Economics

Abstract
The case study examines the conditional return correlations of the temporal variations that exist between the different asset groups (e.g. global stock and bonds) and the commodity futures. The study results and findings discovers that there is a conditional relationship existing between the SP500 futures and commodity futures, which had fell over time This decline is a good indication sign that the commodity futures, in the today economy, have ultimately become good and powerful tools that can be effectively employed in the strategic asset allocation. There was also a drop in the correlations with equity returns when the equity markets are above average volatility. This is no doubt good news for the investors because they require to diversify their portfolio when the equity markets are at high volatility, for instance during the 2008 global financial crisis that heavily struck the stock markets. The study further discovered that the drop in return correlations happening between Treasury-bills and commodity futures are parallel with increase in short-term volatility interest. This brings the suggestion r idea that when we add Treasury-bills to commodity futures portfolio then the investment risks are reduced for the investor.

Key Words DCC Model, Traditional Assets, Commodity Futures, Volatility, Conditional Correlation (CC)
Introduction

Hedge fund can basically be defined as an investment fund that is relatively open to some range of investors limited that have a huge range of investment portfolio and other trading practices than as compared to investing only in the long term investment funds, in addition provides some form of payment to the investment manager as a performance fee. Each and every hedge fund has its own unique and special investment strategy which will at the end determine the type and methods of investments which are chosen. As a class or rather a group, the hedge funds directs a wide range of investments which encompasses commodities and shares which are the key objects of this research. Most people believe that the initial hedge fund created for Alfred Jones Winslow by the law firm in 1949 to be the first hedge fund of its own kind ever created. The hedge fund was created by Seward  Kissel.

The year 2008 and 2009 recorded a positive hedge fund performance this was brought about by more than 1000 managers ( HYPERLINK httpwww.straightstocks.comwww.straightstocks.com). The investors who shifted  their money from equity markets to hedge fund investments made more than 75 return. According to Christopher Grunig, the Harcourt chief investor, the market shakeout that occurred in 2008-2009 brought about little competition to the hedge fund. As a result there was no competition coming from other heavy investors in the industry for instance the powerful investor banks ( HYPERLINK httpwww.straightstocks.comwww.straightstocks.com)

The commodity futures are characterized by low return correlation existing to the traditional assets and are therefore significant tools to be employed in strategic asset allocation (Erb  Harvey, 2006 Jensen et al., 2000). They are also better inflation hedge (Bodie, 1983 Rosanky  Bodie, 1980). Their return distribution is positively skewed (Gorton  Rouwenhorst, 2006), high liquidity. This assist in a big way in provision of leverage, complete transparency and reduced transacting costs. Lastly, recently, say in the financial crisis period, research indicated that that there were abnormal returns generated by the tactical trading in the commodity markets (Fuertes et al., 2008 Vrugt et al., 2007). For these reasons, the investors have been attracted to shift to the commodity futures.

It s clear that commodity futures inclusion into the strategic decision in properly diversified portfolio does not rely on temporal risk return contracts characteristics only it also depends on the correlation between the commodity futures and other portfolio over a time period. With this elaborate, the study evaluates and examines the conditional correlation existing between the traditional securities the commodity futures. This implies that reduction of risk computed by adding the commodity futures long position to a portfolio of equity increased over the analyzed duration. Ultimately, this means that over time the commodity futures have become the best portfolio diversifiers for the investors, and therefore the better tools for asset allocation. When the market risk rises, the correlations existing between equity returns and most of the commodity futures tend to decline.

The research also analyzes the conditional correlations temporal variations existing between fixed-income securities and commodity futures and then relates them to fixed-income indices conditional volatility.

The decline in return correlations existing between some equity and commodity returns that we see at the times of market stress can be expressed to be a  shift to quality . That is investors in Treasury-bills and equities, during the market panic, treat the commodity markets as refuge securities (for instance oils and metals). They reduce losses through sale of traditional asset portfolios and replacing them with commodity futures. The upsurge of volatility in the Treasury-bills and stock markets generates interest increase in the commodity futures markets giving explanation to the correlations observed during market stress. A natural disaster increase equity market volatility. Therefore, increase in market risk could happen concurrently to a decline in return correlation between the equity and commodity.
 Scope of the Paper

Section 3 avails the GARCH-DCC model employed in the estimation of the volatilities and conditional correlations. Section 4 presents the datasets. Section 5 examines the conditional return correlations   temporal variations existing between bond  global stock indices and commodity futures. Section 6 of the paper provides the conclusion.

Methodology
So far the GARCH (1, 1) model has been the most successful and the best volatility forecasting design (Lunde  Hansen, 2005) it was established by Bollerslev (1986). It assists in the description of financial return series volatility dynamics across asset groups and markets (Engel, 2004). The GARCH (1,1) variance, hii,t  is
Xi,t    i,t     ,         i, t          N ( 0 , hii ,t)
hii ,t   i   i 2i ,t-1  i hii ,t-1          i   1, ..,N    
subject to
i  0, , i  0, i  i 1
 and  coefficient finds that the resultant volatility time series short-term dynamics. A large  shows that the conditional variance shocks take a lot of time to dissipate meaning that the volatility is  persistent . A bigger  shows that the volatility acts intensely to the recent movement in the market
In approximating the CC, the research uses the dynamic CC model of Engel (2002). After estimating the GARCH (1,1) model, and using the results, we estimate the DCC (1,1), the time-varying correlation. Therefore the covariance matrix is Ht DtRtDt
Where Dt  diag (h11,t   .h NN,t )
Rt  Q-1 Qt Qt-t , time varying correlation
Qt  (q1jt)

Described by Qt  (1   a   b)   a (Yt-tt-1  )  bQt-1
 as used in the research is the N  N unconditional covariance of  Yt  xtht  that comes from the initial step approximation. Rewriting Rt  Q-1 Qt Qt-t , the CC between assets j  i and the time t is therefore expressed as
it  qij,t (qii,t qjj,t)

The DCC (1,1) model coefficients are calculated by the highest likelihood process through the BFGS.
The log likelihood equation is
L ()  - TNln(2tt1(lnHt  Yt H-1,t
Ht  (Ytt) equal to N  N covariance matrix.

The framework above can be used to study the CC existing between asset groups and commodity futures returns. First, the research looks at how the change over time through regression to time trend and constant. The study then examines the relationship existing between conditional volatilities and CC through regression using the following formulae
TC,t    T HT,t  C (hC,t  t)
Where T  Traditional assets, C  commodity futures.

To illustrate using the SP500, a positive T would mean that the SP500 and commodity futures conditional return correlations increases with equity markets volatility. We can use the evidence provided by Solnik et al. 1996). Alternatively, a negative T would illustrate the equity returns and commodity futures correlations when the equity markets have relatively high volatility. Finally, the research result would strive to prove the importance of commodity futures in diversifying the investment portfolios during the above normal volatility in the equity markets.

Data Sets
The data, obtained from Datastream International, constitute returns from 13 traditional asset groups and 25 commodities. The choice of bond indices and market represents a significant amount of asset allocation of a properly diversified world asset manager. On these criteria, the paper has shortlisted 7 equity asset groups (selected from global and United States markets). These are Russell 2000 Index, SP500 Composite, MSCI Latin America, Russell 1000 Value, MSCI Asia Pacific and Russell 1000 Growth Indexes. For the fixed-income markets, the paper adopts six bond indices.
The datasets also constitute the closing prices of 25commodities. The paper considers five energy futures, 11 agricultural futures, five metal futures and four livestock futures. In compiling the future prices into future return series, the settlement prices are collected on the most near maturity future contracts.

Table 1 indicates the statistics for 25 commodity future returns and the traditional assets group excessive returns. The results illustrate that the commodity futures average annualized returns range 16.6 (wheat) and 9.44 (corn) recording   1.30 on average. Commodity futures market high volatility does not translate automatically to highergreater average returns. For instance, unleaded gas and lumber futures have -9.0 average returns annually and above the average SD (standard deviation) (SD of 28.65, 35.26 respectively). The ration reward-to -risk implies that just a few commodities provide good risk-return trade-offs more than bonds and stocks over the duration considered. Table 1 also illustrates the excess kurtosis, skewness and Jarque-Beta test. It is therefore clear, from the table, that commodity futures return distribution strays from normality, with powerful evidence of excessive kurtosis standing at 1.

Table 2 illustrates correlations of unconditional return between traditional assets groups and commodity futures. As reported earlier, the SP500 returns correlations are very low (Jensen et al., 2000), ranging between 0.0948 (lumber) and -0.0206 (unleaded gas), with a 0.0139 mean. Averagely, 2.87, the research has recorded equally low return correlations with the other equity indices. The bonds record even lower figure at an average of 0.34. It is therefore elaborate that the commodity futures are not affected by the bonds and global stock returns. The commodities investors seek for this concept for risk diversification.

Empirical Results
This part of the research examines the conditional correlations existing between the SP500 returns and commodity futures and then provides an analysis. Table 3 shows the conditional correlations summary statistics estimated using our DCC model. The results from the table raise three comments. First, the average (table 3 0.0408) unconditional correlation is of similar capacity as the average (table 2 indicating 0.0139) unconditional correlation. Furthermore they are significant at 5. Secondly, the conditional correlations records considerable divergence volatilities, with SD ranging from 2.25 to 16.49 for lean hogs and gold respectively. Thirdly, and most importantly, conditional correlations regressions reveals a decline in conditional correlations over time for 19(20) of twenty five commodities recorded at 5 (10). The other coefficients are significantly positive for unleaded gas, coffee, live cattle and crude oil. It was further significant for the heating oil. The correlation decline recorded in table 3 is relevant in economic terms. The conditional correlations declined during 1981-2006 by an average of 5.8. The decrease was specifically more for precious metals i.e. gold (  -18.8)   platinum (  -17.72) and silver (  -28.38). The results show there has been an increase in segmentation between commodity futures and SP500 markets.

Due to this, the advantages of diversification of being commodity futures and long equity and the strategic asset allocation commodity futures have increased significantly. The correlation decrease over time, as seen in table 3, could be further illustrated by table 4 results due to the fact that there is often a decline in correlations at the time of high market volatility.

Table 4 in the appendix examines the relationship existing between the conditional market volatility and conditional correlations. The table indicates the coefficients of 11 T on  (hi,t) retrieved from equation one above  provides negative results at the level of 5. This clearly shows that the conditional correlations that exists between the SP500 returns and the 11 commodity futures declines in the duration when the risks at the market at that time increases. The institutional investors finds this to be positive news because when the volatility in the markets is high then they have more chances of diversification, they therefore shift to the commodity markets. In 10 situations, the T is found to (in four cases) be insignificant from zero and on the other side positive (in 10 cases). This phenomenon of the effects of the market volatility relayed on the equities and the market futures further brings forth the confirmation that different commodities does not behave in the same manner, they are therefore not perfect substitutes (Harvey  Erb, 2006).

Figure 1, for instance, which shows the plot of CC (Conditional Correlations) between SP500 and gold futures surplus returns plotted against the SP500 surplus returns CC. There is a drop in CC when there is a spike in SP500 (e.g. Oct. 2002, Feb. 1991, and Oct. 1987). Alternatively, when there is a decline in SP500, the CC seems to be more than the average e.g. 006-2006 or 1985. Due to this, the Correlation existing between these two series, as can be seen in Table one, becomes very low at -0.1751. This means that the commodity futures contracts (gold futures in this case) experiences some benefit of diversification during the increased or high market stress. Figure 1 further gives a straight line fixed to the CC to show the manner in which they did change over time.  The line slopes downwards, indicating that, the correlation occurring between the gold futures and the SP500 declined during this duration, just like in Table 3.

Over the 25 analyzed commodities, the equation one T average coefficient is found to be -0.2026 (see table 4). This means that one percent increase in the commodity futures leads to 0.020 cline in the correlation, on average. This implies that the SP500 bigger or rather higher volatilities means, ceteris paribas, more allocation to commodity futures. The potential investors, therefore at the turbulent periods, allocates more portfolio to commodity futures. The coefficients of T are significant and particularly low, for the precious metals for instance silver T  -1.5979, gold T  -69796 and platinum T  -1.5638. When the equity market volatility increases some agricultural goods performs better. (Tables 1, 2  3) Gold have recorded a low coefficient T, insignificant (meaning negative), conditional CC and unconditional CC, with the volatility being comparative to the index - SP500. This promotes gold s diversification characteristics and therefore a nice hedge at the market stress durations.

Table 4 illustrates the T coefficients which implies that the commodity futures, for instance the precious metals (silver, gold, platinum) are same to bonds, in that, just like experienced in bonds, they decrease their equity portfolio volatility in the durations when the market experiences higher market volatility, which are above average (Simon  Hunter, 2005). The observed results can be justified by the flight-to-quality by the investors which is a possible and viable economic rationale. When we view this from a different respectively, say, the potential investors may look at the commodity futures for instance the precious metals (gold, silver and platinum) as the major refuge commodities or rather securities when the market experiences high volatility specifically SP500 market. During the times or periods when the equity markets in the region is undergoing high volatility, the continuo resources re-allocation and equity asset managers stop-loss orders to the commodity futures for instance platinum, silver, gold and platinum exert higher downward pressures on the prices of the equities as compared to the prices of the commodity futures. In turn, this would assist in giving an elaborate and clear explanation to the decline in the correlation existing between equity returns and commodity futures that were noted in the duration when there was higher market volatility.

The research findings tally with the previous studies which have found out that when there is an increase of risks in the market, the investors dispose their shares to drastically stop the increase in losses they experience from the equity portfolios they replace this with the refuge assets.
Another reasonable explanation to the research findings lies on difference that most of the cases possess on the 2 types of securities. Particularly, Table 1 indicates that the agricultural futures majorly have return distributions positively skewed due to the natural disasters scenarios, for instance el Nio affect the prices of the commodities positively. On the other hand, the disasters affect the equity markets negatively. They create negative skewness and turmoil in their return distribution (see Table 1, Panel E).

Conclusion
The objective of the paper is to examine the way the commodity futures returns change over a given period from the asset groups (bonds and stock indices - globally). We discover that the commodity futures and SP500 index CC returns declined over time. This means that the equity markets and commodity futures have no doubt transformed over time to become better tools of asset allocation. There have been also an observation that over the half of the cross section studied in the paper, the CC existing between equity returns and commodity futures decline at the times of market turbulence. However, it is also significant to note that the evidence from the research is not parallel thought the commodities some of them have their CC increasing with equity markets volatility. This is however not unique because commodities does not have same characteristics (Harvey  Erb, 2006), they are therefore not substitutes.

Finally, the analysis could be used to account for the fact that the investors should hold in their portfolios diverse grades of company bonds like art work, real estate or hedge funds as other innovative ways of asset allocation.