Chapter 2 DIVERSIFICATION BENEFITS OF COMMODITY FUTURES. stocks, bonds and cash. The inclusion of an asset to this conventional portfolio is

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1 Chapter 2 DIVERSIFICATION BENEFITS OF COMMODITY FUTURES 2.1 Introduction A traditional investment portfolio comprises risky and risk free assets consisting of stocks, bonds and cash. The inclusion of an asset to this conventional portfolio is beneficial if it improves the portfolio s reward to risk relationship. Commodities have negative correlation with stocks and bonds, possess unique risk premium, and perform well during inflation. These properties make commodities a unique investable asset class that can be included in a conventional portfolio to achieve diversification benefits (Gorton & Rouwenhorst, 2006; Erb & Harvey, 2006). After deregulation of commodity futures market (Commodity Modernization Act, 2000), the commodity futures market in USA has attracted a large number of institutional investors seeking diversification benefits. Commodity market witnessed a large inflow of money from commodity index investors (index speculators) who often take long position in the commodity market by investing in instruments linked to broad based commodity indices. Commodity index investors consider commodities as an investable asset class, just like stocks and bonds. They seek exposure to commodity prices by acquiring index swap contracts from swap dealers, or purchasing ETFs (Exchange Traded Funds) and ETNs (Exchange Traded Notes) from fund companies. Swap dealers and funds, then hedge themselves by taking long positions in individual commodity futures (Cheng and Xiong, 2013). The last decade has experienced an increase in commodity index related instruments as well as individual commodity futures. The popularity of such commodity 6

2 futures among institutional investors has been referred to as the financialization of the commodity market (Tang & Xiong, 2012; Irwin & Sanders, 2012; Silvennoinen & Thorp, 2013). The commodity futures market is a zero-sum market where all money flows must by definition net to zero (Irwin et al. 2009). In the commodity market, the amount gained by one participant is equal to the loss made by another (Schneeweis et al., 2008). In such a scenario, it seems difficult to devise active trading strategies involving commodity futures that can lead to diversification benefits. However, recent research has shown that momentum and term structure signals can be used to devise trading strategies (Erb and Harvey, 2006; Miffre and Rallis, 2007). Indian commodity futures markets reopened during 2003 (after a long ban imposed on commodity futures trading by the Forward Market Commission in order to check speculative trading and hoarding) and since then traders (hedgers and speculators) have shown a great interest in trading commodity futures. To make the commodity futures market more accessible to investors, commodity futures of small lot size were introduced. The Indian commodity futures market has undoubtedly excelled in the last decade. At the same time, the studies that report the diversification benefits observed by Indian investors, or foreign investors that invest in Indian commodity futures market, are sparse. This paper tries to fill this gap by studying the diversification benefits observed by adding commodity futures via strategic asset allocation (buy and hold strategy) and tactical asset allocation (momentum strategy and term structure strategy) to a conventional portfolio of stocks and bonds. The present research work attempts to answer three questions, 1) whether commodity futures should be included in the conventional portfolio of stocks 7

3 and bonds, 2) if they are to be included, which commodity futures or a combination of commodity futures are to be selected and 3) what percentage of total investment should be allocated to commodity futures. The paper is structured as follows. The next section 2.2 presents the related literature. Section 2.3 discusses the data and methodology used to select commodity futures and form different portfolios. Section 2.4 discusses the results, section 2.5 concludes the findings, and section 2.6 lists the limitations of the study. 2.2 Literature Review A heterogeneous literature exists in relation to the performance of commodity futures. Individual commodity futures were observed to have negative, zero, and positive risk premiums, whereas portfolios of commodity futures were observed to have positive risk premiums. Gray (1961) reviewed the literature on risk premium in commodity futures and was not clear whether it exist. Similarly, Dusak (1973), Bodie and Rosansky (1980), Kat and Oomen (2007) did not observe significant risk premiums for individual commodity futures. Erb and Harvey (2006) observed average annualized excess returns of the average individual commodity futures to be approximately zero. Some studies have shown that the risk premium for individual commodity futures varied (Gorton and Rouwenhorst, 2006; Erb and Harvey, 2006; Gorton et al., 2013; Woodard, 2008) but a long run portfolio of commodity futures tends to give a positive risk premium (Bodie and Rosansky, 1980; Fama and French, 1987, Gorton and Rouwenhorst, 2006). A number of studies confirmed a time varying seasonal risk premium (Carter et al., 1983; Chang, 1985), equity like performance in the long run (Kaplan and Lummer, 1998) and equitylike average returns (Bodie and Rosansky, 1980; Greer, 2000; Gorton and Rouwenhorst, 2006) for commodity futures. Ruff and Childers (2011) presented the possibility that 8

4 long-term passive investment by index investors permanently lowers the risk premium across all commodity futures. Zero and negative risk premium should not attract investors to invest in commodity futures. Positive skewness and/or low or negative correlation of commodity futures with other asset classes makes a sensible addition to the portfolio even with low expected returns (Kat and Oomen, 2007). Addition of commodity futures need not necessarily enhance portfolio returns; they improve the risk-return tradeoff by reducing the risk of the portfolio (Conover et al., 2010; Belousova and Dorfleitner, 2012) by diversifying nonsystematic risk (Fortenbery and Hauser, 1990). A number of studies have considered allocating a significant portion to commodity futures in a conventional portfolio of stocks and bonds to attain diversification benefits. Initially these studies were confined to broad based commodity index such as Goldman Sachs Commodity Index (GSCI). Later on, individual commodity futures find a place in the portfolios. Patterns of returns for the commodity futures index (GSCI) investment are dissimilar to other asset classes such as stocks, bonds and real estate (Gibson, 1999). Addition of gold futures (Jaffe, 1989), GSCI (Kaplan and Lummer, 1998) increased the return and decreased the risk of diversified portfolios. Addition of commodity futures index (GSCI) and few commodity futures to the conventional portfolio of stocks and bonds resulted in an increased Sharpe ratio (Egelkraut et al., 2005) and shifted the frontiers up for almost all risk levels (Anson, 2006). Woodard (2008) observed that portfolios with GSCI and individual commodity futures provide greater returns with marginally greater risk when compared to a conventional portfolio of stocks and bonds. Greer (1978), Bodie and Rosansky (1980) and Conover et al. (2010) reported that 9

5 commodity futures offer equity investors considerable benefits as a diversification tool. Anson (1999) reported that investors with high risk aversion should allocate 20 percent in commodities. Similarly, Jensen et al. (2000) suggested allocating 5 to 36 percent of the investors portfolio to commodities depending on their risk tolerance. Chong and Miffre (2010) examined conditional correlations between various commodity futures with stock and fixed-income indices. Conditional correlations with equity returns fell over time, which indicates that commodity futures have become better tools for strategic asset allocation. Strategic asset allocation decisions essentially involve determining an appropriate long term allocation of funds according to long term expectations about the future risk and return of asset classes, as well as the expected correlation structure between the assets (Rasmussen and Rasmussen, 2003). Woodard (2008) explained numerous strategic motivations for holding passive long-only commodity futures in a portfolio of stocks and bonds. These include the possibility of earning risk premiums, a low correlation of commodities with stocks and bonds and protection against inflation and business cycles. The presence of time varying risk premiums in commodity futures (Carter et al., 1983; Chang, 1985) suggests that even for rational and efficient markets, it may be optimal to hold futures in some period and not in others (Woodard, 2008). The possibility of timeseries and cross-sectional return predictability may make tactical asset allocation with commodity futures attractive to some investors (Erb and Harvey, 2006). Tactical asset allocation strategies take advantage of the possibility that future returns may vary and dynamic trading schemes can be formulated in response to macroeconomic conditions and short-term aberrations (Woodard, 2008). A number of tactical strategies have been 10

6 observed in literature that include tactical trading schemes based on interest rates, monetary policy (Jensen et al., 2000; Jensen et al., 2002), seasonality, momentum and term structure. In the futures market, taking a short position is as easy as taking a long position, and low transaction cost helps in implementing tactical asset allocation schemes at much lesser cost (Shen et al., 2007). A momentum strategy is a simple trading rule whereby one rank-orders past returns on the assets being investigated, then take long positions in assets that performed relatively well (past winners) and short positions in assets that performed relatively poor (past losers). Following a momentum strategy is a bet that past relative performance will continue into the future (Szakmary et al., 2010). Recent studies reported momentum in commodity futures returns (Georgiev, 2004; Pirrong, 2005; Erb and Harvey, 2006; Shen et al., 2007; Miffre and Rallis, 2007; Woodard, 2008) and momentum returns equal to stock returns (Shen et al., 2007). Fuertes et al. (2010) observed significant alphas for momentum strategies. The role of backwardation in the performance of passive long positions in commodity futures was observed by Feldman and Till (2006). Erb and Harvey (2006) found that portfolios based on term structure (backwarded and contangoed) performed better than long only portfolios. Backwarded (contangoed) portfolios consist of long positions for commodity futures with high (low) past roll returns. Woodard et al. (2008) investigated the impacts of term structure by estimating optimal weights for portfolios that are stratified by whether crude oil is in backwardation or contango prior to the first day of the month. Results showed that the addition of commodities greatly increases portfolio performance for the backwardation portfolios while their inclusion has a slight impact on 11

7 contango portfolios. Fuertes et al. (2010) found a significant alpha of percent for term structure strategies indicating its potential use in trading commodity futures markets. 2.3 Data and Methodology In India, trading in commodity futures started in November To investigate the diversification benefits, commodity futures prices from two Indian commodity futures markets, namely, Multi Commodity Exchange (MCX) and National Commodity & Derivatives Exchange Ltd. (NCDEX) were analysed from 2004 through Daily closing prices, trading volume and open interest for commodity futures were downloaded from MCX and NCDEX websites. The most liquid commodity futures contracts (top 20) were selected each year (January to December) based on trading volume (Appendix A1, A2 and Appendix B1, B2, B3, B4). After selecting the most liquid commodity futures contract, price series were formed from historical closing prices. For constructing price series data - to be used as input for calculating returns - daily closing prices of commodity futures contracts were converted to monthly frequency by sampling futures price of last trading day of each calendar month. Two price series were formed consecutively (monthly basis) - first nearby and second nearby price series. These price series were used to calculate futures return, spot return and roll returns. Spot return is calculated as the percentage change in the spot price of the underlying commodity using first nearby futures contracts. Whereas, futures return is calculated as the percentage change in the futures price using second nearby futures contract (Hafner and Heiden, 2008; Gorton et al., 2013). Roll return (implied yield or futures basis) is 12

8 calculated as the price gap between different-maturity contracts (i.e. the price difference between the futures return and spot return). Computation of futures return, spot return and roll returns has been described in Appendix C. Roll return signals whether a market is in backwardation or contango. A positive roll return indicates that the price of the nearby contract exceeds that of the distant contract, namely, that the term structure of commodity futures prices is downward-sloping and thereby the market is in backwardation. Conversely, a negative roll return signals an upward-sloping price curve and a contangoed market (Fuertes et al., 2010). Roll returns constitute a major part of the futures return and high roll returns are associated with high futures returns (Ruff and Childers, 2011). We use S&P CNX Nifty Total Returns Index to represent the Indian stock market, composite index from Reserve Bank of India (RBI) to represent the Indian bond market and Treasury Bill Index to represent risk free rate. Analysis is divided into two parts. First part (ex-ante) looks at the performance of portfolios on historical perspective. Whereas, second part of the analysis looks the performance of the portfolios assuming that the historical information revealed at time t (ex-ante) is used for investing in time t+1 (ex-post). Ex-ante and ex-post portfolios were analysed on yearly basis to know the diversification benefits obtained by incorporating commodity futures to the conventional portfolio of stocks and bonds. Three unconstrained and constrained portfolios were constructed each year to analyse exante performance. First portfolio consists of stocks and bonds. Second portfolio consists of stocks, bonds and equiweighted portfolio of most liquid commodities (naïve portfolio). 13

9 The third portfolio consists of stocks, bonds and most liquid commodities. Constrained portfolios consist of seventy-five percent stocks, fifteen percent bonds and ten percent commodities (eighty percent stocks and twenty percent bonds when commodities were not included in the portfolio). Portfolio mean, portfolio standard deviation and Sharpe ratio were calculated for all these portfolios study the diversification benefits. An investor needs to address two questions before allocating commodities (ex-post) to the conventional portfolio of stocks and bonds. First, she has to choose which commodity to invest in, from a number of available commodities, and second, how much of the total investment is to be allocated to commodities. To answer the first question, we select commodities based on different strategies, namely, strategic asset allocation (buy and hold strategy) and tactical asset allocation (momentum long, momentum short, momentum long short, term structure long, term structure short and term structure long short) (Diagrammatic representation to explain the formation of commodity futures portfolios has been presented in Appendix F). To address the second question, two types of portfolio were analysed. First, the weights obtained in ex-ante analysis were assigned to commodities in the next year to form optimal portfolios, and second, ten percent of total weight was allocated to commodities to form constrained portfolios. Momentum strategies involve selection of commodities based on previous returns, a bet that past performance will continue into the future (Szakmary et al., 2010). At the end of every year, futures contracts were sorted in increasing order, based on their futures returns in year t. The top and bottom four were selected to form portfolios (equiweighted) in year t+1. Based on ranking and holding periods, investors can formulate a number of momentum strategies. Ranking period refers to the number of past 14

10 periods that are considered for calculating average returns and holding period refers to the number of periods an investor holds a portfolio without rebalancing. The present research work considers one year each (January to December - starting from January 2004 until December 2012) as ranking and holding period for analysis (Miffre and Rallis, 2007). Momentum long strategy involves taking a long position in top four commodities in year t+1 that have highest returns in year t. Momentum short strategy involves taking short positions in bottom four commodities in year t+1 that have least return (among the top twenty most liquid commodities selected) in year t. Momentum long short strategy involves taking long position in the top four and short position in the bottom four commodities in year t+1 that have given highest and lowest returns respectively in year t. Erb and Harvey (2006) introduce a new dynamic asset allocation strategy that seeks to exploit the term structure of commodity futures prices by taking long positions in backwardated contracts and short positions in contangoed ones. Based on ranking and holding period, investors can formulate a number of term structure strategies. The present research work considers one year each as ranking and holding period for analysis of backwarded and contangoed strategies. Roll returns of the previous year determine the term structure of commodities. Positive roll returns exhibit backwarded term structure, whereas, negative roll returns show contangoed term structure. While constructing a portfolio, we consider long (short) position for commodity futures with high (low) past roll returns. The present research work considers one year each (January to December - starting from January 2004 until December 2012) as ranking and holding period for 15

11 analysis. During the holding period, investors hold such a portfolio for one year without rebalancing. Term Structure long strategy involves taking long positions in top four commodities in year t+1 that have highest roll returns in year t. Term Structure short strategy involves taking short positions in bottom four commodities in year t+1 that have least roll returns (among the top twenty most liquid commodities selected) in year t. Term structure long short strategy involves taking long position in the top four and short positions in the bottom four commodities in year t+1 that have highest and lowest roll returns respectively in year t. Based on futures return and roll return, among the most liquid commodity futures contracts, top and bottom commodity futures were selected to form different investment strategies (Summary of futures return and roll return are presented in Appendix G1 and Appendix H1. List of commodities sorted on the basis of futures and roll returns are presented in Appendix G2 and Appendix H2. List of commodities selected for forming investment strategies are presented in Appendix G3 and Appendix H3). First, performance of these investment strategies, namely, momentum long, momentum short, momentum long short, term structure long, term structure short, term structure long short were analysed from year 2004 through 2012 and later these investment strategies were used as an investment tool for allocating commodity futures to conventional portfolio of stocks and bonds in ex-post analysis. Ex-ante generated weights (using Markowitz optimization) were used for constructing ex-post optimal portfolios. Ex-post constrained portfolios consist of seventy-five percent stocks, fifteen percent bonds and ten percent commodity futures. All the trading strategies involve equiweighted commodity futures 16

12 portfolio. A similar analysis was performed on most liquid (top 16) agricultural commodities where the analysis spans from year 2005 through Markowitz optimization The mean-variance paradigm of Markowitz (1952) is by far the most common formulation of portfolio choice problems (Brandt, 2009). The typical Markowitz model prescribes optimization in a mean-variance framework. Efficient or optimal portfolio can be formed by three ways using the mean-variance framework. The first is to, minimize risk for a target return. The second is to, maximize return for a given value of risk and the third is to, maximize risk adjusted return. Optimal portfolios in the present research are formed by maximizing risk adjusted returns i.e. Sharpe ratio. Such portfolios are also called Sharpe optimal portfolios. For a portfolio of n assets, expected return on the portfolio is The variance of return on a portfolio is Maximize the Sharpe ratio to form Sharpe optimal portfolio 17

13 subject to and (sum of all the weights equals to one, and all the weights are positive) Optimization that involves short selling sometimes allocates high negative weights to certain assets that are inappropriate for practical investment. Therefore, in the present study it is assumed that short selling is not allowed. The short selling assumption was removed from mean-variance portfolio optimization by adding a constraint that portfolio weights should be positive and sums up to one. All the portfolios formed in the present research work, which incorporate commodity futures, are fully cash collateralized and unleveraged. Portfolio performance is measured by Sharpe ratio. 2.4 Results Most liquid commodity futures based on volume were selected from MCX and NCDEX. As few contracts were traded on both the exchanges, only unique contracts were selected for analysis. The commodity futures thus selected for analysis represent a broad cross section of agricultural, industrial, precious metal and energy futures markets. These exclude currency futures and financial futures. Most liquid agricultural commodity futures contracts are also analysed subsequently. Descriptive statistics pertaining to these commodity futures is given in Appendix D1 and Appendix D2. Ex-ante unconstrained and constrained portfolios were formed using Markowitz meanvariance framework. The unconstrained portfolios formed include a portfolio of stocks and bonds, portfolio of stocks, bonds and a naïve portfolio (an equiweighted portfolio of most liquid commodity contracts), and, a portfolio of stocks, bonds and individual commodity futures. For unconstrained portfolios, assets can be allocated any positive 18

14 weight, but for the constrained portfolios, weights were fixed. Three different fixed weight constrained portfolios were formed annually. First, stocks were allocated eighty percent and bonds twenty percent. Second, stocks were allocated seventy five percent, bonds fifteen percent and naïve portfolio ten percent. Lastly, stocks formed seventy five percent, bonds fifteen percent and individual commodity futures ten percent. The results obtained are presented in Table 1a (for most liquid commodity futures) and Table 1b (for most liquid agricultural commodity futures contracts). Details of commodities that got place in the portfolios are listed in Appendix E1 and Appendix E2. Table 1a: Ex-ante Portfolio weights and Sharpe ratios for unconstrained and constrained mean-variance portfolios. Unconstrained portfolios Constrained portfolios 2004 WEIGHTS WEIGHTS Stocks Bonds Naïve Portfolio Commodities Sharpe Ratio Change Stocks Bonds Naïve Portfolio Commodities Sharpe Ratio Change Stocks Bonds Naïve Portfolio Commodities Sharpe Ratio Change

15 Unconstrained portfolios Constrained portfolios 2007 WEIGHTS WEIGHTS Stocks Bonds Naïve Portfolio Commodities Sharpe Ratio Change Stocks Bonds Naïve Portfolio Commodities Sharpe Ratio Change Stocks Bonds Naïve Portfolio Commodities Sharpe Ratio Change Stocks Bonds Naïve Portfolio Commodities Sharpe Ratio Change Stocks Bonds Naïve Portfolio Commodities Sharpe Ratio Change Stocks Bonds Naïve Portfolio Commodities Sharpe Ratio Change

16 Table 1a shows the performance of unconstrained and constrained portfolios that incorporate commodity futures with stocks and bonds. Portfolios that include commodity futures have resulted in higher Sharpe ratios when compared to portfolios of stocks and bonds. Sharpe ratios for portfolios that include naïve portfolio (equiweighted portfolio of most liquid commodity futures contracts) are less when compared to the portfolios that include individual commodity futures. Superior performance of portfolios that incorporate individual commodity futures was observed every year during the course of study. The maximum increase in Sharpe ratios for unconstrained portfolios that include naïve portfolio was observed in year 2009 (0.550) followed by 2011 (0.210) and 2010 (0.072). For rest of the years under study, we do not find any increase in Sharpe ratios. The maximum increase in Sharpe ratios for unconstrained portfolios that include individual commodities was observed in the year 2009 (4.441) followed by 2010 (4.119) and 2011(1.130). Increase in Sharpe ratios was observed for all the years under study. The least increase in Sharpe ratio was observed in the year 2008 (0.086) followed by 2005 (0.156) and 2004 (0.171). The maximum increase in Sharpe ratios for constrained portfolios that include naïve portfolio was observed in year 2009 (0.034) followed by 2010 (0.023). A very slight increase in Sharpe ratios has been reported for years 2011 (0.003) and 2005 (0.002). For rest of the years under study, we observed a decrease in Sharpe ratios. The maximum increase in Sharpe ratios for constrained portfolios that include individual commodities was observed in the year 2009 (0.241) followed by 2011 (0.204) and 2010 (0.164). The least increase in Sharpe ratio was observed in the year 2008 (0.027) followed by 2004 (0.030) and 2005 (0.080). 21

17 Similar results were observed for unconstrained and constrained portfolios that incorporate agricultural commodities (Table 1b). The maximum increase in Sharpe ratios for unconstrained portfolios that include naïve portfolio was observed in year 2010 (0.459) followed by 2009 (0.226), 2011 (0.116) and 2005 (0.059). For rest of the years under study, we do not find any increase in Sharpe ratios. The maximum increase in Sharpe ratios for unconstrained portfolios that include individual commodities was observed in the year 2009 (1.383) followed by 2010 (1.247) and 2011(1.113). Increase in Sharpe ratios was observed for all the years under study. The least increase in Sharpe ratio was observed in the year 2008 (0.125) followed by 2006 (0.193) and 2012 (0.197). The maximum increase in Sharpe ratios for constrained portfolios that include naïve portfolio was observed in year 2010 (0.066) followed by 2009 (0.036) and 2005 (0.019). For rest of the years under study, we observed a decrease in Sharpe ratios. The maximum increase in Sharpe ratios for constrained portfolios that include individual commodities was observed in the year 2006 (0.301) followed by 2010 (0.270), 2005 (0.251) and 2009 (0.241). The least increase in Sharpe ratio was observed in the year 2008 (0.035) followed by 2007 (0.056) and 2012 (0.081). Increase in Sharpe ratios clearly demonstrates that the inclusion of commodity futures in the conventional portfolio of stocks and bonds provides diversification benefits. Incorporation of individual commodity futures provides more diversification benefits when compared with naïve portfolios. Results from ex-ante analysis shown in Tables 1a and 1b reveals that commodity futures have potential to provide diversification benefits. However, returns and risk from these ex-ante portfolios are not available to investors (You and Daigler, 2012). Nevertheless, investors can use the information revealed from 22

18 ex-ante portfolios in the form of weights and the commodity futures that finds place in optimal portfolios, to form ex-post portfolios. Investors earn returns and risk associated with ex-post portfolios. Investors who wish to earn these diversification benefits have to address two questions before investing. First, which commodity futures to select from a large group of investable commodity futures and second, what weights should be assigned to different asset classes. Certainly, there is no way by which an investor can be certain about the asset (stock, bond or commodity futures) future returns. In such a risky scenario investors have to select commodities and decide about the weights to be allocated to different asset classes. One way to address this question is to use the commodities and optimal weights obtained during mean-variance optimization (ex-ante) as a proxy for next period (expost) investment. Such investment becomes the basis for strategic asset allocation strategy. Generally investing in an index is considered as strategic (buy and hold) investment, but the in present study we consider only those commodities in ex-post portfolio that were allocated weight in ex-ante portfolio. The investment in naïve portfolio (equiweighted portfolio of most liquid commodities) mimics the traditional buy and hold investment in the present study. Investors can exploit momentum and term structure signals to formulate investment strategies that can be utilized as a portfolio diversification tool (Fuertes et al., 2010; Miffre and Rallis, 2007; Szakmary et al., 2010). Based on ex-ante analysis, top and bottom commodity futures were selected according to momentum and term structure signals. These commodity futures are then used to form ex-post portfolios each 23

19 representing a different type of investment strategy. Six different investment strategies were formulated based on momentum and term structure signals. Table 1b: Ex-ante Portfolio weights and Sharpe ratios for unconstrained and constrained mean-variance portfolios (agricultural commodities) Unconstrained portfolios Constrained portfolios 2005 WEIGHTS WEIGHTS Stocks Bonds Naïve Portfolio Commodities Sharpe Ratio Change Stocks Bonds Naïve Portfolio Commodities Sharpe Ratio Change Stocks Bonds Naïve Portfolio Commodities Sharpe Ratio Change Stocks Bonds Naïve Portfolio Commodities Sharpe Ratio Change Stocks Bonds Naïve Portfolio Commodities Sharpe Ratio Change

20 Unconstrained portfolios Constrained portfolios 2010 WEIGHTS WEIGHTS Stocks Bonds Naïve Portfolio Commodities Sharpe Ratio Change Stocks Bonds Naïve Portfolio Commodities Sharpe Ratio Change Stocks Bonds Naïve Portfolio Commodities Sharpe Ratio Change Table 2a presents ex-post average returns observed for different investment strategies. All investment strategies report positive returns for at least five years out of eight years. This shows that momentum as well as the term structure (backwardation and contango) signals employed to formulate investment strategies are applicable to Indian Commodity futures market. Results show that long only strategies (momentum as well as term structure strategies) perform well when compared to short only and long short strategies. The average returns for term structure long only strategy for the duration of the study was % while the returns for momentum long only strategy was 10.38%. Momentum short only strategy produced negative returns and term structure short only strategy produced nearly zero returns. Long short strategies (momentum and term structure) have produced positive returns because long only strategies worked well in the market. It is 25

21 noteworthy that the last three years of our analysis witnessed positive returns for all investment strategies except momentum short only strategy in year Table 2b presents ex-post average returns observed for different investment strategies that consider agricultural commodity futures contracts. Short strategies (momentum as well as term structure) did not perform well and produced negative returns for a number of years. At the same time momentum long and momentum long short strategies yielded positive returns. This could be attributed to the steep rise in agricultural commodity prices in the last few years. The average returns for momentum long only strategy for the duration of the study was 15.81% while the returns for terms structure long only strategy was 8.64%. Tables 2a and 2b reveals that momentum and term structure signals can be used to formulate investment strategies in commodity futures market. Momentum long and term structure long comes out to be the best investment strategies based on the returns produced. The last three years of our analysis found a considerable difference in the performance of investment strategies that include most liquid agricultural commodity futures with similar strategies that consider all commodity futures. The returns observed for different strategies are based on an equiweighted portfolio of top four and bottom four as well as top eight (long position) and bottom eight (short positions) commodity futures. Term structure long only strategy produced maximum returns when all the commodities were included to formulate investment strategies whereas momentum long only strategy produced maximum returns when agricultural commodities were included to formulate investment strategies. This shows that while investing in commodity futures, investor 26

22 needs to take care about the past performance as well as the term structure of commodities. Table 2a: Ex-post returns for different investment strategies Average RETURNS Momentum Long Only 15.00% -9.12% -8.16% -7.44% 14.40% 48.84% 14.76% 14.76% 10.38% Momentum Long Only (8) 7.68% -6.84% -1.68% -9.84% 30.36% 30.60% 22.44% 2.28% 9.38% Momentum Short Only 0.36% % 2.88% 54.96% % 15.12% % 7.44% -1.68% Momentum Short Only (8) -7.68% -4.68% 7.92% 37.32% % -3.36% -0.72% 2.76% -2.07% Momentum Long Short 7.68% % -2.64% 23.76% % 32.04% 1.56% 11.04% 4.35% Term structure Long Only 5.40% % 17.40% -4.56% 34.80% 53.04% 17.52% 5.88% 14.33% Term structure Long Only (8) 7.68% -1.56% 1.56% % 36.12% 40.32% 14.16% 4.08% 10.53% Term structure Short Only % -3.24% 9.12% 19.44% % 19.32% 10.08% 11.52% 0.09% Term structure Short Only (8) -7.68% -7.56% 19.20% 15.96% % 8.28% % 1.92% -2.01% Term structure Long Short -2.40% -9.12% 13.32% 7.44% % 36.12% 13.80% 8.76% 7.20% Table 2b: Ex-post returns for different investment strategies (agricultural commodities) Average RETURNS Momentum Long Only 23.76% % 1.20% 40.68% 67.32% % 14.76% 15.81% Momentum Long Only (8) -3.24% 5.04% 4.44% 44.52% 44.16% 3.36% 0.84% 14.16% Momentum Short Only % 22.80% 26.16% % % % 3.48% -5.07% Momentum Short Only (8) -3.84% 16.80% 14.64% % % -8.40% -4.32% -3.74% Momentum Long Short 5.04% 5.40% 13.68% 5.04% 21.96% % 9.12% 5.37% Term structure Long Only -9.72% 11.88% -4.56% 43.80% 74.76% % % 8.64% Term structure Long Only (8) -1.08% 3.72% 0.12% 15.72% 54.12% % -0.12% 8.16% Term structure Short Only -3.24% 9.12% 19.44% % % % -6.60% -8.30% Term structure Short Only (8) -1.56% 19.68% 11.04% % -7.80% % -5.64% -6.69% Term structure Long Short -6.48% 10.56% 7.44% 8.64% 28.32% % -8.64% 0.19% Returns observed for all the investment strategies that include commodity futures are not comparable to the stock returns except for those years when the stock market did not perform well (year 2008 and 2011). Therefore, hundred percent allocation of investable money in commodity futures in the form of these strategies is not advisable. However, a 27

23 portfolio of stocks, bonds and commodities might be beneficial. These strategies can act as a portfolio diversification tool as they pave the way for incorporation of commodity futures into a conventional portfolio of stocks and bonds. Equiweighted commodity futures portfolios (in the form of different investment strategies) were combined with stocks and bonds each year to form optimal and constrained portfolios. These newly formed optimal and constrained portfolios were compared with the conventional portfolio of stocks and bonds. Ex-ante weights obtained from mean-variance optimization that included individual commodity futures were used as reference for investment to form ex-post optimal portfolios. Conventional portfolio consists of eighty percent stocks and twenty percent bonds while constrained portfolios consist of seventy-five percent bonds, fifteen percent bonds and ten percent commodities. Table 3a presents ex-post portfolio returns for optimal and constrained portfolios. In a majority of instances, conventional portfolio returns are greater than the returns obtained by optimal and constrained portfolios that incorporate commodity futures. Inclusion of commodities undoubtedly gave better returns when the stock market did not perform well (years 2008 and 2011). Optimal and constrained portfolios produced superior returns in year 2010 for few strategies. Table 3b presents ex-post portfolio returns for optimal and constrained portfolios formed by using agricultural futures. In a majority of instances, conventional portfolio returns are greater than the returns obtained by optimal and constrained portfolios. Inclusion of agricultural commodity futures responded differently during the years when stock market did not perform well. During 2008 all the investment strategies yield similar or higher 28

24 return when compared to conventional portfolio whereas, during 2011 none of the investment strategies produced higher returns than conventional portfolio. Table 3a: Ex-post portfolio returns for optimal and constrained portfolios Conventional portfolio 32.88% 28.32% 40.80% % 57.36% 22.20% % 14.76% Optimal Portfolio Strategic Asset Allocation 33.36% 12.36% 9.96% -4.68% 0.96% 12.48% 5.40% 9.36% Momentum Long Only 24.00% 1.56% 0.96% % 2.28% 47.88% 9.72% 15.00% Momentum Long Only (8) 19.44% 3.24% 6.36% % 7.08% 30.00% 16.20% 5.16% Momentum Short Only 14.76% -1.92% 10.20% 11.04% % 14.88% % 9.24% Momentum Short Only (8) 9.60% 4.92% 14.52% 4.44% % -3.24% -3.24% 5.52% Momentum Long Short 19.44% -0.24% 5.52% -0.60% % 31.32% -1.32% 12.12% Term Structure Long Only 17.88% -2.88% 22.56% % 8.40% 51.96% 12.00% 8.04% Term Structure Long Only (8) 19.44% 7.20% 9.12% % 8.76% 39.48% 9.24% 6.60% Term Structure Short Only 8.04% 6.00% 15.48% -2.16% % 18.96% 5.88% 12.48% Term Structure Short Only (8) 9.60% 2.76% 24.00% -3.48% % 8.16% % 4.92% Term Structure Long Short 12.96% 1.56% 18.96% -6.72% -5.04% 35.52% 8.88% 10.32% Constrained Portfolio Strategic Asset Allocation 33.84% 24.96% 38.64% % 54.36% 35.04% -8.40% 14.40% Momentum Long Only 32.16% 25.44% 37.20% % 55.32% 25.56% -9.84% 15.00% Momentum Long Only (8) 31.44% 25.68% 37.80% % 56.88% 23.76% -9.00% 13.80% Momentum Short Only 30.72% 25.08% 38.28% % 46.92% 22.20% % 14.28% Momentum Short Only (8) 29.88% 25.92% 38.76% % 49.08% 20.40% % 13.80% Momentum Long Short 31.44% 25.20% 37.68% % 51.12% 23.88% % 14.64% Term Structure Long Only 31.20% 24.96% 39.72% % 57.36% 26.04% -9.48% 14.16% Term Structure Long Only (8) 31.44% 26.28% 38.16% % 57.48% 24.72% -9.84% 13.92% Term Structure Short Only 29.64% 26.04% 38.88% % 48.24% 22.68% % 14.64% Term Structure Short Only (8) 29.88% 25.68% 39.96% % 50.64% 21.60% % 13.68% Term Structure Long Short 30.48% 25.44% 39.36% % 52.80% 24.36% -9.84% 14.40% Overall result from Tables 3a and 3b show that portfolio of commodity futures when incorporated to stocks and bonds do not yield higher returns (Holding period returns of conventional portfolio, naïve portfolio, optimal portfolios and constrained portfolios are presented in Appendix I1 and I2). Performance of a portfolio can be enhanced by 29

25 increasing returns, decreasing risk or both. Therefore, any diversification benefits realized by incorporating commodities to the conventional portfolio will mainly result from the decrease in risk (standard deviation) of the overall portfolio. Table 3b: Ex-post portfolio returns for optimal and constrained portfolios (agricultural commodities) Conventional portfolio 28.32% 40.80% % 57.36% 22.20% % 14.76% Optimal Portfolio Strategic Asset Allocation 36.12% 14.28% -4.68% 13.44% 84.12% % 9.00% Momentum Long Only 28.56% 1.92% -9.00% 19.68% 50.04% % 14.88% Momentum Long Only (8) 13.44% 15.12% -7.80% 21.72% 36.84% -2.04% 2.64% Momentum Short Only 7.68% 28.80% 0.36% % -1.44% % 4.92% Momentum Short Only (8) 13.20% 24.24% -3.96% % -0.84% % -1.92% Momentum Long Short 18.12% 15.36% -4.32% 1.20% 24.36% % 9.96% Term Structure Long Only 9.84% 20.40% % 21.36% 54.24% % -7.56% Term Structure Long Only (8) 14.64% 14.16% -9.36% 6.84% 42.48% % 1.80% Term Structure Short Only 13.44% 18.36% -2.16% % 1.56% % -3.96% Term Structure Short Only (8) 14.40% 26.40% -5.40% % 7.44% % -3.12% Term Structure Long Short 11.64% 19.32% -6.72% 3.12% 27.96% % -5.76% Constrained Portfolio Strategic Asset Allocation 23.64% 40.80% % 65.16% 35.04% % 14.76% Momentum Long Only 28.80% 36.72% % 57.96% 27.48% % 15.00% Momentum Long Only (8) 26.04% 38.52% % 58.32% 25.08% % 13.56% Momentum Short Only 25.08% 40.20% % 50.76% 18.36% % 13.92% Momentum Short Only (8) 26.04% 39.60% % 51.96% 18.48% % 13.08% Momentum Long Short 26.88% 38.52% % 54.36% 22.92% % 14.40% Term Structure Long Only 25.44% 39.12% % 58.20% 28.20% % 12.48% Term Structure Long Only (8) 26.28% 38.40% % 55.44% 26.16% % 13.56% Term Structure Short Only 26.04% 38.88% % 51.24% 18.96% % 12.84% Term Structure Short Only (8) 26.28% 39.96% % 50.04% 19.92% % 12.96% Term Structure Long Short 25.80% 39.00% % 54.72% 23.52% % 12.60% Table 4a presents ex-post Sharpe ratios for optimal and constrained portfolios. When compared with conventional portfolios, optimal portfolios and constrained portfolios 30

26 exhibit high Sharpe ratios for most of the years studied. It is also observed that none of the strategies could produce high Sharpe ratios for all the years studied. Average Sharpe ratio of optimal portfolios was lower than conventional portfolio for all the strategies studied. Constrained portfolios have performed better than conventional portfolio (Average Sharpe ratio for the conventional portfolio was 0.203). Highest average Sharpe ratio was observed for strategic asset allocation strategy (0.239) followed by term structure long only (0.220), term structure long short (0.209) and momentum long only (0.208). Table 4b presents ex-post Sharpe ratios for optimal and constrained portfolios that incorporate agricultural commodities. When compared to conventional portfolio, optimal and constrained portfolios produced high Sharpe ratios for most of the years studied. None of the strategies could produce high Sharpe ratios for all the years studied. Average Sharpe ratio of optimal portfolios was lower than conventional portfolio for all the strategies studied. Constrained portfolios have performed better than conventional portfolio (Average Sharpe ratio for the conventional portfolio was 0.175). Highest average Sharpe ratio was observed for strategic asset allocation strategy (0.191) followed by momentum long (0.189) and term structure long (0.180). Tables 4a and 4b show that a small allocation (ten percent) of commodities to a conventional portfolio of stocks and bonds (constrained portfolios) could produce diversification benefits. Average Sharpe ratios show that strategic asset allocation strategy, momentum long and term structure long produced best diversification benefits. When we consider all the commodities, term structure long only appears as the best investment strategy after strategic asset allocation strategy. At the same time when we 31

27 consider agricultural commodities, momentum only appears to be the best investment strategy after strategic asset allocation strategy. Table 4a: Ex-post Sharpe ratios for optimal and constrained portfolios Average Conventional portfolio Optimal Portfolio Strategic Asset Allocation Momentum Long Only Momentum Long Only (8) Momentum Short Only Momentum Short Only (8) Momentum Long Short Term Structure Long Only Term Structure Long Only (8) Term Structure Short Only Term Structure Short Only (8) Term Structure Long Short Constrained Portfolio Strategic Asset Allocation Momentum Long Only Momentum Long Only (8) Momentum Short Only Momentum Short Only (8) Momentum Long Short Term Structure Long Only Term Structure Long Only (8) Term Structure Short Only Term Structure Short Only (8) Term Structure Long Short

28 Table 4b: Ex-post Sharpe ratios for optimal and constrained portfolios (agricultural commodities) Average Conventional portfolio Optimal Portfolio Strategic Asset Allocation Momentum Long Only Momentum Long Only (8) Momentum Short Only Momentum Short Only (8) Momentum Long Short Term Structure Long Only Term Structure Long Only (8) Term Structure Short Only Term Structure Short Only (8) Term Structure Long Short Constrained Portfolio Strategic Asset Allocation Momentum Long Only Momentum Long Only (8) Momentum Short Only Momentum Short Only (8) Momentum Long Short Term Structure Long Only Term Structure Long Only (8) Term Structure Short Only Term Structure Short Only (8) Term Structure Long Short Conclusions A number of portfolios were constructed ex-ante and ex-post, with and without commodity futures to unveil the diversification benefits offered by commodity futures when incorporated in a conventional portfolio of stocks and bonds. Ex-ante unconstrained and constrained portfolios reveal that incorporation of commodity futures to a 33