbaki, Rizk. This paper explores factors that explain variation by employing the Kaufmann-Winters model for an extended period with some modifications.
I want to make a small note here. Kaufmann-Winters model(Kaufmann 1989) is a log-linear formula that derives the price of gold. This formula is achieved by using ordinary least squares regression in logarithmic mode. Kaufmann’s predicted formula states that US implicit GNP deflator index, metric tonnage of world production of gold and weighted index of the exchange value of the US dollar against currencies of ten industrialized countries, act as determinants of the price of gold.
After reviewing the literature the researchers proceed with their analysis, which is separated into three steps. In the first step, they replicate and extend the Kaufmann-Winters model. This replication and extension bring similar results as those achieved by the original data set(model still consistently explained (93% of gold price variability).
The second phase of analysis consisted of modifying the Kaufmann-Winters model. This is done due to the fact that the original model misses many other factors that can be relevant to the price of gold. What they have done is they added more variables, namely Official Sector Sales, Old Gold Scrap, S&P500, Bar Hoarding, and Gold Fabrication.
The model obtained in the second phase did offer exceptionally high 𝑅2, however, it did not meet one assumption of independence of the independent variables and for that reason, it became quite questionable. For those reasons, they proceeded with conducting stepwise regression, which produced a model with only one variable retained, the US dollar index.
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In the last phase, researchers tried to solve econometric problems using factor analysis (this technique is used to reduce a large number of variables into a fewer number of factors). This analysis extracted three factors, which explained 91.1% of the total variance in the response variable.
The results were discussed earlier in chapter 1.2.
2.2.5 Fan, Fang, Lu
In this paper, researchers aim to apply the EGARCH model to test the volatility of gold price and then use the VAR method to validate the idea by decomposing the price of gold into three parts. By doing this, they determine the macro-factors on gold pricing during the financial crisis.
After literature review, they proceed with describing generally accepted factors of economic growth and describing the phases of the financial crisis. This is followed by conducting statistical analysis on various assets, such as Gold, Crude Oil, and Copper. This analysis also presents the EGARCH model, which indicates that the asymmetric information impact effect for the gold price volatility does not exist, which is not the same with that of stock volatility.
Overall, it seems that gold behaves differently from stocks during financial crisis. They also state that gold volatility has the properties of strong clustering and long memory.
The empirical test starts with a stationary test to the time-series data that finds certain trends in all data sequences. This is followed by the ADF test that shows that the data is non- stationary. The following VAR analysis then shows that the price of gold is determined by the CRB index, USDX index and US Treasury CDS.
2.3 M
Y RESEARCH DESIGNThis part will be focused on describing my methodological approach to analysis.
The methodology that is needed to achieve the first objective of this thesis is to simply review the literature and state the determinants of gold price that are often said to be important.
This has already been done in chapter 1.2.
The second objective is rather harder to achieve. To simplify it, I will break the process down into two steps. These steps are: Gathering Data and Analysis. The steps are described below.
10 2.3.1 Data
Data is an important part of the analysis. In my case, the dataset that is to be analyzed will consist of several variables that I chose from the ones presented in chapter 1.2. These will be listed in the part of the thesis that contains the analysis, but right now, I will describe the process of retrieving and examining the frequencies of data.
API based retrieval
It is fairly easy to retrieve data from websites such as Yahoo Finance, FRED, Stooq, Eurostat, etc, if some programming language is used. Namely, Python, which is the one that I will be using. To get the data, it is enough to load the DataReader subpackage of Pandas library as seen in Figure 1.
After loading DataReader, it is enough to just call the function wb.DataReader() that takes several arguments, however, to simply retrieve the data only few are needed. First one is the name of series that is to be retrieved. For example, FRED uses its own name tags, meaning that it is needed to visit the site and obtain it. On the other hand, sites like Stooq and Yahoo use tickers. The name argument can also take a list of names to retrieve more information simultaneously. Example of that can be seen in Figure 2, where variable gold contains just information for gold, while second variable contains information of two tickers.
Next argument is data_source that takes the name of site that the data are retrieved from. In example in Figure 2, first variable retrieves data from FRED, while the second one from Stooq.
Last two arguments are start and end. These two arguments dictate the start and end of the period for which we wish to retrieve the data.
File based retrieval
Source: Own
Figure 2: Retrieving the data through API
Source: Self-made
Figure 1: Importing Pandas library
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Sometimes information can not be found on websites that support the API based method. If this is the case, then it is needed to import the Pandas library as shown in upper cell of Figure 3. Then call the pd.read_csv() function to import data from .csv file or pd.read_excel() to read .xls or .xlsx file. As an argument, input the preferred file name directly(if the file is located in the same directory address as the Python notebook) or input the whole directory address(if the file is located elsewhere). Examples of this are shown in the bottom cell of Figure 3.
Frequency
Unfortunately, the data does not always come in the same frequencies. But the same frequency of data is often required to be able to analyze it. So here, I will describe how to alter the frequencies.
If the data presented is more frequent than desired, the .resample() function can be used. In this case, I input the ‘1M’
argument that stands for one month (the data is retrieved in daily frequency). Other combinations are also possible, like 2 or more months or even years. Then, append the method used for resampling. I used .mean() to obtain the average price for that month. Also, if I wish to retain the old data, it is important to assign this function to new variable, so that the old dataset remains the same. Example can be seen in Figure 4.
However, there is also the opposite problem. Some variables are not provided on monthly or daily frequency, but on quarterly. In that case, it is possible to approximate the missing data points (months) by interpolation.
Figure 3: Importing Pandas library and retrieving data from file
Source: Self-made
Figure 4: Obtaining monthly frequency
Source: Self-made
12 After loading the data it is needed to resample it and to use some method on it like .mean(). It does not matter which method is used as it does not alter the data, however without using it, it just creates a Resampler object that can not be used. This is done to create empty values between the data points that can be filled using interpolation, as seen in Figure 5.
Next step is to interpolate the data. That is done by calling .interpolate() function on the dataset that contains empty values and passing in a method argument that is used to determine the method of
interpolation. In my case, I used the linear method. All can be seen in Figure 5.
2.3.2 Analysis
Selection of crises
Before proceeding with the analysis of the data, I will firstly need to select the crises that I will be analyzing. Note that Bretton woods system was in force until early 1970s, meaning that I can only analyze economic crises that came after, as before that, the dollar was pegged to the gold, meaning that price was not determined on the market.
In their paper, Baur, McDermott (2009) examine the role of gold as a safe haven. Using econometric analysis they found out that in the examined 30 year period(1979-2009) gold was both hedge and a safe haven, however only for major European and US stock markets.
However, after looking at specific crisis periods, they also concluded that gold was a strong safe haven for most developed markets during peak of Financial crisis.
For this reason, I will be focusing on two types of crises. It will be either crises that spanned the whole world, or the ones that were affecting Western countries.
Statistical method
It is clear that there are lots of different statistical methods that can be used to analyze the price of gold. I decided to go with OLS Regression for number of reasons. First of all, OLS Regression is one of the most widely used statistical methods. This means that the process of
Figure 5: Interpolation
Source: Self-made
Source: Self-made
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applying it is very well documented. Second of all, it is rather simple to use and evaluate. Even with basic knowledge of statistics one can assess the quality of any particular OLS model.
Regression analysis is generally used to explain or model the relationship between independent and dependent variables. In the case of OLS regression, it is done by building a line (or a plane) of best fit by minimalizing the value of summed squared errors of each data point. (Barnes, Forde 2021) The general model looks like (2.1) where 𝑌𝑖 is the value of dependent variable, while 𝑥 values are the independent variables, beta coefficients are the parameters of those independent variables and 𝑒 are the error terms that are to be minimalized.
𝑌𝑖 = β0+ β1𝑥𝑖1+ β2𝑥𝑖2+ ⋯ + β𝑛𝑥𝑖𝑛+ 𝑒𝑖 2.1
Calculation
The minimalization of error terms can be done by using the OLS function, but that can be rather inconvenient and for that reason, it is often done through matrix notation of the regression equation. The exact formula for finding the beta coefficients that minimalize the residuals can be seen in (2.2)
𝛃 = (𝑿′𝑿)−1𝑿′𝒀 2.2
However, this is just theoretical background for OLS Regression. The calculations are usually not done by hand, but rather some statistical software is used. In my case, I decided to go with Python. The steps of conducting the analysis using Python are documented in the following chapter.
This part of the thesis is now concluded. The next part will be containing the analysis of the price of gold.
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3 A NALYSIS
3.1 S
ELECTION OFC
RISESThe list of crises I will be analyzing can be found below.
• 1. Early 1970s recession
• 2. Early 80s recession
• 3. Early 90s recession
• 3. Great recession
3.2 S
ELECTION OF VARIABLESIn this chapter I will be listing the variables that I’ll be using in my analysis. Also, every variable will be accompanied by the source of it. It is important to note that at first, the number of variables I’ll be using may seem overwhelming, however, when analyzing every crisis separately, I will go through each variable and then select only the ones that will be deemed most important. That’s why the list may seem rather broad now, but the number of variables will be most likely thinner later according to each individual crisis.
3.2.1 Dependent variable
This one is rather straightforward. As even the name of the thesis suggests, the independent variable will be price of gold. To be specific, price of gold in dollars per Troy ounce. The chart of gold price can be seen below.
Figure 6: Price of gold in $ per Troy ounce
Source: FRED St. Louis, https://fred.stlouisfed.org/series/GOLDPMGBD228NLBM
15 3.2.2 Independent variables
When deciding which independent variables to choose, I used knowledge from first chapter of this thesis, meaning that I will be mostly using variables(or indicators) that are associated with Western countries such as US CPI, Dollar index, GDP etc.
List of indicators:
1. Dollar index
First independent variable I will be introducing is the Dollar index, which tracks the strength of the dollar against a basket of major currencies. This particular index that I will be using is measured against four currencies that are: Swiss franc, Euro, British pound and Japanese yen, and is calculated and provided by website www.stooq.pl. Chart can be found below.
2. S&P 500
Next independent variable that I chose is S&P 500, which is an index tracking 500 large companies listed on stock exchanges in the United States. Also, it is important to note that I will be using the Closing price as variable, not the Adjusted one. Chart can be again found below.
Figure 7: USD Index
Source: https://stooq.com/q/p/?s=usd_i
16 3. Real Gross Domestic Product
The third variable I chose is Real Gross Domestic Product. I decided to go with Real values because in my analysis, I will also be using US CPI growth rate as inflation. That could result in violation of certain assumptions of regression, as these two variables would probably be highly correlated.
4. Consumer Price Index
Next variable is Consumer Price Index(Total all items for the United States). More specifically, its growth rate. It is calculated on monthly basis with growth rate referring to the previous
Source: https://www.investing.com/indices/us-spx-500
Figure 9: Real Gross Domestic Product, USA
Source: https://fred.stlouisfed.org/series/GDPC1 Figure 8: S&P 500, logarithmic scale
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period. I chose this indicator to represent inflation in my analysis. Chart can be found in Figure 10.
5. Spot Crude Oil Price, WTI
I also decided to use price of oil(WTI) in my analysis as according to literature mentioned in theoretical part of this thesis prices of energy products can effect price of gold.
6. Treasury constant maturity rate
Next variable I decided to use for analysis is Treasury constant maturity rate. It is used to compute an index based on the average yield of various Treasury securities maturing at different periods.
Figure 10: CPI growth rate
Source: https://fred.stlouisfed.org/series/CPALTT01USM657N
Figure 11: WTI, dollars per barrel
Source: https://fred.stlouisfed.org/series/WTISPLC
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I will be actually including two maturity rates, which are 10-year and 1-year. However, it is highly likely that they share high correlation and it is expected that one of them will be removed from the model later.
3.3 A
NALYZING GOLD PRICE DURING SELECTED CRISESIn this section, I will be analyzing the gold price during selected crises that I provided in section 5.1. I will be analyzing each crisis individually and while I will be providing Python code used to conduct the analysis, I will do such thing only for the first crisis analyzed, as it will be the same for every that will follow. However, if some deviation from procedure occurs during analysis of other crises, I will provide examples of code for that deviation.
When analyzing each crisis, I will do so in following manner:
1. Assessing relationship between each independent variable and the dependent variable separately
This step ensures that independent variable indeed has linear relationship and is correlated with independent variable enough to make it to the final model.
2. Assessing relationships between all independent variables
In this step, I will be looking into correlation matrix to determine whether there are not any pairs of variables with high correlation.
3. Calculating and evaluating the model
In this step, I will be calculating and evaluating the final model.
Figure 12: Constant maturity rates, 1-year in upper plot, 10-year in bottom plot
Source: https://fred.stlouisfed.org/series/DGS1 - (1-year), https://fred.stlouisfed.org/series/DGS10 - (10-year)
19 3.3.1 1st crisis
First period to be analyzed starts in 1973. At the beginning of that year, major stock markets around the world crashed as the result of collapse of Bretton Woods system. However, later that year, the crisis has been compounded by oil crisis, which was a result of oil embargo proclaimed by OPEC. Overall, according to US business cycle, the 70s recession lasted until March 1975.6
So the period that I will be analyzing starts on January 1973 and ends on March 1975.
Selecting data according to analyzed period
Upon retrieving the data, variables in Python store whole period that is selected. That is since the beginning of 1970. However, it is needed to extract just the period between January 1973 and March 1975.
In order to obtain such period, first it is need to create two Python variables, start_date and end_date which will store the beginning and end of the desired period. After that the function .loc[] is called on the dataset to index based on label. In this case, the filtering is done by
inserting start_date and end_date as arguments as seen in Figure 13. Technically speaking, those two variables are not needed and it is possible to just type the dates as arguments, but creating the variables is more convenient and prevents mistakes.
The same is repeated for every variable and we can proceed to the next step.
1. Assesing relationship between each independent variable and dependent variable separately
Scatterplots
6 https://www.nber.org/research/data/us-business-cycle-expansions-and-contractions
Figure 13: Selecting data according to period
Source: Self-made
20
In this step, I will be trying to determine whether each dependent variable has enough strong relationship with independent variable to even make it to the final model. Firstly, it is good to obtain scatter plots to visually examine the relationship.
Scatterplots of all the independent variables and dependent variable can be seen in Figure 14.
Just upon looking at them, there are few clearly highly correlated pairs of independent variables and dependent variable. The most obvious one is pair with S&P 500 index. Then it seems that variable tenYear, which is the ten year treasury constant maturity rate, also shares a high correlation with Gold. After that, the Dollar, GDP and WTI are also possible candidates while CPI and oneYear do not appear highly correlated. It is already highly possible that these two lastly mentioned variables won’t make to the final model, however, few more steps need to be taken before reaching that conclusion.
After visually observing the relationships, via scatterplots, next step is obtaining correlation coefficients of dependent variable and independent variables.
Figure 14: Gold to Independent variables scatterplots
Source: Self-Made, data taken from FRED and Stooq
21 Correlation table
After obtaining the Correlation table(Figure 15), it should confirm findings from scatterplots.
It appears that S&P 500 index is indeed highly correlated(negatively) with Gold. The same goes for tenYear variable. Slightly lower, but still significant correlation can be also observed between Gold and independent variable GDP. Also, variables CPI and oneYear, which were suspected of low correlation with Gold, truly appear to be lowly correlated. In all of these cases, correlation table serves as confirmation of scatterplots observation. However, while it was suspected that WTI would be correlated with Gold, but not highly, it appears that it is indeed highly correlated, according to Figure 15.
Code I used to obtain correlation coefficients can be seen in Figure 16. This exact function, that I used(.corr()) is called on a DataFrame object, so firstly I created a list of individual datasets and then used a pd.concat() function to create variables DataFrame. After calling .corr() on that object, it returns a correlation matrix, however, I altered it to look like Figure 15. Also, I decided to change the names of the columns in line 4 for better clarity.
So after these two “sub-steps”, I already have an idea of variables that will be left out of the final model, however, there is still one more thing to be done to confirm these findings.
Simple regressions for each pair
Source: Self-made, data taken from FRED and Stooq
Source: Self-made
Figure 15: Correlation table, Independent variable to Dependent variables
Figure 16: Python code for correlation
22
Next sub-section of this step is to conduct simple regression for each pair of independent and dependent variables. This is done to find out what independent variables make good model separately, since that will usually lead to them making a good model when used together.
While it is possible to just conduct the regression analysis on each variable separately, it is way easier to do that using loop that extracts the desired values from the model and then appends it to the list. This can be seen in Figure 18. First, the list info is created that will store the values. Then I created I list of names so that the loop can append them as well for better clarity.
After that follows the actual loop that
loops through the X list that contains the variables. For each of the variables, it firstly fits the intercept, as sm.OLS() function does not do that and without the intercept, the squared R values would be highly inflated. Next we actually create the fitted model by calling sm.OLS() function that takes X and Y argument and appending .fit(). The name variable is there so that the right name gets appended to the list. After that we decide which values we wish to extract and append them to the info created earlier with name, to clarify which variable were the values extracted for. This creates a “list of lists” so on the last line I converted it to DataFrame.
Source: Self-Made
Source: Self-made, data taken from FRED and Stooq
Figure 18: Simple regression loop
Figure 17: Simple regressions values
23
Figure 17 shows the values for each simple regression with dependent variables. As suspected, SPX, WTI and tenYear do indeed look like very good candidates for final multiple regression model, since they do provide a lot of explanation of variance of the dependent variable at significant level.
While GDP appears to explain lower amount of variance of the dependent variable, however it seems like it still is significant enough with p-value of .0002. This means that it is still worth trying to put it into model.
On the other hand, variables CPI, oneYear and Dollar do not explain much of variance in the dependent variable and to not appear to be significant. That means that these variables will most likely be excluded from the final model.
2. Assesing relationship between all independent variables
Next step in the process is to see what the relationships among the independent variables are.
I will again start with scatterplots and then calculate the correlation.
Figure which shows the grid plot of scatterplots can be found in APPENDIX A, as there are 7 independent variables, meaning that the plot is quite large. Upon glancing over the scatterplots, it seems like scatterplots of pairs SPX-GDP, GDP-tenYear, SPX-tenYear and oneYear-tenYear have high correlation. However, to get the precise answer, it is important to look at correlation matrix which can be found in Figure 19.
Upon looking at the correlation matrix, it is rather clear that there are several problematic pairs. It seems like a lot of them indeed share a high correlation, which could result in
Figure 19: Correlation matrix for independent variables
Source: Self-made, data taken from FRED and Stooq
24
multicollinearity within the final model. Since I already determined the most likely non- redundant variables, I decided to produce second correlation matrix, which can be seen in Figure 20, which shows only those variables.
It is quite clear that this data set will most likely indeed have multicollinearity present. That would lead to the fact that coefficients could not be relied on and high p-values. For now, I will leave it at that, proceed with the last two steps and examine the model later to asses just how does the multicollinearity affect the model.
3. Calculating and evaluating the model
Calculating the multiple independent variables model is conducted the same way as simple one, however, instead of passing just one variable as X, the list containing all desired variables is passed to the function.
Firstly, I decided to calculate the model that contains every independent variable.
Unfortunately, it is rather underperforming.
As shown in Figure 21, the model explained 95.4% of variance in the independent variable and overall model is significant. But looking at the lower part of the figure reveals that variables are nowhere near significant enough. This problem most likely comes from presence of multicollinearity.
Figure 20: Correlation matrix containing non-redundant variables
Source: Self-made, data taken form FRED and Stooq
Figure 21: Full Model, 1st crisis
Source: Self-made, data taken from FRED and Stooq
25 So then I tried to calculate the model using four variables that I determined to be the best when it came to simple regressions. But the model not even explains less variance in the independent variable(which is not that surprising, as adding more variables will never result in lower R squared, meaning that it is impossible for the previous model to explain less variance), but it is actually even less significant than the previous model.
After receiving very underperforming results from the previous models, I decided to try to obtain the best model by forward selection.
Luckily, I had more success with this method, as I obtained the model depicted in Figure 23. This model not only explains 94.7% of variance in the independent variable(with adjusted R squared being 0.943) with high overall significance, but the coefficients are significant
as well. For those reasons I will proclaim this as the final model for this crisis. The model can be seen in (3.1).
𝑃𝑟𝑖𝑐𝑒 𝑜𝑓 𝑔𝑜𝑙𝑑 = 318,16 + 9,79(𝑝𝑟𝑖𝑐𝑒 𝑜𝑓 𝑊𝑇𝐼) − 3,23(𝑆𝑡𝑟𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑈𝑆𝐷) 3.1
With this the analysis of the first crisis is done. Next crises will be much shorter in volume of text, since I explained my steps in detail during the first analysis and the steps will be very similar for those that follow.
3.3.2 2nd crisis
Next crisis that I will be analyzing is the early 80s recession jointly with the 1979 oil crisis that was a key event leading to the recession, since rather fast rise in oil prices pushed inflation of developed countries even higher than it was before.
The period that I will be analyzing starts on January 1979 and ends on January 1983.
Figure 22: Model with four selected variables
Source: Self-made, data taken from FRED and Stooq
Figure 23: Model obtained by forward selection, 1st crisis
Source: Self-made, data taken from FRED and Stooq
26 In this case, I will not be adding any more variables.
1. Assesing relationship between each independent variable and dependent variable separately
Scatterplots
The scatterplots for pairs of independent variables and dependent variable can be seen below in Figure 24.
The scatterplots show that there is a suspicion of high correlation of dependent variable with WTI and SPX. GDP also appears to be somewhat correlated, however it seems like there are some outliers that can effect the coefficient, so lets confirm that by calculation correlation coefficients.
Correlation table
The correlation table of dependent variable and independent variables can be seen in Figure 25.
Source: Self-made, data taken from FRED and Stooq
Figure 25: Dependent variable and independent variables correlation table, 2nd crisis
Source: Self-made, data taken from FRED and Stooq
Figure 24: Independent variables versus dependent variables scatterplots, 2nd crisis
27
Upon looking at correlation table above, it is clear that overall correlation of independent variables with dependent one is rather low. However, it indeed looks like SPX and WTI are at least somewhat strongly correlated with Gold. Variables like GDP, CPI, oneYear, tenYear and Dollar have very low correlation.
Simple regression for each pair
Running simple regression for each pair indeed shows that during this crisis, independent variables are not that good at explaining variance in the Gold. Results can be seen in Figure 26.
The table above not only shows that individual variables do not do a good job at explaining the variance in Gold, but most of them don’t appear significant as well. At 5% level, only three of them are significant. Those are WTI, SPX and Dollar.
2. Assesing relationship between all independent variables
Scatterplots of independent variables pairs can be again found in APPENDIX A, as it is too large to fit here.
After looking at the scatterplots, it seems like oneYear and tenYear have high correlation, so it is basically impossible for them both to be in the final model. The same goes for WTI and SPX and few other pairs. However, let see the correlation table before reaching any conclusion. The table can be seen below in Figure 27.
Figure 26: Simple regressions, 2nd crisis
Source: Self-made, data taken from FRED and Stooq
28
The correlation table confirms that oneYear and tenYear are highly correlated. There are more pairs with high correlation, but none is as high as the first mentioned. Lets move onto the final step now and see whether we will have to remove some highly correlated variables.
3. Calculating and evaluating the model
As in the first analysis, I will firstly calculate the model using all of variables. This model can be seen in Figure 28. This model explains 83,7% of variance in the independent variable and is significant, however it seems like most of the coefficients are not. For those reasons, I again decided to go for the model obtained with forward selection. This model can be seen in Figure 29.
Figure 27: Independent variables correlation table, 2nd crisis
Self-made, data taken from FRED and Stooq
Self-made, data taken from FRED and Stooq Self-made, data taken from FRED and Stooq
Figure 29: Full model, 2nd crisis Figure 28: Model obtained by forward selection, 2nd crisis
29
Through forward selection, I finally obtained model the is overall significant and also has significant coefficients. It explains 82.8% of variance in the independent variable.
Unfortunately it doesn’t explain as much as the model obtained during analysis of previous crisis, but R squared is still rather high with adjusted value not being significantly lower. The model can be seen in (3.2).
𝑃𝑟𝑖𝑐𝑒 𝑜𝑓𝑔𝑜𝑙𝑑 = 2824,8 + 10,85(𝑝𝑟𝑖𝑐𝑒 𝑜𝑓 𝑊𝑇𝐼) − 8,61(𝑆𝑡𝑟𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑈𝑆𝐷) 3.2 + 4,5(𝑆𝑃𝑋) − 0,39(𝑅𝑒𝑎𝑙 𝐺𝐷𝑃)
3.3.3 3rd crisis
The third crisis to be analyzed is the Early 90s recession that spanned most of the Western countries. It is said to be the result of 1990 oil price shock and sequent tightening of monetary policy due to fears of rising inflation.
It lasted approximately from beginning of 1990 to beginning of 1992, meaning that I will be analyzing period from February 1990 to February 1992.
1. Assesing relationship between each independent variable and dependent variable separately
Scatterplots
As before, I will start with scatterplots. The scatterplots seen in Figure 30 show that Gold might share have some relationship with variables SPX, oneYear, tenYear and WTI. However, to be certain, the correlation matrix needs to be examined.
Figure 30: Independent variables versus dependent variables scatterplots, 3rd crisis
Source: Self-made, data taken from FRED and Stooq
30 Correlation table
The correlation table in Figure 31 somewhat confirms findings from scatterplots. SPX is indeed highly correlated with Gold, while oneYear and tenYear present slightly lower correlation coefficient. The same goes for CPI, however WTI does not seem correlated enough.
Simple regression for each pair
As suspected from correlation table, SPX does a good job at explaining variance in the independent variable while also being significant. Both Treasury rates (tenYear and oneYear) explain less variance, but still are significant. GDP, CPI and WTI also appear to be significant, however they explain very low proportion of variance in Gold. The worst variable in this cast is Dollar, which explains almost no variance while not being significant almost at all. Complete table containing simple regressions can be found below in Figure 32.
2. Assessing relationship between all independent variables
Scatterplots for each independent variables pair can be found in APPENDIX A. It appears that several independent variables are highly correlated, namely tenYear and oneYear, SPX and tenYear, GDP and SPX and some others.
Figure 31: Dependent variable and independent variables correlation table, 3rd crisis
Source: Self-made, data taken from FRED and Stooq
Figure 32: Simple regressions, 3rd crisis
Source: Self-made, data taken from FRED and Stooq
31
Variables tenYear and oneYear are indeed highly correlated. The same goes for tenYear and SPX and GDP and SPX. Whole table can be seen in Figure 33.
As of right now, I suspect that the best model will be achieved by using variables SPX and CPI.
3. Calculating and evaluating the model I will again start with model that uses all of variables.
This model can be seen in Figure 34. It shows that even when all variables are feeded to the model, it does not explain high proportion of variance in Gold, while the only significant variable is SPX. It seems like the model the model suffers from strong presence of multicollinearity.
Unfortunately, forward selection yielded no better result with the model explaining only 63.6% of variance in Gold and SPX again being the only significant variable.
Figure 33: Independent variables correlation table, 3rd crisis
Source: Self-made, data taken from FRED and Stooq
Figure 34: Full model, 3rd crisis
Source: Self-made, data taken from FRED and Stooq
32 For those reasons, it appears that the best overall model can be obtained by using only the SPX variable. This model can be seen in Figure 35.
However, it explains only 59,8% of variance in the independent variable. This means probably that more variables would need to be included on top of those that I selected.
3.3.4 4th crisis
The fourth crisis that I will be analyzing is the Great depression, which occurred between years 2007 and 2009. The crisis it self was a result of several events, one of them being the USA housing crisis.
The crisis started at the of 2007 and lasted till mid-end of 2009, so the period that I will be analyzing is from November 2007 to July 2009.
1. Assesing relationship between each independent variable and dependent variable separately
Scatterplots
The very first step is again to obtain the scatterplots of individual pairs. These plots can be seen in Figure 36 below.
Figure 35: Model obtained by forward selection, 3rd crisis
Source: Self-made, data taken from FRED and Stooq
33
Scatterplots clearly show that there isn’t much relationship to the pairs. The only plot that at least slightly indicates some correlation is CPI, however it is needed to look at the correlation table to know for sure.
Correlation table
The correlation table, which is shown in Figure 37, confirms what I suspected after examining the scatterplots. It indeed seems that no variable has strong correlation with Gold. Only variable that is at least somewhat correlated with Gold is CPI. So for now, it doesn’t look like this analysis will lead to obtaining a final model, however, there are more steps to be taken before concluding that.
Simple regression for each pair
Table shown in Figure 38, which contains the simple regression for each pair, also confirms my suspicions from scatterplots and correlation table. First of all, no single variable does a
Figure 36: Independent variables versus dependent variables scatterplots, 4th crisis
Source: Self-made, data taken from FRED and Stooq
Figure 37: Dependent variable and independent variables correlation table, 4th crisis
Source: Self-made, data taken from FRED and Stooq
34
good job at explaining percentage of variance in independent variable. Second of all, only one variable is significant, which is CPI.
This tells me that final model will most likely have very low explanatory power.
2. Assessing relationship between all independent variables
As before, the figure containing scatterplots for independent variables can be found in APPENDIX A. Visually, it seems there are quite a few pairs that are highly correlated. And the correlation matrix in Figure 39 only confirms that. It appears that there is a significant correlation among almost all of variables, with CPI being the only exception. This means that final model will most likely only have two independent variables CPI and oneYear, as these two have very little correlation while being top two variables at explaining variance in the independent variable(even though the R squared is very low).
Figure 38: Simple regressions, 4th crisis
Source: Self-made, data taken from FRED and Stooq
Figure 39: Correlation table, 4th crisis
Source: Self-made, data taken from FRED and Stooq
35 3. Calculating and evaluating the model Now I will be calculating model using all of variables first, as I have done before, however, I expected to get very unsatisfying results and that turned out to be true. The full model can be seen in Figure 40 and it is rather clear that it can not be used at all. While it was obvious even before that multicollinearity would be rather rampant, it wouldn’t effect the R squared value, which is too low considering the amount of variables presented(this is reflected in adjusted R squared).
The forward selection yielded no better result so I decided do calculate the model using two handpicked variables mentioned in previous steps, CPI and oneYear. This did provide model(Figure 41) that is not only overall significant but has significant coefficients as well. However, its R squared, and the adjusted value, are rather low as the model only
explains 71.3% of variance in the independent variable. However, it seems that, given the chosen variables, this is the best model for this period. So this analysis is concluded with slightly unsatisfying results. The model can be seen in (3.3)
𝑃𝑟𝑖𝑐𝑒 𝑜𝑓 𝑔𝑜𝑙𝑑 = 915,56 + 64,9(𝐶𝑃𝐼 𝑔𝑟𝑜𝑤𝑡ℎ 𝑟𝑎𝑡𝑒) 3.3
− 28,77(𝑂𝑛𝑒 𝑌𝑒𝑎𝑟 𝑇𝑟𝑒𝑎𝑠𝑢𝑟𝑦 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦 𝑅𝑎𝑡𝑒)
Figure 40: Full model, 4th crisis
Source: Self-made, data taken from FRED and Stooq Figure 41: Model with handpicked variables, 4th crisis
Source: Self-made, data taken from FRED and Stooq
36
C ONCLUSION
As with price of any asset, the price of gold is hard to explain and predict. There truly is a number of different statistical techniques that can help with achieving such prediction and explanation, but only some models are useful, while all are wrong.
Since gold is often considered a necessity when it comes to portfolio diversification, there are many sources that try to find the determinants of price of gold. Some of these sources were reviewed in this thesis and the determinants of price of gold that these sources presented were later used in analysis of my own. The determinants that I decided to use are Dollar index, S&P 500, Real GDP, CPI, Spot Crude Oil price and Treasury constant maturity rate (10 year and 1 year). I decided to use these as they are often mentioned in literature as long-run determinants of gold price.
The goal of this thesis was to find out whether these long-run determinants explain the price of gold in the short span of economic crises. The findings, however, do not always indicate such thing.
The price of gold during the first analyzed crisis was indeed determined by some of the mentioned determinants (WTI, USD) and the model offered exceptional 𝑅2 of 94,7%.
However, with time (and crises), the relationship seems to have faded out. The price of gold during second crisis was not only explained to lesser extent (82.8%), but the variables in the model changed as well (real GDP was added). In the third model (for the third crisis), only one statistically significant variable was retained, the S&P 500 index, which explained only 59.8%
of variance in price of gold. During the last analyzed crisis, the price of gold was determined by CPI growth rate and One Year Treasury Constant Maturity Rate, which explained only 71.3%
of variance in price of gold.
The goal of thesis was to find the determinants of price of gold, and they were indeed found.
However, it seems like, when considering short-term crises, the price isn’t always explained by the same factors and the factors do not always effect the price in the same way as in previous crises. This might happen due to number of reasons, such as increasing complexity of markets coming from rising number of participants etc., but this is just dubious speculation.
37
B IBLIOGRAPHY
BARNES, J. C. and FORDE, David R. (eds.), 2021. The encyclopedia of research methods in criminology and criminal justice. First Edition. Hoboken: Wiley. The Wiley series of encyclopedias in criminology & criminal justice. ISBN 978-1-119-11072-9.
BAUR, Dirk G. and MCDERMOTT, Thomas K. J., 2009. ID 1516838: Is Gold a Safe Haven?
International Evidence [online]. SSRN Scholarly Paper. Rochester, NY: Social Science Research
Network. [Accessed 13 November 2020]. Available from:
https://papers.ssrn.com/abstract=1516838
ELFAKHANI, Said, BAALBAKI, Imad and RIZK, Hind, 2009. Gold price determinants: empirical analysis and implications. J. for International Business and Entrepreneurship Development - J Int Bus Enterpren Dev. 1 January 2009. Vol. 4. DOI 10.1504/JIBED.2009.029010.
FAN, Wei, FANG, Sihai and LU, Tao, 2014. Macro-factors on gold pricing during the financial crisis. China Finance Review International. 1 January 2014. Vol. 4, no. 1, p. 58–75.
DOI 10.1108/CFRI-09-2012-0097.
KAUFMANN, Thomas D. Kaufmann, [no date]. The Price of Gold, a Simple Model. [online].
[Accessed 21 April 2021]. Available from:
https://books.google.cz/books/about/The_Price_of_Gold_a_Simple_Model.html?id=wbeGtg AACAAJ&redir_esc=y
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[Accessed 15 November 2020]. Available from: http://www.gold.org/research/short-run- and-long-run-determinants-price-gold
38
LILI, Li and CHENGMEI, Diao, 2013. Research of the Influence of Macro-Economic Factors on the Price of Gold. Procedia Computer Science. 1 January 2013. Vol. 17, p. 737–743.
DOI 10.1016/j.procs.2013.05.095.
SHARMA, Susan Sunila, 2016. Can consumer price index predict gold price returns? Economic Modelling. 1 June 2016. Vol. 55, p. 269–278. DOI 10.1016/j.econmod.2016.02.014.
L IST OF FIGURES
Figure 1: Importing Pandas library ... 10
Figure 2: Retrieving the data through API ... 10
Figure 3: Importing Pandas library and retrieving data from file ... 11
Figure 4: Obtaining monthly frequency ... 11
Figure 5: Interpolation... 12
Figure 6: Price of gold in $ per Troy ounce ... 14
Figure 7: USD Index ... 15
Figure 8: S&P 500, logarithmic scale ... 16
Figure 9: Real Gross Domestic Product, USA ... 16
Figure 10: CPI growth rate... 17
Figure 11: WTI, dollars per barrel... 17
Figure 12: Constant maturity rates, 1-year in upper plot, 10-year in bottom plot ... 18
Figure 13: Selecting data according to period ... 19
Figure 14: Gold to Independent variables scatterplots ... 20
Figure 15: Correlation table, Independent variable to Dependent variables ... 21
Figure 16: Python code for correlation ... 21
Figure 17: Simple regressions values ... 22
Figure 18: Simple regression loop ... 22
Figure 19: Correlation matrix for independent variables ... 23
Figure 20: Correlation matrix containing non-redundant variables ... 24
39
Figure 21: Full Model, 1st crisis ... 24
Figure 22: Model with four selected variables ... 25
Figure 23: Model obtained by forward selection, 1st crisis ... 25
Figure 24: Independent variables versus dependent variables scatterplots, 2nd crisis ... 26
Figure 25: Dependent variable and independent variables correlation table, 2nd crisis ... 26
Figure 26: Simple regressions, 2nd crisis ... 27
Figure 27: Independent variables correlation table, 2nd crisis ... 28
Figure 28: Model obtained by forward selection, 2nd crisis ... 28
Figure 29: Full model, 2nd crisis ... 28
Figure 30: Independent variables versus dependent variables scatterplots, 3rd crisis ... 29
Figure 31: Dependent variable and independent variables correlation table, 3rd crisis ... 30
Figure 32: Simple regressions, 3rd crisis ... 30
Figure 33: Independent variables correlation table, 3rd crisis ... 31
Figure 34: Full model, 3rd crisis ... 31
Figure 35: Model obtained by forward selection, 3rd crisis ... 32
Figure 36: Independent variables versus dependent variables scatterplots, 4th crisis... 33
Figure 37: Dependent variable and independent variables correlation table, 4th crisis ... 33
Figure 38: Simple regressions, 4th crisis ... 34
Figure 39: Correlation table, 4th crisis ... 34
Figure 40: Full model, 4th crisis ... 35
Figure 41: Model with handpicked variables, 4th crisis ... 35
40
A PPENDIX A
I
NDEPENDENTV
ARIABLESS
CATTERPLOTS, 1
STC
RISIS41
