The Influence of Commodities on Pension Funds’ Portfolios
H.J.D. Schuppers* Master’s Thesis Finance Faculty of Economics and Business
University of Groningen Supervisor:
Dr. P.P.M. Smid†
Faculty of Economics and Business University of Groningen
June 2013
Abstract
This study investigates whether pension funds are made better off by including commodity products to their portfolio that consists of traditional assets. The posed question is examined with four performance measures based on a static out-of-sample asset allocation. Given the choice of the performance measures, evidence has stipulated that adding exposure to commodity indexes, although not overly weighted in one commodity group, do increase performance for a pension fund. For all commodity futures my study shows only limited use for all type of pension funds. Gold and wheat futures do improve performance for all types of pension funds whereas crude oil, copper and live cattle improve performance only in restricted situations. The performance measures show a larger performance increase when a more aggressive asset allocation is applied. The results prove to be robust for three different countries and across various sub-periods.
Keywords: Commodities, Pension funds, Strategic asset allocation, Performance evaluation, Investment horizon.
JEL classification: G10, G11, G23.
* E-mail: rschuppers@gmail.com Student number: s1630075
† I would like to thank my supervisor, Dr. Peter Smit, for his assistance, supervision and for providing me with honest and useful feedback.
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1. Introduction
After the Second World War one of the most salient features of global financial markets was the rise and importance of pension funds. Undeniably, pension funds have been central to the evolution of Anglo-American economies and financial markets, from fuelling the market for corporate control in the 1980s to funding high-technology start-ups in the 1990s (Dixon, 2008).
In 2011 the pension fund assets hit an all-time record of 20.1 trillion USD within Organization for Economic Co-operation and Development (OECD) countries alone (OECD, September 2012).
The OECD weighted average asset-to-GDP ratio for pension funds increased from 67.3% in 2001 to 72.4% of GDP in 2011 (OECD, September 2012). Traditionally pension funds were invested in four main asset classes: equity, bonds, real estate and cash & deposits. The increasing correlation between assets in different local and international markets over the last several decades motivated pension funds to start a search for alternative investment-vehicles to include in their portfolios (You and Daigler, 2013). Subsequent studies report that it is beneficial to include commodity products (commodities and commodity derivatives) as a part of a traditional portfolio (see, e.g., Bodie and Rosansky, 1980; Conover, Jensen, Johnson and Mercer, 2010; Gorton and Rouwenhorst, 2006). However, few studies consider these potential benefits with regards to specific pension fund portfolios or more general to long-term portfolios.
In fact, the absence of studies that research the inclusion of commodity products to long-term portfolios is noteworthy, especially given that research shows that these products possess low correlation with traditional assets, abnormal high returns and are capable to serve as a hedge against inflation (Edwards and Park, 1996; Gorton and Rouwenhorst, 2006). Focusing on the use of commodity products by pension funds, it can be observed that the percentage of direct investments in commodity products by pension funds is close to zero (Amir and Benartzi, 1998).
The purpose of this study is to scrutinize the benefits of pension funds investing in commodity products. More specific, this study examines the potential performance increase or decrease generated by including commodity indexes and commodity futures to a distinct pension fund portfolio. I thereby try to answer my main research question:
Is there evidence for increased portfolio performance as a result of inclusion of commodity products to a pension funds’ portfolio?
To assure robustness of my main question I also try to answer the following sub-question.
Does portfolio performance increase equally for different types of pension funds?
Page 3 My contribution to the existing literature is along three dimensions. Firstly, the performance is evaluated in an out-of-sample setting whereas most previous research uses an in-sample setting. Secondly, the performance is evaluated for different fixed asset allocations and over longer periods of time. To date, researchers evaluated the performance for optimal asset allocations up to a maximum of 5 years and hence not for investors with a longer investment horizon. Finally, my research takes into account the effect of skewness and kurtosis whereas many papers focus solely on return and standard deviation of return, even though it is known that many returns are not normally distributed. Apart from the scientific contributions, this paper contributes to the recent debate concerning the risk and return profile of pension funds around the world.
To answer the main question four different performance measures are applied to examine the inclusion of commodity indexes as well as individual commodity futures to a traditional pension funds’ portfolio. These measures are corrected for both skewness and kurtosis to assure viable results. To answer my sub-question the approach of my main research question is applied to three different countries. All three countries use a different pension plan structure.
The construction of pension fund portfolios is done for the following countries: Germany, the Netherlands, and Italy. The data set used consists of monthly returns starting from January 1991 to March 2013. In general, my research shows that pension funds may increase their performance by adding commodity indexes as long as these indexes are not overly weighted in one commodity group. For commodity futures, my research shows only limited use for increasing performance of pension funds. Gold and wheat futures do improve performance for all type of pension funds where crude oil, copper and live cattle improve performance only in restricted situations and for some particular types of pension funds. The performance measures exhibit larger performance increases when the pension fund applies a more aggressive asset allocation.
The remainder of this paper proceeds as follows. Chapter 2 discusses the key issues associated with commodity products and pension funds. The outline of the methodology as well as the different performances measures are presented in Chapter 3. In chapter 4 the data used for the results is discussed. In Chapter 5 the results are presented and robustness analyses are performed. Subsequent, my results are discussed with respect to my theoretical framework and existing literature in Chapter 6. Finally, Chapter 7 comprises the conclusion of my research.
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2. Literature review
In this section, key issues related to commodity investments and pension funds are reviewed. Based on earlier research the hypothesis and methodology for this research is developed. Traditionally, commodity products have been used and priced as consumption assets and were only of interest to the participants in the market of a particular commodity.
These participants (mainly producers, transporters and users of commodity goods) use the commodity products for production, the delivery of services and to obtain insurance for future value fluctuation in their input and/or output. Probably the main reason why financial investors traditionally did not hugely invest in the commodity market is the striking differences with stock and bond markets. Among these differences are: (1) almost all commodities have, unlike financial assets, pronounced seasonality and supply constraints; (2) event risk is pierced in their price levels and prices experience high short-term volatilities; (3) commodity futures are derivative securities, they are not claims on long-lived corporations; (4) and they are short maturity claims on real assets (Gorton and Rouwenhorst, 2006).
Over the last years an enhanced interest in commodity products can be witnessed in the financial market and many new commodity derivatives and commodity indexes came into existence. This increased interest is caused by a better understanding of commodity price behavior and an increased liquidity of commodity products. A recent paper has estimated the inflow of investments towards commodity products at a record of 60 billion dollar in 2009 and has presented the expectation that this inflow will increase substantially in the future (Sykora, 2010).
2.1. Commodity investing
Prior to the enhanced interest of portfolio managers in commodity products, researchers have described the potential of these commodity products. Early research dates back to Bodie (1980) who argues that portfolio managers can benefit from the inclusion of commodity products to their portfolio. Since the publication of Bodie (1980), several papers have studied the effects of adding commodity products to a portfolio (See, e.g., Daskalaki and Skiadopoulos, 2011; Gorton and Rouwenhorst, 2006; Hoevenaars, Molenaar, Schotman and Steenkamp, 2008). In general, scholars have proposed two main theories suggesting that the addition of commodity products to a portfolio can be beneficial.
Page 5 Firstly, commodity products offer an opportunity for more efficient diversification.
Commodity products exhibit relatively high risk and return and are often described as stock-a- like assets, which mean that they behave in a relatively similar way. This behavior, together with the fact that commodity returns traditionally exhibit low or even negative correlation with return of stocks and bonds, provides the investor with an alternative asset class. The low correlation can mainly be explained by the factors that drive commodity prices and commodity volatility (e.g. weather and geopolitical conditions, supply constraints in the physical production, and event risk). These factors are mostly unrelated and distinct from those that influence the value of the traditional assets classes (Daskalaki and Skiadopoulos, 2011). Conover et al.
(2010), for example, have tested the benefits of adding the S&P Goldman Sachs Commodity Index (S&P GSCI) and the Dow-Jones UBS Commodity Index (DJ-UBSCI) to different portfolio styles based on their return and volatility. Furthermore, the small or negative correlation between commodity products and traditional assets classes is tested and proven in academic literature by different authors (see, e.g., (Bodie and Rosansky, 1980; Conover, Jensen, Johnson and Mercer, 2010; Nijman and Swinkels, 2003). These authors argue that investors are able to reduce their risk without giving up return by adding a certain fraction of commodities to their portfolios. Furthermore, previous studies suggest that commodity products provide investors with the possibility to diversify better and generate higher returns.
Secondly, research shows that commodity products exhibit positive correlations with inflation (Bodie, 1983; Edwards and Park, 1996; Hoevenaars, Molenaar, Schotman and Steenkamp, 2008). The positive correlation suggests that commodity products are able to serve as a hedge against inflation. The hedging capabilities of commodity products result in the reduction of some of the portfolio risk borne by the investor. The effect of using commodity products as a hedge against inflation turns out to be significant, especially when the investment window becomes larger (Gorton and Rouwenhorst, 2006; Spierdijk, 2011). Another currently believed aspect is that commodity products can provide protection against financial crises and political distress (Chow, Jacquier, Kritzman and Lowry, 1999). This feature is attributed to commodity products because it is likely that such an event will cause commodity prices to rise while at the same time stock prices fall or remain constant (Choi and Hammoudeh, 2010). Both opportunities, to better diversify or to hedge against inflation, are likely to be beneficial for investors and hence it is a rational choice to expose a portfolio to commodity products.
Page 6 2.2. Portfolio choices
The guidance in creating exposure to commodity products is efficient diversification. That is: the attempt to achieve the maximum expected return by a given level of risk. As pointed out by Campbell and Viceira (2002), an optimal portfolio with time horizon T is the same optimal portfolio with time horizon 100T. The T horizon portfolio and 100T horizon portfolio are only similar when an opportunity for rebalancing exists at every T. The argumentation above only generates the same returns in an ideal world in which rebalancing is costless and the return and volatility are constant over different time-periods. In the real world these costs are present and also the parameters return and volatility change over time. So different investment horizons lead to different portfolios depending on the assumptions made during construction of a portfolio. For example, it is likely that the choice to rebalance less often leads to fewer transactions and, consequently, less transaction costs. The situation described above causes various portfolios to behave differently when exposed to commodity products. Hence, in order to understand the implications of adding commodity products to pension funds, a better understanding of the characteristics of pension fund portfolios is crucial.
2.3. Pension funds
In developed and emerging countries the structure of the pension systems is organized as a two- or three-pillar system. The first pillar comprises the public pension scheme financed with an unfunded type of fund, which is explained in more detail later. The first pillar offers a basic pension with flat settlements to all retirees (Bikker, Broeders, Hollanders and Ponds, 2012).
Often the level of benefits is linked to the minimum wage of that particular country. The second pillar entails individually funded pension plans managed by pension firms. A possible third pillar comprises tax-deferred personal savings, which individuals undertake at their own initiative. The third pillar is again a funded pension plan (Heeringa, 2008). In most countries the first pillar is obligatory or absent whereas the second and third pillar are facultative.
2.3.1. Types of pension funds
Despite the fact that pension systems and plans vary a lot in design and structure, we can discern two main types of pension plans. The first type of pension plan is the unfunded pension plan (UPP), also referred to as the defined benefit plan. The UPPs are the dominant type of pension plans within the first pillar. This type of plan promises a specified amount of pay-out during retirement. This specified amount is based on the retiree’s earning history, tenure of
Page 7 service and age, rather than directly on individual contributions and investment returns. A commonly used variant of an UPP is applied by governments in which working individuals pay an amount to fund settlements of current retirees. An UPP is a device created to share income risks with others. These income risks are shared inter-generationally (with the young of the same country), intra-generationally (with other elderly of the same country), or internationally (with foreigners) (Shiller, 1999). The second type is the funded pension plan (FPP), also called:
the defined contribution plan. The FPPs are the dominant type of plans within the second and third pillar of many pension systems. A FPP assumes that an individual, and possibly his employer, invests in his individual retirement account. The benefits depend on the contribution and investment returns of the accumulated account. In an FPP wealth and risks are not transferable from one individual to another; this absence of sharing individual portfolio risk results in the fact that workers face high uncertainty on their future pension wealth (Gollier, 2008).
2.3.2. Pension funds’ long-term characteristics
Even though FPPs and UPPs differ significantly, they also have some characteristics in common. One of the most important similarities is that they are both viewed as long-term investment portfolios. Construction of long-term pension fund portfolios has some difficulties compared to short-term portfolios. First of all, constructing a pension fund portfolio only with riskless assets is not feasible due to uncertainty about the re-investment rate of the riskless assets and the level of inflation. Rolling over bonds, for example, is not necessarily a safe strategy to pension funds because bonds must be reinvested at unknown future real interest rates. The previous possibility leads to a mismatch in timing and size between income from bonds and the liabilities of the pension funds. The impact of inflation makes the minimal required return of pension fund equal to the level of inflation, because only such a minimum return supports a stable standard of living in the long-term (Campbell and Viceira, 2002). As a result, a pension fund portfolio should differ significantly compared to short-term portfolios.
Another difference is caused by the mean reversion effect observed in risky assets.
Brennan, Schwartz, and Lagnado (1997) point out that a long-term investment horizon has a significant effect on the composition of the optimal portfolio. A pension fund, which uses a long- term investment strategy, typically invests a larger fraction of its portfolio in stocks than a short-term investor does. The reason is that the mean reversion in prices causes the volatility of
Page 8 the distribution of future prices to grow less than proportionately with time, so that stocks are less risky for those with a long horizon (Brennan, Schwartz and Lagnado, 1997).
The last important difference between a long-term pension fund portfolio and a short- term portfolio concerns the time a particular asset is hold within the portfolio. A longer holding period implies that fewer transactions must be made within the portfolio and the effect of mean reversion, explained above, is likely to be stronger. Research shows that the US pension funds hold 24% of their (non-equity) assets with a maturity of up to three years and have an average maturity that reaches 9.55 years (Opazo, Raddatz and Schmukler, 2009). In addition, the employee benefit research center (EBRI) (1993) has discovered that approximately 80% of the domestic equity managed by US pension funds is kept within the portfolio for at least six months. This indicates that pension funds have a large proportion of assets in their portfolio which are kept for relative longer periods. It also indicates that they trade with only a small percentage of their portfolio on a more frequent basis.
The three aforementioned arguments support the notion that pension funds differ significantly from a conventional short-term portfolio. However, academics so far have only studied exposure to commodity products for myopic short-term portfolios, up to a maximum investment window of six years, and in which radical changes in asset allocation where possible after every short period (see, e.g., (Daskalaki and Skiadopoulos, 2011; Nijman and Swinkels, 2003). To circumvent this unrealistic behavior for pension funds it is crucial to identify the key issues which drive the performance of a pension fund.
2.4. Investment policy
The first key issues which drives the performance of a pension fund is the investment policy (Andonov, Bauer and Cremers, 2012). Investment policy has a broad spectrum of definitions, but in this study it comprises the allocation of assets among investment classes, rules for taking capital gains and losses and the accepted level of risk within the portfolio.
Andonov, Bauers and Cremers (2012) have demonstrated that investment policy dominates investment strategy (market timing and asset selection) by comparing total returns for different pension funds. Research shows that asset allocation as part of the investment policy can be accounted for most of the time-series variation in pension portfolio returns, while active investment strategies appear to have been far less important (Ibbotson, 2010). This is especially true if the overall portfolio is invested in multiple funds, each including a number of
Page 9 securities, which holds for almost all pension funds (Sharpe, 1992). More specifically, research suggests that pension funds, especially large pension funds, would have performed better if they applied passive investment strategies with only few rebalancing activities across asset classes (Andonov, Bauer and Cremers, 2012). The aforementioned elaboration on some distinct characteristics of a typical pension funds’ investment policy, the urge for a decent and realistic initial asset allocation becomes apparent. In addition, literature suggests that only limited rebalancing activities should be performed and that the asset allocation is key for success.
2.5. Inflation
Besides the allocation of funds over different asset groups, there is another key issue that drives the performance of pension funds. This issue, as already mentioned in section 2.1, is the implications of inflation. Whereas for a short-term investor the effects of inflation are small and can possibly even be neglected, this cannot be said for a long-term investor. At a normal inflation level of 2.5%, 100 dollar today will be worth only 77.63 dollar after ten years. This amount will diminish even further if the investment horizon increases. Pension fund managers or, more general, long-term investors therefore try to invest in assets that provide some protection against inflation. Furthermore, it is very likely that the liabilities of pension funds will increase with inflation, and thereby, resulting in the need of an even better protection against inflation compared to short-term investors. The importance of inflation risk for long-term investors has received much attention in literature. This attention was a priori initiated by Bodie (1976), who was the first scholar to investigate the hedging potential of stocks and was, subsequently, followed by many others (Ely and Robinson, 1997; Luintel and Paudyal, 2006).
Besides testing the inflation hedging potential of stocks, many other investment classes were tested as inflation hedge, among others: real estate (Liu, Hartzell and Hoesli, 1997; Rubens, Bond and Webb, 1989), gold (Beckmann and Czudaj, 2013), commodities (Bodie, 1983;
Hoevenaars, Molenaar, Schotman and Steenkamp, 2008; Spierdijk, 2011), and commodity futures (Edwards and Park, 1996; Irwin and Landa, 1987). The long-term orientation of pension funds creates the urge to protect themselves against inflation. Traditionally, pension funds have held a small percentage of real estate in their portfolio, approximately between two and five percent over the last ten years, as protection against inflation (OECD, 2012). Until a few years ago, real estate was conceived as a decent hedge for both anticipated and unanticipated inflation (Edwards and Park, 1996; Rubens, Bond and Webb, 1989). However, as a result of the recent unexpected downward movement of the real estate prices, the inflation hedging
Page 10 potential of real estate vanished and pension funds had to find other assets that could serve as a hedge against inflation.
So far, I have stretched the importance of a proper asset allocation and the implications of inflation for a pension funds’ performance. In addition, arguments that support the notion that commodity products should be used as an extra investment class for pension funds are stretched. It is now possible to conclude that a decent asset allocation, with only few rebalancing activities between asset classes, is able to mimic a typical pension fund at best.
Furthermore, it is likely that from a theoretical point of view a pension fund portfolio exposed to commodity products will experience an increase in performance due to the diversification benefits and the hedging ability against inflation offered by commodity products.
2.6. Empirical findings
In congruence with our theoretical framework empirical studies show that commodity products can be used as an inflation hedge (see, e.g., Spierdijk, 2011). Additionally, a number of studies examine the effects on the risk/return performance of adding commodity products to a traditional portfolio existing of stocks and bonds (Edwards and Park, 1996; Gorton and Rouwenhorst, 2006). More specific, Conover et al. (2010) show that a well-diversified investor could have reduced his return variability by one-third without sacrificing any of his return.
Conover et al. (2010) test his hypothesis for different commodity exposure levels, namely 5%, 10%, 15% and show that an appropriate level of exposure would be between 10 and 15%.
Georgiev (2001) and Anson (1998) demonstrate that the addition of commodity indexes to a traditional portfolio increases the Sharpe ratio significantly. Erb & Harvey (2006) and You &
Daigler (2013) show positive results for adding individual commodities.
Most of the previous mentioned research has certain shortcomings this paper tries to circumvent or overcome. Firstly, all previous mentioned authors investigate the influence of commodity products in an in-sample setting in which they construct optimal portfolios based on return and volatility. Daskalaki and Skiadopoulos (2011) and also Nijman and Swinkels (2003) argue that the benefits should be tested in an out-of-sample situation. Daskalaki and Skiadopoulos (2011) test for different risk profiles in an out-of-sample setting and show evidence for the fact that the addition of commodity futures and commodity indexes does not improve performance of a traditional portfolio. Nijman and Swinkels (2003) on the other hand test specifically for pension funds and argue that adding commodities does indeed increase
Page 11 performance. The papers of Daskalaki and Skiadopoulos (2011) and Nijman and Swinkels (2003) both use utility functions to construct dynamic optimal portfolios. Next, both papers test these portfolios against a variety of performance measures in an out-of-sample setting. The second flaw in many papers is the dynamic optimal portfolios, which possibly causes the asset allocation to alter completely between two consecutive periods. As seen in section 2.3, the use of dynamic optimal portfolios is not workable from a practical point of view. Or to put it more precise, pension funds should maintain a relative constant asset allocation for longer periods of time in order to be beneficial. One could also imagine that from a liquidity point of view it is impossible for a pension fund to rebalance more than one billion dollars every period. The third flaw in many papers is that they ignore the non-normality of the return distributions. Many studies do not correct for skewness and kurtosis in return distributions and use inappropriate performance measures like simple returns and volatility levels to evaluate performance. Also, previous articles devote little attention to the risk of large downside-deviations arising from non- normal returns (tail risk), even though it is well known that returns of commodity products are not normally distributed (Conover, Jensen, Johnson and Mercer, 2010). This problem is circumvented by You and Daigler (2010) who test individual futures with the value at risk (VAR) measure which is adjusted for skewness and kurtosis; by doing so, they take the non-normality of the return distribution of commodity futures into account.
The presented theoretical framework and empirical results both suggest a positive relationship between commodity exposure and pension funds’ performance. Thus, based on these theories and empirical results, I expect to see a performance increase when pension funds are exposed to commodity products.
2.7. Types of pension funds
Before continuing with the methodology section, this paper will elaborate on some distinctions between different types of pension funds. This is done in order to be able to answer the question whether some types of pension funds are more able to increase their performance with exposure to commodity products than others. Till so far, only exposure of commodity products to pension funds is discussed in general. However, one could argue that different types of pension funds benefit differently from exposure to commodity products. As mentioned earlier, there are basically two types of pension funds, namely funded and unfunded pension plans. In general, an FPP account exists during most of the lifespan of an individual, typically
Page 12 from the age of 20 till the end of their life. As a result, based on life cycle arguments, one could argue that a particular FPP should hold a different portfolio with different levels of risk over the lifespan of its client (Cocco, Gomes and Maenhout, 2005; Viceira, 2001). An important outcome of these models is that the proportion of financial assets invested in risky assets, mainly equity, decreases over the life cycle, thereby increasing the proportion of relatively safer assets. The key argument is that young workers have more human capital, the ability to create income from work, than older workers do and, therefore, are able to compensate with their human capital for unwanted changes in their wealth and income (Bikker, Broeders, Hollanders and Ponds, 2012).
On the other hand, UPPs are basically pools of assets that serve as collateral for the pension liabilities to its sponsors. The ability of current retirees and current generations to share their risks with other generations, even generations who are not born yet, creates a market with extra diversification opportunities compared to the situation in which this possibility does not exist (Gottardi and Kubler, 2011). However, since the main goal of an UPP is to roll over money from the workforce to retirees, they still need sufficient buffers in order to be trustworthy. These buffers are normally only addressed in periods of less economic prosperity, up until that moment the buffers are invested and accordingly generate profits. These generated profits should in the long run at least be equal to the inflation rate in order to be able to keep on functioning. Previous argumentation assumes that in periods of economic prosperity the UPPs take relative high risk in order to make up for possibly insufficient buffers during periods of economic distress. The sponsors of UPPs are to a relatively high level ignorant to the risk taken by the UPPs because it normally does not affect their future payments directly.
Together with the fact that UPP portfolio managers are still being judged on their short-term performance possibly leads to relatively aggressive asset allocations by UPPs. On the other side of the spectrum are the FPPs. Their goal is to maintain the assets in the portfolio rather than to generate high profits. Sponsors of an FPP are very averse to larger losses and, thus, it can be argued that FPPs take relatively save strategies to minimize the possibility of a large loss. To my knowledge, differences in asset allocation between the two types of pension funds are an undiscovered area. Therefore, this paper argues that at least three countries with different pension systems, and hence asset allocations, should be included in order to be able to conclude whether types of pension funds show different performance increases when exposed to commodity products. Commodity products exhibit, as stated in section 2.1, a relative high
Page 13 risk and return profile. From a theoretical point of view it can be argued that such a high return and return profile is needed to be able to increase performance of a risky portfolio. Off course the aforementioned argument is only feasible if the correlations are low enough, that is the case for commodity products as we saw in section 2.1. Empirical results also suggest that more risky portfolios benefit more from exposure to commodity products. For example, Nijman and Swinkels (2003) and Conover et al. (2010) suggest that portfolios with a riskier profile benefit more from exposure to commodity products. Therefore, I expect to see a larger performance increase for UPPs, which, as argued in section 2.7, apply a more aggressive asset allocation.
By making use of different commodity products, non-normality performance measures and specific asset allocations, this paper tries to overcome all stipulated flaws in the existing literature. The aforementioned literature has stipulated evidence that investors are better off by investing in commodity product as part of their portfolio. With the understanding of the different mechanisms influencing portfolio choices by pension funds, this paper suggests that it is beneficial for pension funds to be partly invested in commodity products. Investing in commodity products is necessary to be fully diversified and to be able to benefit from the inflation hedging property of commodity products. In addition, this paper tests whether different types of pension funds benefit equally from the addition of commodity products.
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3. Methodology
The methodology used in this paper is similar the one used by Daskalaki and Skiadopoulos (2011) and Conover et al. (2010). In general, several tests examine the implication of adding different commodity products to different pension fund portfolios. Starting from previous research, a few steps have to be taken in order to come to the methodology used. In most previous papers, researchers use stocks, sometimes in combination with bonds, to identify the potential of commodity products. By doing so, researchers ignore other investment classes, which eventually can result in an oversimplified representation of the reality. This effect is more profound for pension funds, because of their vulnerability to inflation.
Leaving out some categories would not be appropriate and, therefore, this paper adds two extra investment classes: cash & deposits and real estate. I do so under the assumption that by adding these investment classes the tested portfolios are more in congruence with reality.
Furthermore, a major flaw in the approach of most previous research is the fact that they use an in-sample setting for testing. This is not appropriate when estimating a real world phenomenon and should be circumvented by using an out-of-sample situation (Daskalaki and Skiadopoulos, 2011). Portfolio choices should be examined in an out-of-sample situation, given that at any point in time the pension fund manager decides upon its assets allocation and the returns to be realized over the investment horizon are uncertain. The papers of Kostakis, Panigirtzoglou, and Skiadopoulos (2011) and DeMiguel, Garlappi, and Uppal (2009) use an out- of-sample situation with a static assets allocation similar to this paper. To circumvent the problem of uncertainty about exact asset allocation and the timing of the portfolio manager to change its portfolio composition, in this paper it is assumed that pension funds are well diversified at all moments in time. Additionally, it is presumed that pension funds managers are not able to beat the market consistently and thereby their performance is rather equivalent to the market performance in the long run (Burton G. Malkiel, 2003). Hence, commonly used, well- diversified indexes are used in this paper to proxy for the returns generated by different investment classes. The allocation of assets is a fixed asset allocation based on the average asset allocation over previous years. In Appendix 1 the asset allocation over the previous years for the countries Germany, Netherlands and Italy is exhibited. These countries are selected because of their dominant type of pension fund and similarity in currency. Germany has mainly UPPs within their retirement structure, Italy has mainly FPPs and the Netherlands uses a hybrid variant in which they use both FPPs as well as UPPs for their retirees.
Page 15 In addition to the historic portfolios, alternative portfolios are constructed. Constructing alternative portfolio begins with a copy of the historic portfolios, named “traditional portfolio”.
Thereafter, this study adds a proportion of one of the commodity indexes to the traditional portfolio and the other asset classes decrease accordingly. For example, a traditional portfolio with 80% stocks and 20% bonds is transformed to a portfolio with ten percent commodity index, 72% stocks and 18% bonds. Because commodity futures do not require an initial investment, the traditional portfolio is exposed by simply adding an amount of futures. This amount of added futures is equal to the percentage exposure times the value of the portfolio divided by the settlement price of the future contract. If a portfolio is worth one million and we want to expose it for 10% to gold futures which has a settlement price of 50 I add gold future contracts to the traditional portfolio. The return of a portfolio exposed to commodity futures is calculated as follows:
(1)
Where is the initial price of the traditional portfolio at time t, and is the price level of the traditional portfolio after month t. In addition to this the return for the futures is added. is the initial price level of the futures and is the final price level of the futures. The percentage exposure, PE, can be varied depending on the desired level of exposure to a particular future.
To ensure the robustness of our results this paper considers four alternative commodity allocations, including a limited allocation (5%), a mediocre allocation (10%), a prominent allocation (15%) and a dominant allocation (20%). This allocation to commodity products is similar to the allocation suggested in the papers by Conover et al. (2010) and Greer (1987).
They outline that the limited allocation is a very conservative portfolio given the average risk aversion of investors and the mediocre or prominent allocation being more appropriate on average.
The out-of sample nature in this paper is guaranteed by the use of a “rolling window sample”. Let the dataset consist out of T monthly observations for each asset under consideration and let K be the size of the rolling window with K≤T. At any given point in time (t) this paper incorporates the return over month t and the succeeding K-1 months. This process is repeated by incorporating the return for the period K+1 while ignoring the first observation. The portfolios are rebalanced after every month t and returns are calculated monthly just before rebalancing.
Page 16 To ensure the robustness of the results, a variety of rolling window sizes is tested. Based on the characteristics of pension funds, this paper uses relatively long portfolio existence periods ranging from 5 years to a maximum of 15 years. Consequently, the rolling window sizes used are K= 60, 96, 120, 144 and 180. This approach results in the opportunity to vary entry and exit moments. It also provides a series of T-K portfolio returns, given the preferences of the pension fund and the length of the estimation window K. The reason why a buy-and-hold strategic is not applied is because this paper argues that pension funds managers frequently rebalance their portfolios to a desired asset allocation. Therefore, holding a portfolio for periods ranging from 5 to 15 years without rebalancing is not realistic in my opinion. Appendix 1 shows that in the long run pension funds keep their asset allocation relatively stable over time. To achieve such consistency, rebalancing actions are necessary. The five different window sizes and four levels of exposure results in 20 tested portfolios for each applied commodity product.
3.1. Performance measures
Following Kostakis, Panigirtzoglou, and Skiadopoulos (2011) and Anson (1998) and You &
Daigler (2010) this paper employs a number of performance measures. First the arithmetic returns, also called simple returns, and the standard deviation is calculated for all tested portfolios. Besides this basic comparison, between returns and volatilities, more advanced performance measures are applied, namely: the Sharpe ratio, Sortino ratio, upside potential risk and the conditional value at risk.
The Sharpe ratio (SR) is used due to its extensive use and acceptance in both academic literature and industry. The SR is also applied as performance measure because now there is no need for a generic market return as is for example the case with Jensen’s Alpha. The absence of a market return increases the reliability of my research, because not the market return but inflation is the key driver for pension funds’ performance. The estimate of the SR is defined as the average of K monthly excess returns divided by the standard deviation of K monthly returns. For calculation of the excess return the three month interbank interest rate is used as the risk free rate. The three-month interbank rates are used to partially exclude very short-term fluctuations as a result of e.g. events. Obvious, the three month interbank rate is converted to monthly returns. Aforementioned leads to the following formula:
̂ ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
, (2)
Page 17 where ̂ is the SR of portfolio p initiated at month i. The is the return of portfolio p at moment t and is the return of the risk free rate at moment t. Both return vectors contain monthly returns for K consecutive months starting at month i. Thereafter, these returns are subtracted from each other and averaged. The standard deviation is calculated over K months and initiated at month i. If K equals 60 months this will result in 267(T-K) different ̂ for each portfolio p. Following, the average of these SRs is calculated and with a regression the SRs are compared to those of my traditional portfolio. To test whether the SRs of the traditional and alternative portfolio differ significant, the statistics proposed by Jobson and Korkie (1981) and later corrected by Memmel (2003) is used. The SRs and the corresponding tests are commonly used in literature and provide an insight whether the relationship return divided by the volatility improves by adding commodities. However, the SRs are only suitable to assess the performance of portfolios if the underlying returns are normally distributed and only when portfolios are well diversified. As stated earlier there is ample evidence that returns are not distributed normally, especially not for commodity futures (Daskalaki and Skiadopoulos, 2011).
Hence, alternative performance measures are used to get a better understanding of the impact of adding commodity products to a pension fund portfolio.
The first alternative performance measure applied is the Sortino Ratio (SOR). The SOR measures the risk of negative deviations of the returns realized with respect to a minimal acceptable return ( ). Since the SOR considers only negative deviation from the minimal accepted return, it is a more appropriate measure of pure risk than the standard deviation, which considers both positive and negative deviation from expected return (Sortino and Van der Meer, 1991). Sortino and van der Meer (1991) state that realizations above imply that goals are achieved and should thus be regarded as ‘positive volatility’. Vice versa, realizations below the reference point imply failure and should be considered as ‘negative volatility’. The SOR is calculated as follow:
and √ ∑ , (3) where are K returns of portfolio p which is initiated at moment . By using a chosen preference rate ( ) a share of the investors risk preference is added as part of the risk calculation. Consequently, the results are only applicable for investors sharing the same risk attitude. For this paper applies the consumer price index (CPI) of the relevant country.
This paper uses the CPI as benchmark, the absolute minimal performance of a pension fund is
Page 18 to generate a return equal to the time value of money. In other words, when a pension fund outperforms the CPI it has a positive result and it is thus likely to have an existence. When is negative the SOR is not defined however this did not occur in the data used. The individual are statistically compared to the SORs of the traditional portfolio by making use of a regression, this regression is discussed below. Next, the K-T SORs are averaged and reported, resulting in a single reported SOR for each portfolio ( .
In addition to the SR and SOR also the upside potential ratio (UPR) is applied. In contrast to SOR the UPR evaluates both the profits and losses by incorporating the upside deviation as well as the downside deviation (Sortino, Van der Meer and Plantinga, 1999).
∑
, (4)
where is equal to the one used in equation (3), and the upper part is the average of all deviations above the minimal accepted level of return during the existence of the portfolio.
Similar to the SR and SOR the is averaged for each portfolio p and window size K and statistically compared to the traditional portfolio. By using both the upside as well as the downside deviation, the UPR is more consistent in evaluating the minimal accepted return leading to a more balanced score, and in a more transparent score as well.
Finally, the conditional value at risk (CVAR) measure is applied. This measure is used, because it is also applicable in case of non-normality in returns and is similar as used by You and Daigler (2010). The CVAR measures the possible weighted downside risk of an investment over a fixed period, which is not exceeded with a given probability of , whereby often is referred to as confidence level. The CVAR has some important advantages over the classical value at risk (VAR) measure. The most important advantage is that it takes into account the extent of the losses that might be suffered beyond the threshold amount indicated by the VAR (Rockafellar and Uryasev, 2002). The original VAR measure is expressed as the negative average return over an investment plus the standard deviation times the confidence multiple for the VAR.
̅̅̅̅̅ ) , (5)
where expresses the -percentile of the standard normal distribution. For the confidence multiple a 95%confidence level is used, resulting in a multiple of -1.65. The 95%
confidence interval is chosen arbitrary; for a robust CVAR measure different confidence levels
Page 19 should be tested. The ̅̅̅̅̅ and are the average return and standard deviation of portfolio p initiated at moment i. As discussed earlier, returns used in this paper are not per se normally distributed and hence this paper uses the modified VAR (MVAR) measure described by Favre and Galeano (2002) to correct for possible skewness and excess kurtosis. The formula for the MVAR is as follow:
( (
)), (6)
where is the skewness of the returns in portfolio p starting at moment i and the excess kurtosis of the returns of portfolio p started at moment i. Once the is calculated the average of all returns below the MVAR value is taken. Resulting in the CVAR:
∑ , (7)
Where q indicates the number of deviations below . With the CVAR measure the lower tails of the two portfolio return distributions are tested for significant differences. Next the average over the K-T is calculated and the are statistically compared with the traditional portfolio.
As mentioned, the four performance measures are compared statistically with the performance measurements of the traditional portfolio. Therefore, a test is conducted on the different performance measures whether the newly constructed portfolios differ significantly from the traditional portfolio. All four performance measures are tested with a basic regression as described by Nijman and Swinkels (2003). This basic regression tests whether the portfolio with a specific percent of one of the commodity products differs significantly from the traditional portfolio. This is performed with the following regression.
, (8)
where is a constant which measures the structural out- or underperformance of the newly constructed portfolio. is the performance measurement of the portfolio which is initiated at time i of the newly constructed portfolio and is the performance measurement of the portfolio which is initiated at time i of the of the traditional portfolio. The last term is the error-term. Formula (8) can be rewritten to ; what remains is a standard t-test
Page 20 which checks whether differs statistically from zero. The null-hypothesis of these regressions is that the performance measure of the traditional portfolio provides equal performances as the constructed portfolio. If this does not hold, one is able to conclude whether the two portfolio performances differ significantly.
By making use of a rolling window approach, the number of observations is increased substantially. However, by doing so the same information is used several times and the overlapping samples in the regression model result by definition in autocorrelation within the error-terms. To deal with this problem, similar to Nijman and Swinkels (2003) this paper uses the method proposed by Newey and West (1987), which accounts for heteroskedasticity and autocorrelation in general form. To compare different countries this study chooses two iterations. Firstly, the performance increases per country are compared between the three different countries. Secondly, the asset allocation belonging to a specific type of pension fund is used within the other two markets. This set-up can provide evidence for the fact that various types of pension funds react differently when exposed to commodity products.
To be able to interpret the results in case of opposite results for different performance measures the following rules are applied. The performance measures SR, SOR and UPR are the three most important performance measures and are equally weighted. This paper argues that if not all three of these performance measures exhibit positive significant results, the performance increase does not hold undeniably. You and Daigler (2010) show for their sample, 1992 to 2006, that they are not able to improve the CVAR measures by making use of commodity indexes. They suggest that it is not very likely that the CVAR measures of a naïve portfolio, consisting of American stocks and bonds, can be improved with exposure to commodities. An explanation is that this is the result of the systematic large jumps in commodity prices. If large negative jumps occur more often for commodity prices compared to stocks and bonds it is likely that I will not be able to improve the CVAR-measure. Resulting from the use of rolling windows a single negative jump is incorporate in as many as K CVAR measures, implying that it will heavily decrease the results of the CVAR. The results of You and Daigler (2010); the large jumps in commodity prices; and the application of the CVAR in combination with rolling windows suggests that it is not very likely that this study is able to increases CVAR compared to the traditional portfolio.
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4. Data
This section will describe the data set used for my study as well as descriptive statistics of the data set. In the first section assets used for the traditional portfolio will be discussed. The second section will elaborate on the different commodity products used to create exposure to the traditional portfolio. In the last section the used asset allocation and descriptive statistics will be described.
4.1. Traditional assets
The data consists of monthly closing prices for a number of assets and commodity products, which are provided by DataStream. This paper first focuses on the German market and uses the Deutscher Aktien IndeX total return index (DAX 30), German Bonds all Lives Government Index (G Bond Index), German Real Estate total return index (G Real Estate) and the three month Frankfurt Interbank Offered Rate total return index (FIBOR) to proxy for the equity market, bond market, real estate market and the risk-free rate respectively. The monthly change in the German Consumer Price Index (GCPI) is used as benchmark for the calculation of some of the performance measures and is interpreted as a proxy for inflation. As proxies for the different parts of the Dutch market this paper uses theAmsterdam Exchange total return indeX (AEX), Dutch bonds all Lives Government Index (NL Bond Index), Dutch Real Estate index (NL Real Estate) and the three months Amsterdam Interbank Offered Rate total return index (AIBOR) to proxy for the equity market, bond market, real estate market and the risk-free rate respectively. The monthly change in the Dutch Consumer Price Index (NLCPI) is used as proxy for inflation in the Netherlands. For the Italian market the Milan Italia Borsa total return index(MIB), Italian bonds all Lives Government Index (IT Bond Index), Italian Real Estate index (IT Real Estate) and the three months Milan Interbank Offered Rate total return index (MIBOR) proxy for the equity market, bond market, real estate market and the risk-free rate respectively.
The monthly change in the Italian Consumer Price Index (ITCPI) is used as proxy for inflation in Italy.
4.2. Commodity products
To create exposure to the commodity investment class various investment vehicles are used separately. The different commodity investments vary from two commodity indexes to six well selected commodity futures. This paper chooses to assess both, individual commodities and more general indices to test specific regions within the commodity market as well as the market
Page 22 as a whole. In particular, the S&P Goldman Sachs Commodity total return index (S&P GSCI) and the Dow Jones-UBS Commodity total return Index (DJ-UBSCI) are applied to proxy for the commodity market. Since direct investing in indices is not possible, this paper assumes that investing in trackers that benchmark the indices will yield the same returns as the indices itself.
The argumentation for this assumption is that both indices are most popular and most benchmarked in the large universe of existing commodity indexes resulting in well mimicked and liquid trackers (Stoll and Whaley, 2010; Tang and Xiong, 2010). As proxy for the exposure to different commodities this paper employs the following six commodity futures: Continuous 100 OZ Gold COMEX, High Grade Copper Continuous COMEX, Light Crude Oil Continuous NYMEX, Wheat continuous Minneapolis Grain Exchange, Live cattle continuous CME. As a word of caution I want to stress the fact that the futures contracts on commodities are zero- investment instruments. Therefore, they do not require an initial investment and their respective returns are considered to be excess returns. Returns of portfolios exposed to commodity futures are calculated in congruence with equation (1). The dataset for all assets span the period from January 1991 to March 2013, with the exception of the German Real Estate index, which covers the period from October 1993 to March 2013 due to lack of data.
The S&P GSCI was launched in January 1991 and currently invests in 24 commodity classes. These 24 commodities are divided into five subgroups: precious metals, industrial metals, energy, agriculture and livestock. The S&P GSCI exhibits large exposure to the energy sector, this sector dominates by almost 70% of the total index. The DJ-UBSCI was launched in July 1998 with historical data backfilled by the index providers, beginning from January 1991 onwards. The DJ-UBSCI is constructed with 17 commodities divided into the same subgroups as the S&P GSCI. In contrast with the S&P GSCI the DJ-UBSCI is based on two guidelines to prevent exorbitant large subgroups and ensure diversification: The minimum and maximum weight for any commodity is between 2%and 15%, and the maximum allowable weight for any subgroup is 33%. The returns of the DJ-UBSCI and the S&P GSCI are unlevered, fully cash- collateralized long-only investments in commodity investments with full reinvestment.
The five individual commodity futures contracts are chosen based on the fact that they are representatives for the five commodity sectors, which match the subgroups of the selected indices (precious metals, industrial metals, energy, agriculture and livestock). Traditionally gold has been a hedge against inflation and proven to be a safe haven in periods with severe
