Commodity futures as a hedge and diversification tool for Norwegian investors
Recent global economic turmoil has inspired investors all over the globe to look for ways to protect their portfolios and to continue to make them grow despite a weak economy. Investments in commodities have been suggested as a solid hedge against future turmoil in the markets. The question is whether this is good advice or not for investors of all types and operating in different home economies. It is difficult to make a suggestion that will work for every investor and in all parts of the world. Therefore, the potential for commodity investing as a hedge against future instability is a question that must be answered for every country in the world on an individual investor basis. This research will explore whether commodity futures can be added to the portfolios of a Norwegian Investors as a means to reduce risk and to diversify opportunities for growth in the future.
✍️ How to write this paper — guide & tools ▾
Commodity Investing
Are there potential risk reduction and diversification opportunities in adding commodities to a Norwegian investor's asset portfolio?
Recent global economic turmoil has inspired investors all over the globe to look for ways to protect their portfolios and to continue to make them grow despite a weak economy. Investments in commodities have been suggested as a solid hedge against future turmoil in the markets. The question is whether this is good advice or not for investors of all types and operating in different home economies. It is difficult to make a suggestion that will work for every investor and in all parts of the world. Therefore, the potential for commodity investing as a hedge against future instability is a question that must be answered for every country in the world on an individual investor basis. This research will explore whether commodity futures can be added to the portfolios of a Norwegian Investors as a means to reduce risk and to diversify opportunities for growth in the future.
1.1 Background of the Problem
Several reasons exist for this sudden interest in commodity markets. With fluctuations and market uncertainty on a global scale, diversification and risk reduction have become key topics of interest. Investors are now exploring all types of investments as potential options. Commodities can be volatile, but so can stocks, bonds, and other investments in the current global economic climate. Commodities can provide high returns, but they also carry high risk as well. Commodities are not traditionally considered the investment of choice for those that are not afraid to take risks. In some markets, commodities are negatively correlated with bonds, but show very little correlation with stocks. In these markets commodities can be an excellent diversification tool (Stoll and Whaley, 2010). However, to what extent this is true in other market situations is the question that must be asked in order to understand the importance and roll of commodities in creating a balanced and diversified portfolio.
Li, Zhang, and Du (2011) addressed a similar issue concerning commodity- equity correlation. Their research differed from other researchers of the same topic in that they examined both short-term fluctuations and long-term trends. For this reason, their research would pertain to a greater variety of investors. They found that when volatility increases in equity markets it also causes an upward spike in commodity futures. Their findings demonstrated that commodity futures are volatile in the short run, but if one looks at long run trends, commodities appear to be less volatile. This would suggest that whether one goes short or long in their investment strategy can be a determing factor in whether commodities are a smart investment.
Chueng and Miu (2010) also explored the diversification benefits of commodity futures. They found that although literature supports the diversification benefits of commodity futures. Based their research on findings, no empirical work had been performed to support these opinions. They surmise that due to a lack of empirical evidence claims that commodity futures have benefits for diversification are unfounded. Their study asked several questions that are relevant to the present research study. They asked, first, whether diversification benefits are statistically significant and to what extent. They explored the resource-based economy of Canada and the effect of adding commodities to their portfolio. They found in their literature review that correlations exist between international equity returns more so during bear markets than in bull markets. They wanted to find out if the same types of switching regimes exist in commodity futures. They surmised that when investors are in a bearish market at home they will receive lower diversification benefits from International investments. They wanted to find out if the commodity futures would have the same or similar switching behavior. They also explored what types of investor should hold commodities.
According to Rafiee (2011), the correlation between the commodities market and other types of investment tools has been a topic of study by many researchers. Rafiee explored numerous studies on the topic. The overall conclusion was that the correlations, both negative and positive, differed from country to country. One cannot make a general statement that would apply to every situation around the world. Rafiee's study also found that certain sectors can have a greater impact on correlation between commodities and other stocks, depending on the nature of the economy. Given these differences, it is difficult to make a generalization that will hold true for every situation around the world. Each country must be taken on a case by case basis, and in accordance with consideration of their major products and services.
Rafiee's findings concur with those of Chueng and Miu, as well as those of Li, Zhang, and Du, The market conditions, major products, and the individual situation of the investor all have an impact on whether commodities represent a suitable investment instrument for diversification and risk management.
1.2 Discussion of the Problem
As one can see, whether commodities futures are an excellent strategy to hedge against risk and to provide diversification to portfolios is not an easy question to answer. Many factors must be considered in making this investment decision. As one can see, the economy of the home country plays a significant role in the effectiveness of a commodity-based diversification strategy. To launch a comprehensive, all-encompassing study that included results from different countries would be a difficult task. Not only would it be a difficult task, the results of such a study would not provide an accurate picture of the effects of commodity investment on various markets and situations. Advice based on such a study would not result in advice for the investor. For this reason, studies have focused on a certain country as the basis for this study. This is a better approach to this research question, but it too has caveats. The first is that the results obtained for one country do not necessarily apply to another.
Commodities are an interesting topic in the Norwegian economy. This is because the Norwegian economy depends on a commodity as a major income producer. Norway's largest economic sector lies in oil products and other industries that are intertwined in this industry, such as refining and shipping. Volatility in the oil industry has a major effect on the health of the Norwegian economy. This makes commodity investing an important topic for those who wish to obtain a portfolio on the Norwegian Stock Exchange.
Lately, Norway's, oil industry has been called a "sunset industry" (Karasu, 2009). Norway gained rights to control North Sea oil in 1963. Since that time it has been able to establish huge oil fields and become one of the top world oil producers. However, it seems that the oil wells are beginning to decline in production and the North Sea seems to have reached its capacity for production. Norway needs another big oil strike or the oil industry may be on a decline, according to Karasu. If this happens, it could have a devastating effect on the Norwegian economy that has become dependent upon oil to support a growing sovereign nation.
Conclusions are mixed as to whether diversification can be achieved through commodity futures for the reasons previously mentioned. Rafiee's performed a study that used quantitative methods to determine if commodities were an acceptable strategy for investors in Sweden. This study concluded that the commodities were not an acceptable risk reduction strategy in the Swedish markets because correlations were inconsistent, at best. Commodities were not the sole answer to risk reduction in portfolios containing stocks on the Swedish market. This research will explore a similar set of research questions, only it will focus on the oil commodity-based market of Norway.
1.3 Contribution
This study will investigate how the commodity market correlates to the Norwegian stock market and will explore various explanations for its findings. The risk tolerance of the investor will play a significant role in determining whether the investor utilizes commodities as a diversification strategy or whether they choose other options. This study will assume that home bias will define the set of investors for this study. That is to say that Norgwegian investors will hold a majority of their portfolio in Norwegian stocks.
This study will contribute to the knowledge base on commodity investment tools by exploring their usefulness in a commodity-based economy that depends largely on oil as its major product. The impact of the oil industry on whole market volatility will be further discussed in the literature review. The Norwegian market is a unique world market due to its dependence on primarily two major product categories, oil and shipping. It will fill the gap in knowledge by answering how commodities will perform as a diversification tool in a market that is heavily commodity based, and more subject to market shocks do to its size and dependence on these tow key industries
1.4 Research Questions
This study will explore the following research questions.
1. How does the Norwegian stock market correlate with the commodity market?
2. Does a correlation exist between the Norwegian stock market and other commodities sectors?
3. Are commodity investments an appropriate tool for Norwegian Investors who wish to add different types of assets to their portfolio?
1.5 Purpose
The purpose of the study is to explore the relationship between the commodity market and the Norwegian stock market. It will also explore other diversification instruments in comparison to commodities. The results of this study will provide Norwegian investors with solid information that they can utilize in their investment decisions.
1.6 Delimitations
This research paper has limited its research to correlations between the Dow Jones commodity index and its various commodities sectors with the Norwegian stock market. It will utilize the years between 2000 and 2010. This period of time should provide sufficient data points for comparison.
In our assumptions it was noted that it would be assumed that Norwegian Investors would invest in Norwegian commodities. The home bias phenomenon is recognized any time it is assumed that an inve stor will invest in their home stocks rather than international markets.
1.7 Definition of Concepts
The following operational definitions will be utilized in the conduct of this study.
Asset Allocation refers to a collection of investments held by an investor utilizing various types of instruments.
Correlation is defined as synchronous movement between various types of assets
Diversification is defined as the practice of reducing risk by investing in a variety of different investment instruments.
Norwegian investor for the purpose of this research is an investor that invests in the Norwegian securities market. The exact nature of the investor's portfolio cannot be determined within the scope of this research study. The assumption that Norwegian Investors will hold a majority of their stocks in the Norwegian market is a generalization, but one that is necessary for practical reasons in the course of the study.
OBX stock index (Norwegian stock index) is an index that follows the top companies in the Norwegian stock index. It covers companies from a sampling of different sectors and is used as a benchmark for the overall movement of the stock market. It only takes into account stock price, not reinvested dividends.
Risk averse is a term that refers to an investor that prefers to avoid high risk investments at the expense of higher returns. This type of investor is the opposite of the risk-tolerant investor who will often take risks if the potential for return is significantly high.
2. Literature Review
Volumes have been written about commodity indices and their relationship to the stock market. Diversification and risk management are global issues that grow in importance as the future of the global economy becomes more uncertain. With a topic that has such a wealth of information one must refine their search and discuss only those studies are directly influence the current research. This literature review will be divided into two major headings. The first explores the characteristics of commodity investing and its performance under various market conditions. The second major heading will provide an overview of other commodities that investors could use to diversify their portfolios. It will explore the strengths and weaknesses of these investment tools.
Before we begin a formal investigation of literature related to the research questions, let us first begin with an introduction to the Norwegian stock exchange and some common facts that are known about it. The Norwegian stock exchange, Also known as Oslo BOrs (OSE:Oslo) is the main Norwegian market. It offers a wide selection of domestic stocks as well as international companies, particularly within the petroleum industry, shipping, and other related areas. This high number of companies in the petroleum industry makes the OBX Index highly price sensitive to significant changes in the petroleum industry.
By comparison to the Swedish stock exchange, the Oslo stock exchange is much smaller. However, the Scandinavian stock exchange also has an affect on the Norwegian exchange, as the Norwegian exchange purchased the 10% strategic stake in the pan -- Scandinavian exchange group. The small size of the Norwegian exchange, and its primary index make it more volatile than larger exchanges. The OBX consists of the 25 most traded securities on the exchange. The energy sector contains 74 stocks, a majority of which are connected to the oil and gas industry (www.oslobors.no). The Oslo stock exchange has 214 total domestic stocks listed. It has 49 foreign stocks listed for a total of 263 individual stocks. The energy sector comprises 28% of the Oslo exchange (TopForeignStocks.com). As one can see, the energy sector comprises a major portion of the exchange. Circumstances that affect the oil and gas industry have a major impact on the Oslo stock exchange and its related indices. Now that we have an introduction to the Oslo stock exchange and the key factors that affect it, let us now delve into a detailed discussion of literature related to the research topic.
2.1 Commodities and Risk Reduction
The first topic to be discussed will explore literature regarding commodity futures and the various factors that influence its suitability as a risk management and diversification strategy. Studies on this topic are numerous, but tend to be highly opinionated with very little substantial positivist research to support it. For the purposes of this study, only studies that use positivist quantitative methods will be considered.
Li, Zhang, and Du (2011) altered one of the most comprehensive studies in the area of short-term and long-term fluctuations in the commodity -- equity correlation. Their research encompassed global markets in different economic circumstances. They explored both short- term volatility and long-term trends. Their key finding was that in general, as volatility increases in the equity markets, it causes a short-term upward spike in commodity futures. If one takes only a short-term look at commodities, they would appear to be more volatile than the equity markets. However, when one smooths out the trend over a longer period of time, the commodity markets are much less volatile than equity markets. Let us take a closer look at their study.
Li, Zhang, and Du used a sample population of 45 equity markets from around the world. This makes it one of the largest comparative studies in existence concerning correlation of commodity futures and other indices. This study takes a different approach than the current research study in terms of sample population size and the ability to generalize the results. Li, Zhang, and Du found that 32 of the equity markets demonstrated an upward trend in the long run and that these markets correlated with commodity futures in the decade preceding this study. The study used the time period for its data set that the current study will use. Of the 45 equity markets studied all of them had sharp spikes when the economic turmoil occurred. In many cases the short-term spikes rose above the level of their long-term trends.
The method used in the study is similar to Pearson product moment correlation. This meant that allowed the authors to examine a variety of time periods for comparison. Correlation coefficients were used to determine whether the data were positively, negatively, or not related at all. They could calculate the short-term and long-term periods. The overall conclusion of the study was that commodity futures have potential for risk management and diversification strategies in the long run. The volatility of the spikes in the short run makes them unsuitable for this type of investing. The conclusions drawn were supported by the data collected and analyzed through the course of the study.
When one examines the conclusions and methodology utilized by Li, Zhang, and Du, one will find many similarities between this larger study and others that only examined a single country. The study examined 43 indices on an individual basis. The indices were not as analyzed in aggregate, but were analyzed to obtain a view of their trends. These trends were compared in the final analysis. The conclusions of the study are valid based on the diversity of markets and economic conditions that the data encompassed. The research was written in such a way that one could extract the results from one country and take a closer look at the specific conditions that influenced it. When he results of the study are applied over different market and economic conditions, it increased the validity and reliability of the study.
Chueng and Miu (2010) performed another important exploration of the benefits of commodity futures and diversification strategy. Rather than utilizing correlation studies their study involved the Time-series plot of smooth probabilities of two hypothetical states. State one represented low return and low volatility of the commodity index over time. This work is highly cited in other works about commodity futures and diversification. However, this study only deals with probabilities not actual market occurrences. Unlike the study by Li, Zhang, and Du, this study only results in the probability of two different hypothetical situations. In reality there are many other possibilities that could exist given the circumstances being explored by these authors.
Literature supports the diversification benefits of commodity futures. Chueng and Miu criticized literature on commodity futures that promoted the benefits for diversification, stating that no empirical work had been performed to support these opinions. At that time, their work brought up an important point, a void which was later to be filled by the academic community. Empirical studies soon followed after the publication of this well cited research. They used the resource-based economy of Canada and explore the effect of adding commodities to a portfolio of Canadian stocks. In their literature review they found that a correlation exists between international equity returns during bear markets, more so than during bull markets. They wanted to determine if investors during a bear market will receive fewer benefits from diversification than during bull markets. They wanted to find out if the commodity futures would have similar switching behavior as the equity markets.
Based on their findings the authors made suggestions as to which type of investor would be best suited for using commodity futures for diversification. Although their work was quantitative and used statistics to derive its conclusions, it was not based on actual market results. Their work was theoretical in nature, yet they made recommendations as if the results were based on actual data. This is one of the key flaws of this widely cited research study. They claim to have "resolved" many issues concerning the supported benefits of using commodities to diversify a portfolio. However, the results of the study cannot be conclusive, but remain theoretical because only theoretical data and analysis was used. It is not known if real markets would perform as Chueng and Miu propose. On this account, the work of Li, Zhang, and Du hold much more credibility because it is based on actual historical market performance and investor decisions.
A comparison of the works of Chueng and Miu and Li, Zhang, and Du exposes one of the caveats of financial research. They also use the two hypothetical states as the basis of making general statements concerning financial advice. Zhang, and Du take a historical approach using actual data, and results. They were able to apply their results over 43 different markets and to take an individual look at the conditions in the markets themselves. Of course, there is no guarantee that the results will be applicable in the future, but if past patterns hold true, their work is much more predictive of future results than that of Chueng and Miu, which can only result in probabilities and theory about future events. A comparison of these two studies was a key reason for choosing to take a historical, rather than a predictive stance in the current research study.
Chong and Miffre (2010) examined the volatility of commodity markets using data from the returns of 25 commodities and 13 traditional asset classes. He used GARCH method for predicting volatilities on the sample population. The study was quantitative and relied on empirical results to draw a conclusion. Based on the results of the study it was concluded that for institutional investors long positions in commodity futures represented a successful diversification strategy. In periods of high volatility in the equity markets the authors found the precious metals an excellent diversifier. These findings coincide with the findings of Li, Zhang and Du. The conclusions drawn by the author coincide with the data and analytical results of the study.
Willenbrock (2011) studied diversification return in the re-balanced portfolio. In a balanced portfolio returns are realized as small, regular increments. However, an unbalanced portfolio can result in small incremental losses over time. In this case the portfolio needs to be re-balanced so that it returns to increasing my small regular increments. Each asset within the portfolio must have an increasing rate of return so that it does not harm the average of the entire portfolio. This makes predictable commodity investing difficult. Commodities are volatile and re-balanced on a monthly basis. Using the principle discussed by Willenbrock a commodity is difficult to manage as a diversification strategy. Diversification results in a reduction of risk and regular return. Willenbrock relied on many theories and paradigms that are widely held by the financial sector. Although some formulas were used in his calculations, this article was largely theoretical.
Kazemo, Schneeweis, and Spurgin (2007) produced a research report that supports direct and equity investment in commodities. However, the authors of the report have a direct financial relationship with some of the Investment Instruments that were presented in the report. The results of the report were decidedly skewed in favor of the investments in which the authors were involved. It does provide an excellent overview of the sources of returns on commodity investments, the history of commodity index indices and how commodities have historically performed against equity and inflation.
Daskalakia and Skiadopoulos (2011) investigated whether investor increases their portfolio by including commodities among traditional asset classes. Empirical methods were used by employing mean-variance methods and non-men-variance methods to the data. They then took into account higher order moments of the portfolio a distribution and examined their out of sample performance. They took the data and applied it in settings that mimicked the real world and compared it to the performance of the asset when it was used in the sample set. They found that in the tests adding commodities were beneficial only to of those investors that used non-mean-variance methods. The authors concluded that the method used to analyze the commodity can have an effect on whether it is deemed to be beneficial or not. Analytics in setting can change the performance and risk reduction characteristics of commodity investing.
Bodie and Rosansky (1980) used mean rate of return to examine differences in stock in commodity futures. Rate of return was calculated through pricing changes over a three-month period. These researchers found that in years where stocks were doing poorly, commodities futures were doing well. They suggested switching a 100% stock portfolio to one that included 60%, commodity and 40% stock to hedge against volatility in the market. This study used a direct comparative method to draw its conclusions. They also found that commodity futures tended to be excellent hedges against inflation. The study used the direct comparative method upon which to base its conclusions. The study seems to produce sound advice and a clear strategy when volatility strikes. However, the study did not provide enough information about the environment.
Garrett and Taylor (2001) used the Goldman Sachs Commodity Index to examine futility of commodities in the portfolio during periods of booms in commodity prices. This study observed that commodities will exhibit Comovement in seemingly unrelated commodity classes. They suggested that this Comovement suggests market wide changes are not a result of the individual commodities. A second potential explanation offered by the authors is that this represents a type of herd mentality among investors. This study relied on the results of a previous study conducted by Pindyck and Rotemberg (1990). They did not conduct any new research themselves. Using the same data they performed analytical tests to determine the significance of weight on commodity returns. The authors found that the greatest comovement occured during times when commodities were being held, rather than sold or bought. The greatest contribution this study made to the topic is that it used empirical methods to arrive in their conclusions. This provides credibility to using study as a source.
Conover, Jensen, and Johnston et al. (2010) asked the question when is the proper time to add commodities to one's portfolio? This study used evidence found in earlier studies to evaluate the consistency of commodity contribution across various equity styles. The authors found differences in equity styles when compared the studies that only used equity indices to make their comparison. This article summarizes the findings of previous research. They did not provide the sources of research they used, nor did they provide critical analysis, which weakened the robustness of the research findings. They found that commodity futures can offer benefits to equity investors regardless of their equity strategy.
Buyuks, Haigh, and Robe (2010) examined the benefits and risks of the volatile commodity market for passive investors. They found considerable switching between equity and commodities depending on market conditions. They found small comovements in equity snf commodity tools, but over the long run commodities appeared to be the more stable choice.
Yamori (2011) suggested that commodity ETFs are beneficial to traditional commodity future markets.Home bias had been viewed as an anomaly by many researchers. However empirical evidence supports that existence of home bias through the utilization of a mean-variance statistical framework (Gorman and Jorgensen, 2002).
Commodity futures display several properties. Fully collateralized commodity futures offer the same return and Sharpe ratio as U.S. equities. The risk premium for commodities is essentially the same. However, they are negatively correlated with equity bonds and bond returns. This negative correlation was largely a part of fluctuations over the business cycle. Commodity futures are positively correlated with inflation and volatility in the inflationary index (Gorton and Rouwenhorst, 2006).
Mining and agriculture are the two major industries in the Australian economy. Not surprising, these two sectors play an important role in the Australian stock exchange. Commodity futures on the Sydney exchange are set in large international markets, rather than domestically, this is due to the role that export plays in the Australian economy. The Australian exchange is heavily dependent on returns from commodity indices and the energy, metals, and agriculture sector of the United States, United Kingdom and Canada (Heaton, Mullonovich, and Passe, 2011).
Portfolio composition theory states that the optimal portfolio should take into consideration the mean-variance of all assets. The home-bias affect is where investors hold a higher-than-optimal portion of domestic assets. A study of German mutual funds took into consideration data from 2000-2003 found strong evidence for the home-bias effect in German portfolios. Investors are taking into consideration feelings of loyalty, rather than a statistical theory in creating their portfolios. Portfolios have a behavioral component as well as a financial one. The study demonstrates that financial theory does not tell the whole picture (Oehler, Rummer, and Wendt, 2008).
It has been mentioned briefly that some commodity stocks futures do well when stocks are not performing well. Simimou (2010) found that this was true of European agricultural futures. Their article concluded that an investor can achieve overall risk reduction by holding a European agricultural commodities contract in their stock portfolio (Simimou, 2010).
3.1 Research Approach
This research will utilize a positivistic approach to its research methodology and discussion. Positivism and quantitative research methods are compatible in that both strive to be as objective as possible. Unlike subjective qualitative research methods, the positivistic approach is carried out to be as objective as possible with as little influence from the author's personal experience or opinions as possible. The purpose of positivistic quantitative research methodology is to produce findings that meet the empirical scientific method requirement of replicability. If an identical study were to be carried out, the positivistic quantitative approach means that the same results could be expected.
This is not the case with qualitative studies were the results are dependent on the researchers observations and opinions. The positivistic quantitative approach is best suited for topics where a pinpoint piece of data can be obtained. This is the type of data that we are collecting in this study. Therefore the positivistic quantitative approach is best suited for this study.
This study will utilize a deductive and analytical approach based on existing theory and research questions derived from these theories. First, the research questions will be tested and analyzed. A logical conclusion will be drawn from the results. This method will create a set of findings that will fill a current gap in research and the chosen topic area. Statistical analysis will be utilized is the key tool for analyzing the data and discussing the findings.
Positivist quantitative studies utilized two types of data. The first is primary data that does not exist previously. The researcher must collect this type of data. The second type of data is known as secondary data. In financial research, this is available by means of financial reports institutions, in the research conducted by earlier studies. This research is historical research and therefore will use secondary data to derive its findings. To increasevalidity, it is important to screen the data to make certain that it meets necessary criteria.
3.2 Validity and Reliability
Validity refers to the ability of the study to answer the research questions in to measure what the researcher intended to measure. A study that is not valid loses its purpose and intent. In the case of this study, indices must be chosen that reflect price movement of both markets. Those that reflect movement of both markets must be given the most weight.
If research studies must be valid in order for them to be useful in answering the questions for which they were intended. The research study that is not valid it will not fill the gap in research and the gap in research will remain. However, in order to fill the gap in research, the results of the study must also be reliable. Earlier the topic of the ability to reproduce the results of the study was discussed. Reliability in a research study that derives from historical data depends on the credibility of sources. Credible sources improve the robustness of the calculations and ensure that the models function correctly. This study will rely on formulas and calculations that have a proven academic track record in other studies. Inventing new formulas and algorithms would mean that the researcher cannot rely on them until they have been proven and tested. Using formulas and calculation that have already demonstrated the ability to perform as expected allows the researcher to use them with confidence. It also allows the researcher to have greater confidence in the results of the study.
3.3 Procedures
This research will explore day-to-day data from the Dow-Jones commodity indices and the Norwegian stock exchange. It will explore both the indices of the whole as represented by the Dow-Jones -- UBS commodity index (DJ-UBSCI), as well as making a comparison to reach of the some indices. The sub-indices will include the agricultural index (DJ-UBSAG), energy (DH-UBSEN), industrial metals (DJ-UBSIN), livestock (DJ-UBSLI), and precious metals (DJ-UBSPR) commodity indices. The day-to-day prices of these indices will be compared to market index prices on the Norwegian stock exchange.
A survey period of 10 years will be used, which is considered sufficient to take into consideration business cycles in changes in the global market. The time period selected will be from January 1, 2000 to December 31, 2010. Daily, as well as average quarterly prices will be utilized to determine daily effects as well as general trends. Pearson product moment will be used to determine if a correlation exists between these factors.
The results these analyses will be discussed in conclusions drawn in relation to the thesis and research questions.
Create your account
Always verify citation format against your institution’s current style guide requirements.