Universiteit van Amsterdam – Amsterdam Business School Executive Master program in International Finance
On the diversification benefits of adding commodities index products in a stock and bond asset portfolio
Student: Roberto Colombo Student ID: 11081961
Master Thesis Supervisor: Prof. Esther Eiling Course: Advanced asset management Academic year: 2015/2016
On the diversification benefits of adding commodities index product in a stock and bond asset portfolio, an in sample mean spanning test.
Roberto Colombo
Abstract
In recent years investors and financial advisor have shown (and offered) an increased interest in commodities and in general terms in alternative instruments as part of financial portfolio. Standard literature support their view since from a theoretical point of view commodities should provide a good hedge against inflation and they should have a correlation with standard financial asset negative or close to zero.
A second stream of work challenges this view and instead proposes the idea of a financialization of commodities, that is the real asset class over time has lost some of its features and no longer improves the risk-return combination of a standard portfolio. The reason behind is due to the larger number of investor looking for a way to diversify their position and looking for commodities as a way to achieve their goal.
Literature will be presented, then analysis considering recent data for a commodity index will be performed. Analysis will be focused on a mean spanning test across different time horizons in order to assess whether the commodity index should be effectively included among the investable asset class from the point of view of a US investor.
Also I will construct two out of sample portfolios in order to compare moments in the distribution of a two and three assets portfolios. Portfolios will be constructed in a rolling and an expanding fashion to assess for potential differences over time.
In sample conclusions support the presence of diversification (although very close to zero) during and after the US financial crisis. At the same evidence on the emergence after the crisis of a positive correlation between equity and commodity asset excess returns has been found, which support the financialization theory. Also analysis shows that after the crisis return correlation between commodity and equity is significant and positive.
Out of sample test on the other hand strongly indicates that the three asset portfolio does not provide significant changes to the benchmark portfolio.
Given the above, presence of diversification cannot be ruled out, however by taking into consideration the size of diversification and the results found on commodity and equity return correlation, analysis indicates that the financialization theory cannot be ruled out.
Section I: Introduction
On the 23 September 2016 the Federal Reserve released a proposed new regulation1 which would strengthen the capital requirements and limit the trading activities in commodities for financial companies. Following the memo2, it is reported that the existing Gramm-Leach Biley Act (GLB) allows a small number of US financial holding to invest in metals, oil and agricultural commodities by means of trading, participation in derivative contracts and involvement in physical settlements. The new proposed regulation aims to modify the current situation given the potential legal, reputational and financial risks associated with the commodity trading activity. In the event of a catastrophe the environmental damages involved by physical commodities can exceed their market value and can also exceed the committed capital and insurance. This in turn could lead to the imposition of fines, costs and reimbursements which could put in pressure on the financial systems.
It is worth noticing that this is not the first attempt from the FED to impose stricter regulations on Wall Street with respect to commodities In 2014 the US senate permanent subcommittee on investigations released a report3 which highlights a number of commodity market operations for major Wall Street banks. Among their remarks, US senate states that a number of Wall Street financial companies (JP Morgan, Goldman Sachs, Morgan Stanley) having allocated a non-sufficient amount of capital was prepared to withstand losses resulting from a catastrophic event in physical commodities
As a result of the proposed new regulation, the majority of US banks disinvested their commodity portfolio and sold their activities (including energy plants, terminals, stocks, warehouse companies) to specialized commodity trading firms. One of the few companies still involved in this line of business is Goldman Sachs which as a result lost 1.7% of its share price on Friday immediately after the FED notice. The new proposed regulation on natural resources is in line with a recent global attempt to establish a stricter regulation framework on alternative investments. In April 2009, the European Union proposed a directive4 to be imposed on alternative Investments Fund Managers to boost supervision at the
European level, given the amount of invested assets by manager of alternative funds.
1 https://www.federalreserve.gov/newsevents/press/bcreg/20160923a.htm 2 https://www.federalreserve.gov/newsevents/press/bcreg/bcreg20160923a2.pdf 3 https://www.hsgac.senate.gov/download/report-wall-street-involvement-with-physical-commodities 4 http://ec.europa.eu/finance/investment/alternative_investments/index_en.htm#maincontentSec2
In particular the directive states that the impact of alternative investments asset manager, although beneficial , carries significant risk to investor and financial markets in general.
If the proposed directive receive sufficient support from EU institutions and public opinion, its approval would be the recognition from the authorities on the substantial importance and the impact that alternative assets have nowadays in the market and countries’ economic activities generally.
Motivated by the growing importance of commodities (and alternative assets in general) for regulators and industry professional, this paper documents on both the economic rationale behind this investment strategy and whether it would be efficient for an investor to devote part of his allocation in the
commodities asset class.
Study aims to address if from a classic mean variance optimization framework an investor would find himself in a better risk and return combination by adding commodity assets to his portfolio. The analysis will be conducted initially with an in sample mean spanning test, and secondly with a rolling and an expanding window out of sample test.
Study will also address on the economic rationale behind commodity investing. Accepted theory concludes that commodity linked instruments being an alternative asset classes provide a return hedge against inflation and uncorrelated returns with common instruments. A second and more recent line of work on the other hand, addresses the possibility that investing in commodities is no longer an efficient solution given the so called financialization process, that is the emergence of institutional investor dealing with alternative asset classes and the correlation increase among and standard and alternative instruments. I will show that my results are in line with this second stream of literature.
The remainder of this paper is organized as follows. Section I provides an overview of alternative investments trends and commodity asset class feature’s by proposing industry and academic studies. Section II discuss relevant literature review on the diversification properties of different financial instruments, such real estate, international equities and studies on the diversification benefits of commodities and economic interpretation behind those. Section III describes the data and empirical methodology. Section IV reports the main results. Section V concludes.
Section I: Overview of alternative investments and commodity asset class features
2.1) Market outlook and industry paper on alternative instruments
Alternative investments involve resource allocation in asset classes which historically might be perceived as illiquid/inefficient and often are traded outside of exchanges with considerable transaction costs. Among the alternative instruments available to investors, the standard choices are Real Estate, Hedge Funds, Private Equity, Credit derivatives, Commodities and natural resources.
Standard view followed by investment managers prescribes that alternative assets provide good diversification benefits within a portfolio since they display a low correlation with equities and bonds and can provide a positive return (both absolute and relative). This argument is similar to the one used in the construction of portfolios inclusive of international bonds that is, given a lower correlation of international bonds to domestic equities (compared with domestic bonds), adding them to a portfolio provides a better risk-return combination. Additionally, since returns on alternative investments are heavily correlated to global economic activity, a small allocation might enhance portfolio returns in times of unexpected inflation.
Generally speaking, active management has been looking to alternative investments as a way to grasp alpha especially after the 2008 financial crisis when equities plummeted and since the introduction of quantitative easing with consequent reduction of interest rates and bond returns.
Overall the ways in which an investor can get exposure to alternative asset classes are diverse, for instance, an investor can enter the commodity markets through future contracts exchanged on the CME (Chicago mercantile exchange) or those who can get exposure to funds by buying shares of investment companies get exposure to real estate by investing in real estate investment trusts, funds where the primary aim is to invest in real estate properties (either commercial or residential).
Given that some asset classes are not traded on the stock exchange, a number of problems arise when an investor tries to assess risk and returns of alternative assets. One of those problems is that such an investor must consider that real estate investment prices often fluctuate as a result of an independent assessments and can be heavily influenced by prices in the surrounding areas. The result of this would be that the returns display smoothing problems. In order to avoid this problem, a proxy method would be to invest in equities share of listed companies who invest in specific asset classes, so that their company prices are supposedly heavily influenced by the underlying allocation.
That being said, investment strategies in alternative classes are normally followed by specialized asset managers who look to grasp alpha for their portfolios.
Having presented the standard view, I report also a number of drawbacks to be taken into consideration by investor willing to allocate resources in alternative investments. In particular it might be harder to disinvest and a lock up period might be put in place, also Incentive fees might be present and measuring risk within the industry is harder.
In addition a minimum large investment is often required, less regulation currently in place and finally active investment strategies might suffer of transparency issues and limited information disclosure. The following paragraphs introduce some industry papers and reports which highlight how the asset management business is changing to take into account alternative asset classes.
2.2) Growing importance of alternative assets in the investment landscape
According to a several industry research papers, the rapid growth and popularity of alternative instruments has become a common trend in recent years thanks to the increased allocations by institutional investors and the movement to alternatives in the retail investment landscape.
Following two PwC reports,56 it is estimated that by 2020 global assets under the management industry will increase to more than $100 trillion, a growth fueled by pension funds, high net worth individuals and wealth funds. Additionally, AuM will increase thanks to alternative assets which will grow between $13.6 and 15.3 trillion, a 9% increase from the current $7.9 trillion and this rapid increase in alternatives allocation will be followed by a standardization of firms and investment processes.
Similar considerations have been drawn by a McKinsey report7 which clearly states that for asset managers, alternatives are one of the biggest opportunities for next year thanks to their high fees and segmented market. Alternatives have been growing faster than traditional assets and the trend will likely persist in the future since it is the consequence of structural forces and not investors chasing returns.
5
Alternative asset management 2020: Fast forward to centre stage; http://www.pwc.com/alts2020
6 Asset Management 2020: A brave new world;
http://www.pwc.com/gx/en/industries/financial-services/asset-management/publications/asset-management-2020-a-brave-new-world.html
7
McKinsey&Company: The Trillion-Dollar Convergence: Capturing the next wave of Growth in Alternative Investments
In particular, the McKinsey reports identify four structural forces which are accelerating the adoption of alternatives by asset managers: Investors perception on alternatives as an insurance policy to reduce portfolio volatility; alternatives as a way to reach alpha and take advantage of low fees tracking index products for their portfolio beta; adoption of alternative instruments to hedge against inflation; allocation strategies on alternative asset classes to meet demands of investors and pensions funds. The following chart reports growth rates on AuM based on the Mckinsey Report for both traditional and alternative assets. As can be seen from the chart, the average annualized growth rate for alternative instruments is almost double compared to the one of traditional investments (11% vs 6%).
Figure 1: McKinsey report Global AuM Tr $ growth rate: The chart provides the compound annual growth rate on traditional and alternative assets under management from 2006 until 2013 in Trillion $. Source: Hedge fund research, Preqin, Mckinsey analysis.
Interestingly, the main conclusion from the McKinsey report is that investments in alternative asset classes will not be a prerogative of specialized investors. On the other hand, retail investors will likely start to allocate a higher proportion of their wealth thanks to technological and product innovation.
15.36% 7.48% -17.61% 12.93% 6.78% 0.00% 9.85% 12.95% 28.13% 21.95% 0.00% 6.00% 11.32% 6.78% 7.94% 5.88% -20.00% -10.00% 0.00% 10.00% 20.00% 30.00% 40.00% 2006 2007 2008 2009 2010 2011 2012 2013 Trillion USD
A State Street market commentary8 is in line with Mckinsey conclusions’, that is retail investor are expected to generate a strong demand for alternative investments in a similar fashion to what happened with ETF before.
Preqin, a leading source of data and intelligence on alternative asset markets, releases every half year a report with performance overview for different asset classes. The 2016910 monitor reports that
alternative classes are worth $7.4 trillion globally and that funds operating in natural resources have outperformed the public market. Growth in alternatives has been driven mostly by private equity and hedge funds, as well as investment in US real estate. Investment in natural resources on the other hand displayed a decrease in returns in the past few years.
Even though a decrease in commodity prices started in 2010 and is still going on in 2015, the Preqin report also shows that 37% of institutional investors still allocate part of their funds into natural resources – more than the number of institutional investors allocating in infrastructure. It is worth noticing that according to the report, investors are concerned about the natural resources market’s performance due to low commodity prices in 2015 but they will maintain the allocated capital in the long term and 28% of investors expect to increase the size of their portfolio. Specifically, within the natural resources sectors, investors are looking mostly to energy and metals since those two categories experienced the strongest price decline in the past and opportunities may come forward.
Unfortunately, 2015 was not a good year for commodity prices as well. In fact, 62% of investors have fallen short for their expectations and their key concerns for the coming years is brought upon by ongoing volatility in global markets and the market’s performance. Overall, investors seem to be cautious in their approach to natural resources and 41% of investors plan to allocate less capital in this particular asset class compared to 2015.
Generally speaking, the outlook for alternative classes remains positive. A June 2016 report by BNY Mellon11 shows that capital flows in alternative assets will increase and 93% of respondents met their expectations in terms of returns. The report states that 53% of respondents are prone to increase their future allocation in Private Equity and particular interest in PE will derive from institutional investors. 8 http://www.statestreet.com/content/dam/statestreet/documents/Articles/RiseOfAlternatives_February%202015 .pdf 9 https://www.preqin.com/docs/reports/2016-Preqin-Alternative-Assets-Performance-Monitor-Sample-Pages.pdf 10 https://www.preqin.com/docs/reports/Preqin-Investor-Outlook-Alternative-Assets-H1-2016.pdf 11 https://www.bnymellon.com/_global-assets/pdf/our-thinking/institutional-investment-in-alternative-assets.pdf
Similar conclusion can be derived from a Booz&Company strategy report,12 that predicts that alternative asset investments will grow to $18.1 trillion by 2020 due to rapid change in the types of investments (more liquid with transparent fees and products) and investors (retail investors will be part of the pool). The next chart provides details by asset class with forecasts for 2018 and 2020.
They conclude that overall, investments in alternatives are becoming more mainstream with most of the growth due to private equity and hedge funds.
Figure 2: Booz&Company global alternative assets by class type: The chart provide institutional and retail investors allocation in dollar terms on different alternative instruments (private equities, hedge funds, Real estate, Institutional loans, Liquid alternatives and Commodities) from 2004 until 2012 and allocation forecast for 2018 and 2020 in Trillion $. Source: Booze&Company and PwC.
Two different outlooks made by a financial institution and an asset management firm will now be presented as part of Section I.
A quarterly market outlook13 released by the World Bank is dedicated on commodities and provides detailed analysis and price forecasts for 2016 onward (data reported in figure below).
12 http://www.strategyand.pwc.com/media/file/Alternative-investments.pdf 13 http://pubdocs.worldbank.org/en/328921469543025388/CMO-July-2016-Full-Report.pdf 3.5 6.7 8.1 10.9 14.7 18.1 0 2 4 6 8 10 12 14 16 18 20 2004 2007 2012 2015 2018 2020 Trillion USD
Figure 3: World bank price index report and forecasts: The chart provides the world bank commodity prices forecast’s in index term for Energy, Agriculture and Base Metals index products. Source: World Bank
As per figure 3, World Bank expects that by the end of 2016 a rebound in prices starts. Such a rebound would terminate the declining trend started in 2014 and by jointly considering it with the expected reduction in inventories, the financial institution does not only support an increase in next year prices but also they amended upwards their forecast elaborated in the previous quarter.
From the figure above, it clearly appears how commodities have been struggling in the past few years in terms of prices, a situation highlighted also by a September 2015 outlook from Blackrock14 which summarizes the situation well.
According to their report, the joint slowdown of emerging market economies, the slow growth of developed markets and the consequent fall in demand and inflation, combined with global policies on oil supply, have led to a steady decline in commodity prices. The report interestingly mentions how on the other hand the previous price surge of 2011 was due to fear on the high inflation which might be caused by central banks QE policies.
The asset management firm contrary to the financial institution however, does not predict a rebound in prices since according to their report the structural causes which lead to a price decline in the first place are still present.
14 http://www.blackrock.com/corporate/en-is/literature/market-commentary/outlook-for-commodities-market-perspectives-september-2015.pdf 0 20 40 60 80 100 120 140 2012 2013 2014 2015 2016 2017 2018 2019 2020 2025 Price Index (2010 = 100)
Having briefly discussed the growing importance of alternative instruments, I will devote my attention now to the commodities asset class by listing its main feature.
2.3) Key features of commodity asset classes
As seen in the introduction section, asset managers consider commodities (and in general, alternative classes) as a useful instrument for portfolio selection thanks to their diversification capabilities. The following passages provide why this might be the case.
Asset pricing theory (such as the dividend discount model) explains that capital assets (such as stocks and bonds) can be valued by discounting future cash flows at an appropriate rate. Contrary to that, commodities do not provide a claim on a future set of cash flows. For this reason, the discounting cash flow model cannot be applied to them.
Prices for commodities on the other hand should be evaluated by taking into account changes in fundamentals, that is the supply and demand. Under this perspective, is clear how many different factors come into commodity price evaluation, for instance global trades, weather, international agreements on production and new technologies all have an impact on supply and demand components.
It is worth stressing also that the geographical location of commodities is a determinant, for most of the commodities production sites are located in emerging markets while on the other hand demand flows have a global nature, hence commodity prices depend on both global trades and currencies exchange rates.
A second feature is that compared to stocks and bonds, expectations play a role but are less important, prices are bound to react to swift changes in supply and demand forces and are much more dependent on a short time event. As a consequence commodity prices might display strong volatility.
Another important component is the link between commodity prices and inflation. In particular,
commodities are often the input component for goods and productive processes and as such they enter directly and indirectly into the statistical calculation behind the inflation rate. As such commodity prices and inflation display a positive correlation, they are perceived as a way to hedge against inflation.
As a final consideration, commodities for many manufacturing firms consists in the input source for their operations. A decline in commodity prices might result in unexpected additional profits and hence cause an increase in the company’s stock prices.
Given the above, accepted theory suggests that commodity price should display a low correlation with equities and hence this kind of instrument should be employed by investors looking to efficiently diversify their portfolio.
The next section will address the literature review. Section III: Literature Review
3.1) Review on commodity futures and portfolio diversification
Portfolio selection and portfolio diversification have been extensively analyzed in academic literature, starting from H. Markovitz (1952), Sharpe(1964) and Lintner(1965) to name the pioneers. The literature expanded to include different methodologies (such as index and multi index models), to account for expectations and how to evaluate performances.
Regarding the inclusion of different asset classes to a portfolio, Friedman (1971) showed that the models for stock selection can be applied to real estate. He concluded that highest returning portfolios are mostly inclusive of real estate, especially after tax. In the end according to Friedman financial institutions should evaluate more favorably the inclusion of real estate in their asset mix, the same logic however might prove to be inefficient for individuals due to transaction costs.
A similar result has been obtained by Curcio et al. (1988), in particular the authors addressed a similar the inclusion of real estate into a portfolio but with an expanded dataset. Results are in line with Friedman’s, that is the optimal portfolio employs in real estate two-thirds of total allocation. Moving a different asset class, Grubel(1968) addressed the point of international diversification- allocation in stocks listed on foreign exchanges - by including eleven industrialized countries and he found that an investor can reach higher returns for its portfolios compared to the result in which he only invest in US stocks.
International diversification has been tackled in many different works in academia, for instance Errunza et al(1999) examined the position of a US investor who wanted to achieve the same level of
conclusion is clear, diversification benefits can be achieved by investing in domestic assets which grant claims on foreign returns, so reliance on ADR to trade abroad is not necessary anymore.
Curcio and Ziobrowski(1991) jointly considered the topic of international diversification and foreign real estate in order to address whether international investors would be better off in terms of
mean-variance portfolios by including US real estate in their portfolios. Their conclusion is negative, the level of risk introduced by exchange rates offsets the diversification benefits.
Moving on to the commodity asset allocation, a first common topic addressed is whether commodities should be considered as a separate asset class.
On this perspective Froot(1995) studied the properties of real assets (that is real estate and commodities) in order to evaluate their correlation with inflation and whether they hedge against adverse shocks. In his evidence, oil and commodity futures display overall the best results in terms of portfolio diversification since real estate works well in order to hedge against inflation but not against adverse shocks. In his paper author starts by defining first real assets, that is assets which increase in nominal value when unexpected inflation appears, a feature not present in equities and bonds according since discount pricing models lose value in times of unexpected inflation.
E. Anrkim and C. Hensel (1993) on the other hand tried to evaluate the correlation between GSCI (Goldman Sachs commodity index) and S&P indices between 1972 and 1990.
The authors decided to opt for an index product since these kinds of instruments are fully collateralized, allowing long position only and to consider a broad base commodity exposure. According to their results a low correlation exists between the two indexes and the majority of diversification is provided during period of high volatility. Given these results, they conclude that commodities should be
considered as a separate asset class.
Further in the literature different authors tried to analyze further the concept of portfolio selection inclusive of commodity futures. For instance, R. Greer (1978) shows that an investor can hedge against inflation by using commodity futures in his portfolio.
Similar conclusions have been obtained by Z.Bodie (1983) where he explored how commodity futures can be used to support traditional investments in an inflationary framework. In particular the author makes the point of retail investors who are more concerned about the dollar value of their endowment
in contrast to the nominal rate. The author concludes that this should lead fund managers to provide investment alternatives where the aim is to hedge for the real rate of return.
C. Conover et al(2005) analyzed the relationship between commodity investment and FED policies for an equity investor. The authors conclude that in order to enhance performance by adding commodities, investor should consider an allocation greater than 5% and only during times in which the Fed is pursuing a restrictive monetary policy (that is interest rates are bound to increase).
A similar conclusion has been found by G. Jensen et al(2002). They examined the effect of adding managed and unmanaged commodity futures to a portfolio consisting of US and foreign equities, T-Bills and corporate bonds. In their study, the authors conclude that adding commodity futures to an investor portfolio provides the best results only in time of restrictive monetary policy.
Erb and Harvey (2006) looked at historical returns of commodity futures and concluded that only corn had a statistically significant return in a data set spanning from 1959 until 2004. Also in their paper the authors investigated the determinant of commodity returns and thy also found that different
commodities have little co-movement, a result in contrast with financial assets which normally displays highly correlation across themselves.
Finally the two authors tackled the point of equally weighted portfolios inclusive of commodity futures commenting on the work of Z.Bodie and Rosansky(1980), who found out that an equally weighted portfolio inclusive of stocks, bonds and 23 commodity futures had an excess return similar to the one from the S&P, and Fama and French(1987) who on the other hand only found a slight evidence of significant returns in commodity investments.
Erb and Harvey concludes that an equally weighted portfolio is not representative of the market as a whole since small caps dominate in relative weight, hence an equal allocation of commodity futures in their view would not be representative of the market and should not be used to compare returns across asset classes.
Abanomey and Marhtur (1999) also studied whether including commodities futures into an existing standard portfolio of international stock and bonds improves risk/return combination. Their conclusion is straightforward: the Sharpe ratio of the portfolio inclusive of commodities dominates the standard portfolio and hence is an efficient strategy for investor.
G. Gorton et al (2006 and 2015) extended the literature by analyzing the relationship between commodity future and equities; they found that historically commodity futures have provided both a risk premium similar to equities and a diversification thanks to little co-movement with stocks.
Interestingly the authors conducted the same analysis ten years later and according to their conclusion, main results found in 2006 still hold.
Of particular interest for this study is a second conclusion Gorton (et al) found by adding other ten years of data in their model. Among their results, they found evidence of an increase in correlation between different commodities and between commodities other asset classes and in times financial distress. Their result introduces a core part of my studies, that is the notion of financialization which can be defined as the adoption of commodity instruments by institutional investors and the consequence in terms of correlation and return dynamics. In general terms by the concept of financialization literature refers is a closer integration between commodities and other financial assets.
3.2) On the financialization of commodity investments
The theory behind financialization of an asset class can be as part of the literature stream related to the integration of capital markets and the propagation of volatility and returns dynamics across different assets. Literature on this topic is extensive and a review is not in scope for this study, however further material can be found in Longin and Solnik (2001), Solnik et al (1996), Bekahert and Harvey (1995) and de Santis and Gerard (1997) to name a few.
In recent years a range of studies addressed commodity financialization and an overview will hereby presented here.
Domanski and Heath (2007) addressed whether the growing presence of investor had an impact on the commodity asset class. In particular they searched for evidence on an increased trading activity on commodity linked products from managed money traders and hedge funds (so non-commercial traders). The authors show that the numbers of non-commercial traders involved in the commodity trading and the commission paid to them has increased over time. In their study, they conclude that the rise of new actors looking for yield will unlikely change in the future
Tang and Xiong (2012) support the thesis of an increased financialization in commodity market, specifically they report that even though earlier studies demonstrated that commodity markets dynamics were not aligned to typical financial assets and hence a good way for investor to diversify
portfolio and hedge against inflation, by considering more recent data they found that prices correlation between non energy commodities and oil prices has increased. Additionally authors found also evidence of an increased correlation between emerging market and commodities indexes. In their conclusion, authors states that as a result of financialization, risk appetite in financial classes has an impact on commodity prices
Tang and Xiong in the same study motivates the evidence of a commodity market financialization with the growth in commodity investment by institutional and retail investors; implication for producers and traders in terms of allocation strategies might be significant, in fact according to the authors view, reliance on commodities investment to enhance portfolio return is a consequence of the small perceived correlation observed in historical data, which in turn lead to an overestimation of the diversification benefits.
A similar conclusion has been found by Cheng and Xiong (2013), in particular they present in their work how correlation between commodity index and emerging markets has increased significantly from the US financial crisis onwards, and the same happened between commodities index and emerging market. Also Silvennoinen and Thorp (2009) studied the correlation between commodity futures and other financial assets and they found evidence of stronger financial market integration expressed an increased correlation with stock and bonds.
Finally Basak and Pavlova (2015), expanded the literature by analysing the relationship between future prices and financialization. In their study they found evidence of a positive relation between institutional investor activity and commodity index. The same is true for future volatility and for the
equity-commodity correlation. Overall the authors concludes that as a consequence of the financialization, diversification benefits of commodity investment diminish.
3.3) On mean spanning test
Spanning tests were introduced by Huberman and Kandel in 1987 as a way to address diversification benefits of adding assets to a benchmark portfolio. The authors identity three possible cases:
i. If the mean variance frontier of the two portfolios intersects then there is a combination out of which there is not benefits of adding the additional asset class
ii. If the frontier of the extended portfolios coincides with the frontier of the benchmark, we have spanning, hence no benefit for investors from adding new assets to their portfolio.
iii. If the frontier of the larger portfolio (in terms of asset classes considered) dominates the
frontier from the benchmark portfolio, investors would benefit from allocating their endowment in the larger portfolio.
Academic literature elaborated extensively on the notion of mean spanning test and portfolio diversification, however I found mixed results.
Huang and Zhong (2006) employed mean spanning test in order to investigate whether commodities, TIPS and REITS provides diversification benefits over a portfolio of US and international equities and bonds. Also they test whether TIPS, commodities and real estate are substitute for each other. They concludes that additional assets are not substitute of each other and that the efficient frontier inclusive of TIPS, commodities and REITS improves the investors’ portfolio diversification (so the frontier is not spanned by the traditional classes).
Similar results have been found by Galvani and Plourde (2010) and Belousova and Dorfleintner (2012) In particular Galvani and Plourde tested whether the inclusion of energy future contracts for WTI, gasoline, natural gas and Brent crude enhance the investment possibilities for investors. They conclude that the inclusion of all energy commodities is beneficial for investors.
Belousova and Dorfleintner on the other hand investigate the inclusion of a large pool of commodities in an equity and bond international portfolio. In particular the two authors includes Energy, Industrial and precious metals, agriculture and Livestock commodities. Their results differ from the one obtained by Galvani and Plourde since they do not find evidence of enhanced diversification coming from the inclusion of natural gas, on the other hand adding precious metals is beneficial for investors looking to diversify their portfolio for both risk and returns. Agriculture and livestock diminish the risk of the portfolio but do not improve its return side, hence only very risk averse investors should consider them in their asset allocation choices.
Contrary to the above results, Cao et al (2010) address a similar research topic by using future contracts on physical commodity with recent data and they do not find evidence of enhanced diversification by adding the commodity future, also returns from commodity future are not significantly different from zero. Overall they conclude that passively adding commodity future in a portfolio, even though perceived as a way to diversify and hedge inflation, may not be the right choice.
Section IV: Methodology
The aim of the study is to address whether by considering different time horizons, evidence is found on the commodity market financialization process as expressed by Basak and Pavlova and other authors. Significant evidence would rules against the perceived the diversification properties of commodities. I will proceed by selecting first an index which is fairly representative of commodities in the economy and which is based on liquid data and provide exposure to diverse commodities in order to encompass the whole commodity asset class. With these goals in mind I selected the Bloomberg commodity total return index which is constructed on six different commodities weighted in order to reflect the relative market liquidity of each commodity contract.
Given the purposes of the analysis, I employ the following model:
Let T defined as the number of observations, N1 as the number of base assets and N2 (>N1) as the asset class object of my test, in sample mean spanning test can be employed by regressing the excess returns of the commodity assets over the benchmark ones.
𝑅𝑁2,𝑡= 𝛼 + ∑ 𝛽𝑗∗ 𝑅𝑁1,𝑡+ 𝜖 𝑡
𝑁1 𝑗=1
Significance in the constant term would be evidence on whether the commodity index provides diversification benefits (either by assuming a long or short position) hence in line with the standard theory on commodity diversification.
On the other hand, following the financialization theory, a not significant value in the constant terms or a beta coefficient significant and close to one, would suggest that the dependent variable should not be considered an asset on its own since its diversification features are no longer present.
A significant estimate for the beta term would provide evidence on correlation between the
endogenous and exogenous series however theory implication has to be evaluated depending on the size of the coefficient. If the commodity index displays a beta term significant and close to 1, it would imply that its excess returns tracks the equities or the bonds ‘ones, however a coefficient close to 0 or negative would support standard theory.
A more severe test involves out of sample portfolio returns. In sample estimates are useful to develop and test the model, however from an investor perspective, performances tested on an out of sample
estimation are more relevant. The logic behind this statement is straightforward, an investor portfolio return at time “t+1” will be achieved with weights estimated at time “t” and returns at time “t+1”, hence the practical case for investors is to decide on asset allocation at time “t” for the subsequent periods and reallocate portfolio weights accordingly.
Comparison between main moments resulting from out of sample portfolios allows the study to conclude on the most efficient diversification strategy.
Given the above construction of the out of sample estimates will be done according to two different time horizons, a rolling window and an expanding one. The logic behind is the same as for the mean spanning test, that is with different time framework I intend to capture evidence of the emergence of financialization in commodities. Having found out of sample point estimates for my return, I will propose the main moments and compare them.
Methodology behind out of sample portfolio construction will be briefly presented here:
- Rolling window analysis has been conducted by considering first the initial 36 observation starting from 31-8-2003 until 31-7-2006. As per methodology presented before, efficient weights for equities, bond and commodities were found and the out of sample portfolio return calculated. The same procedure has been repeated for the next 36 months starting from 1-9-2003 until 31-8-2006 and so on for the whole dataset.
- Expanding window technique on the other hand is achieved by expanding my initial sample by 1 observation for each step, efficient weights were calculated in the same fashion as before. In both rolling and expanding window analysis, procedure has been conducted for both the two assets portfolio (equities and bonds) and 3 assets portfolios (equities, bonds and commodities).
Section V: Data and summary statistics
I will start by proposing statistical analysis for my assets, then the concept of standard portfolio optimization will be introduced and the results for my data set reported.
4.1) Statistical analysis
Analysis will be performed on three different indices mimicking the following:
1. ^GSPC: S&P 500 stock market index. Dataset consists of monthly data from 31 August 2003 to 31 July 2016.
2. AGG: Blackrock iShares Core U.S Aggregate bond ETF. Dataset consists of monthly data from 31 August 2003 to 31 July 2016.
These are the two main price series to be considered for the analysis which will be conducted from the point of view of US investor looking to expand his standard portfolio of US stocks and bonds with a third assets.
Investor goal is to maintain portfolio volatility as low as possible for a given expected return. To exploit the perceived diversification features of commodities, investor decided to orient his choice toward commodity investment index:
3. BCOMTR: Bloomberg commodity index total return: total return index which includes the positive or negative returns caused by either by rolling future contract or holding the physical asset. It is an investable product and the dataset considered consists of monthly data from 31 August 2003 to 31 July 2016.
As stated by Bloomberg15, commodity index is designed to be highly liquid and diversified benchmark for commodities investments. Also from the product leaflet the stated benefits of including a commodity index in the a portfolio are “positive returns over time” and “low correlations with equities and fixed income”, also in the index no single commodity or commodity sector dominates the asset class choice but rather the index goal is to represent the commodity market.
In the table below some statistical measures for my data sets are reported.
Equity Index Bond index Commodity index
Mean Return 0.51% 0.06% -0.13%
Variance 0.17% 0.01% 0.26%
Standard Deviation 4.07% 1.07% 5.14%
Skewness -1.02 0.54 -0.84
Excess Kurtosis 3.04 4.59 2.63
Table 1: Assets Statistical measures: The table provides statistical measure for each assets considered in the portfolio analysis. Sample data spans from September 2003 until July 2016.
As per table 1, in terms of risk-return combination my commodity index delivers the worst results over the time given a negative mean return and the largest standard deviation.
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At the same time the skewness for the commodity index is negative (as for the equity index) so that its tail distribution is longer compared to the bond index. Implication are well known, a non-symmetric distribution but especially a skewed one makes negative returns more likely compared to a normal distribution case.
Economic implication are well known, within portfolio selection normality assures that standard deviation is a complete measure of risk and therefore Sharpe ratio is a complete measure of
performance. A negative skewed distribution on the other hand implies that the standard deviation as a measure of risk will underestimate volatility.
Looking at the excess kurtosis we see that for all my assets the value is positive, hence my distribution is leptokurtic, in other words my distribution displays fatter tails compared to the normal one.
Kurtosis provides a measure for the likelihood of extreme values, in general terms a leptokurtic distribution there is more probability mass in the tails compared the center of the distribution , as it would be for the normal distribution case.
Overall in investing terms this is not a positive result, likelihood of negative and extreme outliers does not make the instruments (commodity in particular) particularly attractive.
Figure 7 : Equity returns empirical distribution histogram: Histogram reports the empirical distribution of equity index returns. Sample data spans from September 2003 until July 2016, 155 observations.
Figure 7 reports the return distribution for the equity index. Visual inspection supported by Table 1 indicates that the distribution is negatively skewed
Figure 8 : US bonds index returns empirical distribution histogram: Histogram reports the empirical distribution of bond index returns. Sample data spans from September 2003 until July 2016, 155 observations.
Figure 8 reports the return distribution for the bond index. Visual inspection supported by Table 1 indicates that the distribution is positively skewed
Figure 9 : Commodity index returns empirical distribution histogram: Histogram reports the empirical distribution of commodity index returns. Sample data spans from September 2003 until July 2016, 155 observations.
Figure 9 reports the return distribution for the commodity index. Visual inspection supported by Table 1 indicates that the distribution is negatively skewed
Overall a risk averse investor would prefer a return distribution displaying a negative excess kurtosis since it would imply a lower probability of extreme negative values. Given the distribution characteristic
of my commodity sample, that is a negative skew and positive excess kurtosis, initial analysis does not suggest allocation resources into commodities.
Testing normality assumption in the empirical distribution can be done via Jacque Brera test. In case of normal distribution, excess kurtosis assumes a value of 3 which lead to a Jacque Brera t-statistic equal to 0. The following equation reports the JB test:
𝐽𝐵 = 𝑁
6∗ ( 𝑆2+ 1
4∗ (𝐾 − 3)2)
where N corresponds to the sample size, S corresponds to the skewness and K-3 to the excess kurtosis. Null hypothesis and the tests’ output are the following:
𝐻0: 𝑟𝑒𝑡𝑢𝑟𝑛 𝑓𝑜𝑙𝑙𝑜𝑤 𝑎 𝑛𝑜𝑟𝑚𝑎𝑙 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝐻1: 𝑟𝑒𝑡𝑢𝑟𝑛 𝑑𝑜𝑒𝑠 𝑛𝑜𝑡 𝑓𝑜𝑙𝑙𝑜𝑤 𝑎 𝑛𝑜𝑟𝑚𝑎𝑙 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛
Equity Bond Commodity
JB test 80.84 133 58.46
Probability 0.00 0.00 0.00
Table 2: Jacque Brera test on asset returns: Table reports the JB test and probability for each return series, Sample data spans from September 2003 until July 2016 (155 observations)
As per Table 2, the null hypothesis is rejected, hence returns series do not follows a normal distribution. Attention will now be devoted to correlation measure, Table 3 reports the correlation matrix for my asset classes returns.
Equity Bond Commodity
Equity 100.00% 5.29% 47.60% (**)
Bond 5.29% 100.00% 3.86%
Commodity 47.60% (**) 3.86% 100.00%
Table 3: t-statistic values for asset returns correlation: Table reports sample correlation among instruments, Sample data spans from September 2003 until July 2016.
As per table 3, correlation between equity and commodity is quite high while the correlation between equities and bonds is close to being zero. I will proceed now with significance test by constructing a t-statistic for my sample correlation. In the following notation 𝜌 denotes my sample correlation.
𝑡 = 𝜌 ∗ √𝑁 − 2
1 − 𝜌2 ~ 𝑡𝑁−2 𝑢𝑛𝑑𝑒𝑟 𝐻0
The following hypothesis apply:
𝐻0: 𝜌 = 0 𝐻1: 𝜌 ≠ 0
The null hypothesis states that in the population the correlation is 0 while the alternative one states that the correlation is different from 0. Under the null hypothesis, the t- statistic is distributed with a t distribution with N-2 degrees of freedom (with N larger than 100 in my sample), critical values at 95% level equals to 1.98. The following table reports the two sided t-statistic for my assets, let’s define:
𝜌𝐸,𝐵 as the correlation betweeen equity and bond returns
𝜌𝐸,𝐶 as the correlation betweeen equity and commodity returns 𝜌𝐵,𝐶 as the correlation betweeen bond and commodity returns
𝑡 − 𝜌𝐸,𝐵 𝑡 − 𝜌𝐵,𝐶 𝑡 − 𝜌𝐸,𝐶
0.66 0.48 6.69
Table 4: t-statistic values for asset correlation: Table reports t statistic on assets correlation. Significant values have been found only for the correlation between commodity and equities. Sample data spans from September 2003 until July 2016. 155 observation, t distribution double tailed critical values equal to 1.98. Significance level at 5% denoted by double asterisk (**).
As per Table 4 results, the correlation between equities and bonds and between bond and commodity is not statistically different from 0 since test statistic are smaller than critical value, however the test does not reject the hypothesis of a correlation between equity and commodity, test statistic is greater than critical value and hence the correlation coefficient is not significantly different from 0.
These initial results goes against the standard theory on commodity diversification as saw in the previous sections. In particular it has been explained how correlation between equity and commodity according to historical data is zero even in downward trending market. Initial results on the other suggest that correlation is significant thereby the case for portfolio diversification might not be present. 4.2) Portfolio construction and mean variance frontier.
I will follow standard theory of mean portfolio construction in order to calculate my efficient frontier, references can be found in any investment textbook, as a reference I closely follow S. Benninga and his textbook financial modelling (4th edition).
Consider N risky assets, each with expected return E(𝑟𝑖), matrix E(r ) is the column vector of expected
returns of the assets:
E(r )= [ E(𝑟1) E(𝑟2) ⋮ E(𝑟𝑁) ]
Consider now as S the N x N the variance covariance matrix
S= [ 𝜎11 𝜎21 … 𝜎𝑁1 𝜎12 𝜎22 … 𝜎𝑁2 ⋮ ⋮ ⋱ ⋮ 𝜎1𝑁 𝜎2𝑁 … 𝜎𝑁𝑁 ]
A portfolio of risky assets is a column vector in which its component sum is equal to 1. Each component x is the proportion of the portfolio invested in risky asset i.
x= [ 𝑥1 𝑥2 ⋮ 𝑥𝑁 ] , ∑𝑁 𝑥𝑖 = 1 𝑖=1
The expected return on the portfolio x is defined as E(𝑟𝑥) and is given by the product of x and E(r).
The sample variance of the portfolio x’s return is defined as 𝜎𝑥2 = 𝜎𝑥𝑥 and is the result of the product
𝑥𝑇𝑆𝑥 = ∑ ∑ 𝑥 𝑖𝑦𝑖 𝑁 𝑗=1 𝜎𝑖𝑗 𝑁 𝑖=1
𝜎𝑥𝑦= 𝑥𝑇𝑆𝑦 = ∑ ∑ 𝑥 𝑖𝑦𝑖 𝑁 𝑗=1 𝜎𝑖𝑗 𝑁 𝑖=1
To calculate the efficient frontier, Merton’s(1973)propositions 1 and 2 will be taken into consideration. By jointly considering the two propositions the optimal investment portfolio for investor whose preference are defined solely in terms of mean and standard deviation can be derived by considering the following equation, with ”c” being a constant equal to the risk free rate.
𝑥𝑖 = 𝑧𝑖 ∑𝑁𝑗=1𝑧𝑗
= 𝑆
−1(𝐸(𝑟) − 𝑐)
𝑠𝑢𝑚(𝑆−1(𝐸(𝑟) − 𝑐))
The resulting weight estimates would define the optimal portfolio allocation.
By taking into consideration my price series, the resulting sample variance covariance matrix and the propositions presented above, I was able to define the frontier for both the 2 assets portfolio (equities and bonds index) and the 3 asset portfolio (equities, bonds, commodities). Below my graphical result
Figure 10: Efficient frontier set for 2 and 3 assets portfolios: Figure reports the efficient frontier for the two assets portfolio (equity and bonds) and the three assets portfolio (equity, bond and commodity)
-0.20% -0.10% 0.00% 0.10% 0.20% 0.30% 0.40% 0.00% 0.50% 1.00% 1.50% 2.00% Portfolio Mean Return
Portfolio Standard Deviation
As per figure 10, graphical view seems to indicate that the three asset portfolio does not improve globally the two asset portfolio frontier, in particular in proximity of the global minimum variance portfolio the two portfolios intersect, hence the frontier for three assets does not shifts up for all possible weights combinations.
This result goes against the standard theory on the diversification benefits presented before which on suggests that commodity investment allows to attain a more efficient risk/return position.
Portfolio choice interpretation is the following: an investor does not achieve globally a more efficient risk return combination by adding the commodity index into his equity and bond portfolio, hence employing commodities as a diversification choice is non optimal.
The efficient frontier provides all combination attainable in terms of risk and expected return, higher the desired return, the more risk investor has to accept. As per standard theory, the efficiency gains of including commodities into a portfolio would be reflected in upward movement of the efficient frontier for all level of risk, an expansion of the investment opportunity set.
Standard theory advocated the inclusion of commodities and the expansion of the investment opportunity set given the positive correlation between commodity returns and inflation and the negative or zero correlation between commodities and equity, or in other words, a countercyclical movement. Among the main reasons behind this countercyclical movement, theory suggest that the impact of expectations is much higher for equities rather than for commodities . Equity pricing based on discounted future cash flows which takes into account expectations on the future level of the economy, that is less relevant for commodity pricing which are more adherent to the current level of economic activity.
It is worth noticing that the analysis does not take into consideration transaction costs, however
efficient frontier seems to indicate that an investor would be able to attain the same combination of risk and return by relying only on equities and bonds, by including also transaction costs the incremental cost necessary to allocate resources in the commodity index would have a negative impact on the portfolio return.
Section 5: Results
5.1) In sample mean spanning test
After having presented the efficient frontier, I will employ a formal test procedure to test whether the shift in the efficient frontier is significant. The following paragraph will report in sample mean spanning test results for different time horizon. Recall that in each and every mean spanning test I conducted, the endogenous variable is the commodity index while the test ones are the equity and bond indexes.
Variable Coefficient Std. Error t-Statistic Prob.
Constant term -0.009 (**) 0.004 -2.160 3.23%
Equity excess returns 0.598 (**) 0.088 6.817 0.00%
Bond excess returns 0.017 0.191 0.088 92.96%
Table 5: In sample mean spanning test, total sample: Table reports coefficient estimates for the in sample spanning test on commodity index excess return over equity and bond index excess returns. Sample data spans from September 2003 until July 2016. 155 observation, t distribution double tailed critical values equal to 1.98. Significance level at 5% denoted by double asterisk (**). Significant evidence is present for the coefficient on the equity excess return and on the constant term.
According to the in sample mean spanning test, the constant coefficient is negative and significant at 5% level, hence commodities provides diversification to a standard portfolio. In terms of portfolio choices, this results suggests that commodity index should be considered as an asset class on its own since diversification features are present. However although constant term is significant, is very close to 0. Significance is found between the excess returns for commodity and the equity Index as well, as a result commodity tracks the excess returns of the equity. Coefficient is less than one nevertheless, 60% is relatively large.
In terms of portfolio choice results illustrated in table 5 imply that, given the is positive correlated with the equity series and the diversification benefits, an investor looking to allocate its resources among different assets should consider a short position on commodities, at the same returns will positively related to the returns generated by a long position on equity.
In conclusion result in table 5 is provide mixed evidence. Aligned with the standard theory on the inclusion of commodities within an existing portfolio, mean spanning in sample test provides evidence of risk return payoff improvement, on the other hand the positive coefficient for the equity index can be
considered as evidence of the presence of integration between financial market as suggested by Pavlova and other authors discussed before.
In the following paragraphs, different time horizon will be considered as part of the analysis to address whether over time a change in return dynamics has occurred.
5.2) Analysis on recent US recession
In order evaluate different time windows, a common choice relies on the pre and post financial crisis analysis. The national bureau of economic research identifies the US financial recession from December 2007 until June 2009. Daily data has been employed in order to extend the sample observation. I will start by first reporting correlation among returns and significance test during the US recession.
Equity Bond Commodity
Equity 100.00% -4.18% -1.18%
Bond -4.18% 100.00% -5.05%
Commodity -1.18% -5.05% 100.00%
𝑡 − 𝜌𝐸,𝐵 𝑡 − 𝜌𝐵,𝐶 𝑡 − 𝜌𝐸,𝐶
-0.85 -1.02 -0.24
Table 6: correlation estimates and t-statistic values for asset returns correlation: Table 6 on top provides the correlation matrix between asset returns while on the bottom it reports t statistic values. Significant values have not been found for the return correlation between assets. Sample daily data spans from Dec 2007 until June 2009. 412 observation, t distribution double tailed critical values equal to +/- 1.96.
Table 6 illustrates an interesting result, during the US recession correlation between assets returns was not significant. As seen in table 3, by considering the complete sample evidence of significant correlation is present only between commodities and equity returns, however during the crisis that was not the case.
Hence by considering different samples evidence is found of a change in the significance of assets returns correlation. In general terms this can be reconciled with a closer integration between capital markets and is in contrast with the standard theory. In particular, following standard theory, it would have been expected a countercyclical on commodities compared to equities during the financial crisis, however this does not seem the case.
The following table reports in sample test results for a daily observations restricted to the US financial recession.
Variable Coefficient Std. Error t-Statistic Prob.
Constant term -0.038 (**) 0.001 -34.680 0.00%
Equity excess returns -0.009 0.035 -0.271 78.67%
Bond excess returns -0.130 0.075 -1.734 8.37%
Table 7: In sample mean spanning test, US recession sample: Table reports coefficient estimates for the in sample spanning test on commodity index excess return over equity and bond index excess returns. Sample daily data spans from December 2007 until June 2009. 412 observation, t distribution double tailed critical values equal to +/-1.96. Significance level at 5% denoted by double asterisk (**). Significant evidence is present for the coefficient on constant term.
Table 7 interestingly provide significant estimates only for the constant terms and not for neither the equity or bond excess return coefficients. The constant is negative (although very close to 0). Interesting conclusion can be derived from table 7 results, in particular the constant significant term suggest that commodities do provide diversification measures and can be considered as an independent asset class. Table 5 illustrated that the commodity index tracks the returns on the equity index, however in this case the coefficient is not significantly different from 0, hence a different results emerges. Similar to previous result, constant term is significant and negative.
This result is quite significant, estimates provide evidence on the diversification benefits of commodities, overall during the financial crisis an investor would have obtained a more efficient risk return payoff by entering into a short position on the commodity index.
The following tests will be devoted to analyze efficiency improvement before and after the US financial crisis. As before I will provide measure and test on correlation significance among asset returns.
Equity Bond Commodity Equity 100.00% -22.31% 11.41% Bond -22.31% 100.00% 3.31% Commodity 11.41% 3.31% 100.00% 𝑡 − 𝜌𝐸,𝐵 𝑡 − 𝜌𝐵,𝐶 𝑡 − 𝜌𝐸,𝐶 -1.62 0.23 0.81
Table 8: correlation estimates and t-statistic values for asset returns correlation: Table 8 on top provides the correlation matrix between asset returns while on the bottom it reports t statistic values. Significant values have not been found for any asset returns. Sample monthly data spans from Sep 2003 until December 2007. 52 observation, t distribution double tailed critical values equal to +/- 2.
Variable Coefficient Std. Error t-Statistic Prob.
Constant term 0.014 0.011 1.196 23.74%
Equity excess returns 0.323 0.203 1.588 11.87%
Bond excess returns 0.806 0.334 2.413 1.96%
Table 9: In sample mean spanning test, pre US recession sample: Table reports coefficient estimates for the in sample spanning test on commodity index excess return over equity and bond index excess returns. Sample daily data spans from December 2003 until December 2007. 52 observation, t distribution double tailed critical values equal to +/- 2. Significance level at 5% denoted by double asterisk (**). Significant evidence is not found.
Interestingly no significant evidence has been found neither on correlation nor on the in sample test. Overall Table 8 and 9 shows that correlations are not significantly different from 0 and also that an investor before the US recession would have not improved its risk return portfolio payoff by allocating resources in the commodity index.
In terms of economic interpretation, even though the non-significant constant would suggests that financialization is already in place, having found no significant return correlation and by considering that access to alternative investments by institutional and mass investors is a recent phenomenon, I believe that no definite conclusion should be appropriate.
I will report now results for the correlation and the in sample spanning test for the period immediately after the US recession.
Equity Bond Commodity Equity 100.00% -19.63% 52.44% (**) Bond -19.63% 100.00% -8.72% Commodity 52.44% (**) -8.72% 100.00% 𝑡 − 𝜌𝐸,𝐵 𝑡 − 𝜌𝐵,𝐶 𝑡 − 𝜌𝐸,𝐶 -1.82 -0.80 5.61
Table 10: correlation estimates and t-statistic values for asset returns correlation: Table 8 on top provides the correlation matrix between asset returns while on the bottom it reports t statistic values. Significant values have not been found for any asset return correlation. Sample monthly data spans from July 2009 until July 2016. 85 observation, t distribution double tailed critical values equal to +/- 1.9
Variable Coefficient Std. Error t-Statistic Prob.
Constant term -0.011 (**) 0.004 -2.569 1.20%
Equity excess returns 0.640 (**) 0.117 5.444 0.00%
Bond excess returns 0.024 0.490 0.049 96.07%
Table 11: In sample mean spanning test, pre US recession sample: Table reports coefficient estimates for the in sample spanning test on commodity index excess return over equity and bond index excess returns. Sample daily data spans from July 2009 until July 2016. 85 observation, t distribution double tailed critical values equal to +/- 1.9. Significance level at 5% denoted by double asterisk (**). Significant evidence have been found on both the constant term and the equity excess return.
By considering more recent data, interestingly the mean spanning test reports that the constant terms is significant, however it has a negative sign (although very close to 0). At the same time evidence have been found on the equity excess return component. Apparently a positive relationship exists between the two variables.
The result in terms of portfolio choice are the same as in the case addressed in the total sample. Overall the analysis performed by considering US recession as a breaking point provided some useful information, that is before the crisis no relationship seemed significant, on the contrary from the crisis an investor looking to diversify its portfolio should have considered a short position in the commodity index. At the same time, after the crisis emerged that the commodity and the equity excess returns are
positively correlated, hence it appears that commodity returns have been tracking closely the equity ones.
In conclusion I found mixed evidence, that is a diversification benefits of including commodities into a portfolio seems to be present (although very small and by assuming a short position) and at the same time commodity and equity returns have become more aligned. Of particular interest the presence of diversification benefit during the crisis, it is well know that diversification is hard to achieve during adverse shocks given the presence of spillover effects which have an impact across different asset classes. Results provided show that this might not be the case, hence standard theory conclusion have been met. At the same time evidence of the financialization theory have been found. Interestingly no evidence of any relationship have been found before the crisis, however this might due to the fact that the data sample is too short.
5.3) Commodity index sub samples
So far I have considered as time boundary the financial crisis, however a different time window to be useful to investigate relies on the trend underlying the commodity index. To be precise many authors argues that commodities have become a popular asset class for investor after the early 2000 commodity price surge, hence by taking this into account analysis on how mean spanning changes by considering boom and collapse period for the commodity index will be here presented. In particular the commodity index peaked on May 2008, hence I will consider it as the discrimination point.
In the following chart I report the commodity index price dynamics to have a visual reference.
Figure 11: Commodity index price time chart. Chart report the price index from August 2003 until July 2016.156 monthly observation. 0 100 200 300 400 500 1-08 -03 1- 02-04 1- 08-04 1- 02-05 1- 08-05 1- 02-06 1-08 -06 1- 02-07 1- 08-07 1- 02-08 1- 08-08 1- 02-09 1-08 -09 1- 02-10 1- 08-10 1- 02-11 1- 08-11 1- 02-12 1- 08-12 1- 02-13 1- 08-13 1- 02-14 1- 08-14 1- 02-15 1- 08-15 1- 02-16
