“Does commodity exposure benefit traditional portfolios? Evidence from India”

Commodities and commodity futures are expected to benefit stock and bond portfolio diversification because traditional asset types like equities and bonds have low correlations with commodities. During periods when stocks and bonds may underperform, commodities may provide a hedge against inflation and other economic uncertainties. This study investigates the diversification benefits of adding commodities to a traditional portfolio of stock and bonds from the perspective of an Indian investor. It employs several commonly used asset allocation strategies such as mean-variance, equal risk contribution, most diversified portfolio, and equal weight portfolio on different commodity derivative groups. The performance of various portfolios indicates that not all commodity groups provide substantial diversification benefits to a traditional portfolio. Agricultural commodities enhance performance (with an Omega ratio of 1.654), whereas metal and energy-related commodities do not diversify the traditional portfolio significantly (Omega ratio of 1.087 and 0.945, respectively). Gold and different equity sectors also provide some diversification benefits. This study also supports the hypothesis that the behavior of different commodity groups is quite different.


INTRODUCTION
Commodities are alternative investments generating considerable interest among researchers and portfolio managers.With the advent of commodity indices, commodity-specific funds, and ETFs, many institutional investors allocate their assets to commodity markets, especially commodity futures.According to Citigroup, global commodity assets under management stood at $391 billion in January 2017, up 50% from the previous year.Commodities differ from financial assets, as these are the real assets produced, consumed, and stored.Commodities are seen as an alternative asset class due to these qualities.Earlier research has found evidence that commodities returns are weakly correlated with stock and bond returns.However, the correlation between equities and fixed-income securities and commodities has increased due to a surge in commodity investments.The two markets are now becoming more integrated.Commodities are also considered a hedge against inflation.Since commodity price level is an important cause of inflation, commodity prices positively correlate with inflation.These characteristics make commodities attractive candidates for investment.The exchange-traded commodity futures are the most convenient instruments to add commodity exposure to one's portfolio.
The futures trading in commodities started in India in 2003.Since then, the commodities futures market in India has grown substantially.MCX (Multi Commodity Exchange of India) ranks among the top twenty exchanges in the world in terms of traded volume 1 .For the participation of small retail investors, the exchanges have also introduced small lot sizes for different commodity futures.Not much research has been conducted on the diversification benefits of commodity investments in the Indian capital market.This study will answer the benefits of adding commodities to a portfolio for an investor in the Indian capital market.It also tries to understand the heterogeneous properties of different commodity groups.The research would also put some light on the possible influence of asset allocation strategies on the benefits of diversification.

LITERATURE REVIEW
Following the 2000 stock market meltdown, investors looking for an alternative asset class began to focus increasingly on commodities.Since then, investment in commodity futures has risen exponentially.Gorton and Rouwenhorst (2006) show that commodity futures and stocks have roughly the same average return, but equities have a somewhat larger risk.Furthermore, the skewness of the return distribution of stocks is negative, whereas the skewness of commodities returns is positive.This means that stocks have a higher downside risk than commodity futures.Commodity futures positively link inflation and are inversely related to stocks and bonds.(Erb & Harvey, 2006; Gorton & Rouwenhorst, 2006).
According to Bodie and Rosansky (1980), portfolio risk is reduced by one third if 40% of the portfolio is invested in commodity futures, vis-avis with a portfolio of stocks only, without compromising return.Their results also suggest that commodity futures provide a good inflation hedge.Several studies document that the efficient frontier of stock-bond portfolios improves by including commodities ( The benchmark portfolio of Nifty and Gsec (without any other asset) is used for judging the performance of different commodity groups and sectoral indices.The portfolio diversification improvement brought about by including various commodity groups and sectoral indices in the portfolio is then examined.Gold is studied as a separate class of investment (a special commodity) due to its characteristics.The diversification benefits of adding sectoral equity indices to Nifty and Gsec are also examined.The selected sectors are banking, FMCG, IT, auto, energy, financial services, and metals.Some sectors, such as energy and metals, may act as indirect investments in the corresponding commodities and provide similar diversification benefits.

Asset allocation strategies
While testing the diversification benefits, different commonly used asset allocation strategies are implemented to ensure that a particular asset allocation strategy does not bias the results.The methods employed are Naïve equally weighted portfolio (EW), mean-variance optimization (MV), minimum variance portfolio (Minvar), equal risk contribution portfolio (ERC), and maximum diversified portfolio (MDP).

EW strategy
In this strategy, the wealth is equally distributed among all the investments.The main advantage of this strategy is that no parameter needs to be estimated, and the implementation is straightforward.There is a good amount of empirical support in favor of this strategy.For instance, DeMiguel et al. ( 2009) report that the equal-weighted strategy outperforms the mean-variance optimization strategy in their out-of-sample tests.The portfolio weights are given by 1 , where N is the total number of assets in a portfolio, and w i is the weight of the i-th asset.

MV strategy
In this framework, the investor trades off between the risk and expected returns, maximizing her utility (Markowitz, 1952).The mean-variance optimization problem is where the investor's utility is denoted by U, μ is the (column) vector of expected return estimates, w is the (column) vector of portfolio weights (estimated by maximizing U), covariance matrix is ∑, and δ is the of risk aversion coefficient.The risk aversion coefficient used in this study is 2, corresponding to a low-risk aversion level.

Minvar strategy
This method chooses portfolio weights to minimize the portfolio return variance.The minimization problem is min , where w is the (column) vector of portfolio weights.
This strategy implicitly assumes a very high-risk aversion.The key advantage of this technique is that no return estimation is required, which is normally vulnerable to substantial estimation errors. http://dx.doi.org/10.21511/imfi.20(4).2023.04

ERC strategy
If the risk of a portfolio is measured by R(w), and the risk contribution of an asset i is C i (w), then ( ) ( ) .
If we use standard deviation as a proxy for the risk of the portfolio, then ( ) and the risk contribution of the asset i is where ∂ wi σ(w) is the marginal risk contribution from the asset i.For an equal risk contribution portfolio, the portfolio weights are chosen so that the risk contribution of any asset i equals the risk contribution of any other asset j.

MDP strategy
Following Choueifaty and Coignard (2008), the diversification ratio of a portfolio is defined as ( ) .
It is the ratio of the weighted average of volatilities to the portfolio volatility.The portfolio has the optimal weights, for which the diversification ratio is maximized, and is the most diversified portfolio.
Each asset allocation strategy has additional constraints on the portfolio weights for ensuring full investments and long-only positions.

Performance evaluation
For out-of-sample analysis, this study employs the rolling window approach used in several previous studies (DeMiguel et al., 2009; Daskalaki & Skiadopoulos, 2011; Bessler & Wolff, 2015).The optimal portfolio weights for a month t are calculated using data up to and including month t to estimate the mean returns and covariance matrices.The re-alized portfolio return from t to t+1 is then calculated using these optimal weights.This procedure is repeated by advancing the sample period by one month and determining the optimal weights for the following month.A rolling window of 60 months is used to calculate the optimal weights, with monthly rebalancing.
This study uses various out-of-sample performance measures to evaluate the benefit of including commodity futures and sectoral indices in the traditional portfolio.These measures include risk-to-return ratios (Sharpe, Sortino, and Omega), downside risk measures (modified VaR and maximum drawdown), and upside potential ratio.The study also examines the annual return and volatility for the different asset allocation strategies.Sharpe ratio, the first measure, is the ratio of the average excess return of the portfolio to its standard deviation.Because it penalizes both the upside and downside risk, we use two more risks-to-return performance measures that account for the downside risk only.The Sortino ratio accounts for the downside risk by using the downside deviation as the risk measure.The Omega ratio is the probability-weighted ratio of gains over losses for a minimum acceptable level of return.Omega has the advantage of not assuming any specific return distribution and is non-parametric.A higher value of Omega would be preferred by a rational investor for a given level of expected return.
Modified VaR is used to adjust for the non-zero skewness and excess Kurtosis of the distribution of portfolio returns among the downside risk measures.This study also uses the upside potential ratio to measure the gain per unit of downside risk.It allows the investors to identify investments with better upside performance per unit of downside risk.A minimum acceptable return (MAR) is required to calculate the performance measures Omega, Sortino, and upside potential ratio.MAR is the lowest rate of return an investor is willing to accept to meet her financial objective.This study uses the risk-free rate of return as the MAR.

Note:
The table provides the summary statistics of the assets' returns for the full period."Mean" is the annualized average of the monthly returns, while "Std.Dev." is the annualized standard deviation.Sharpe ratio is the annualized Sharpe ratio, and Kurtosis is the excess Kurtosis.VaR 95% is the historical VaR at the 95% confidence level.
modity group also varies.The aggregate index correlates more with energy and metal group futures than the agriculture index.The agriculture index shows a low correlation with other commodity groups and an insignificant correlation with all the asset classes.
The out-of-sample risk and returns of the portfolios with and without commodity futures are presented in Table 3. Separate portfolios have been created with commonly used asset allocation strategies EW, MV, Minvar, ERC, and MDP.The summary results include the average annualized monthly return, the average annualized standard deviation, and the mean absolute deviation.Table 3 shows that the benchmark portfolio returns are higher than those of the portfolios consisting of an aggregate index, Nifty, and Gsec, for all the strategies (max 7.51% in MV strategy as compared to 4.39%).The out-of-sample returns of the three portfolios of the futures indices of energy, metal, and agriculture-based products, with Nifty and Gsec, are also reported.From the view of return maximization, there is not much benefit to adding energy and metal-related commodities to one's portfolio.The benchmark portfolio is better than the portfolios, including the futures indices of composite commodities, energy-based products, or metals.
The portfolio's performance comprising the agriculture index, Nifty, and Gsec is the best for all the strategies among all the portfolios.The portfolio's performance having an energy futures index, Nifty, and Gsec is the worst.It can be attributed to the fact that, since 2012, there has been a consistent decline in the prices of energy-related commodities and metals.Due to the low weight of agricultural commodities, and the high weight of energy and metal-related commodities, the portfolio's performance consisting of an aggregate index with Nifty and Gsec is also poor.From the strategy point of view, MV is the best, with the highest out-of-sample annualized return; but it also has the highest volatility(11.64%return 16.91% as the volatility).The combined effect of returns and risk is discussed in the following section.The maximum drawdown value indicates that the investor would lose the most following the EW strategy, with the portfolio of futures index of energy products, Nifty, and Gsec (-0.256).This is because the weights are equal for all the assets in the EW strategy, and the energy futures index can pull down the portfolio returns much more with its low returns.In terms of maximum drawdown and value at risk, the best performance is shown by the portfolio of an aggregate index, Nifty, and Gsec, under the three risk-based strategies (Minvar, ERC, and MDP)( with as VaR of -0.015, -0.019 and -0.019, respectively).
As against the maximum drawdown, which measures the chances of losses, the upside potential ratio measures the chances of upside gains, and the Nifty and Gsec with the agriculture index have the highest upside potential ratio under the EW portfolio strategy.The metals futures index provides the lowest ratio.
The risk and returns of the portfolios, including gold/gold futures or sectoral indices, combined with Nifty and Gsec, are presented in Table 5.
Nifty and Gsec with sectoral equity portfolios generally provide higher returns than the benchmark portfolio or the portfolios consisting of Nifty, Gsec, and gold/gold futures.The MV strategy offers the highest returns with the Nifty, Gsec, and sectoral equity indices portfolio (10.29%).The returns for gold and gold futures portfolios are similar to those of the standalone benchmark portfolio.Similar is the case with the annualized standard deviation.The portfolios of Nifty and Gsec with sectoral equity indices are generally the most volatile(15.43%for EW strategy) The volatility of Nifty, Gsec, and gold/gold futures portfolios is the least, except for the MV strategy(4.11% for minimum variance portfolio).There is no significant difference between the portfolios having gold or gold futures as the portfolio components.The portfolio's performance comprising gold futures, Nifty, and Gsec generally dominates the others for most strategies and measures.The portfolio's performance comprising gold, Nifty, and Gsec closely follows.The benchmark and the portfolio with sectoral equity indices are the best for MV strategy.Probably this strategy can effectively balance the high volatility and high returns of a sectoral index.
The performance indicators for the portfolios comprising Nifty and Gsec; Nifty, Gsec, and gold/ gold futures; and Nifty, Gsec, and sectoral equity indices are presented in Table 6.Gold portfolios provide the best values for most of the performance measures.The risk/ reward performance of gold futures portfolios is the best.They also have low downside risk and sometimes high upside po-tential.The values of performance measures for the benchmark portfolio, and the portfolios with sectoral equity indices, are generally the worst.The high returns of sectoral equity indices cannot improve their portfolio performance due to their high volatility.However, these portfolios perform well with the MV strategy.
The downside risk measures support adding gold and gold futures as a diversification asset to one's portfolio.Such portfolios have the lowest drawdown and the lowest value at risk.On the other hand, adding sectoral equity indices to Nifty and Gsec portfolios does not significantly decrease the maximum drawdown and value at risk.Only for the MV strategy, it gives better results than the other portfolios.Comparing the portfolio with the agriculture index (the best portfolio in Table 4) with the portfolios having gold or sectoral indices confirms the overall dominance of the portfolio with the agriculture index.For all the strategies, almost all the portfolio performance measures comprising agriculture index, Nifty, and Gsec are substantially better than those of the other portfolios (including the portfolio containing gold futures).The only exception is the MV strategy, for which four performance measures (out of six) of the portfolios with sectoral equity indices are marginally better than those of the portfolio with the agriculture index.
There is evidence that all the commodity groups do not perform similarly.Contrary to the results of the more developed commodity markets, this study finds that the aggregate commodity basket, industrial and precious metals, and energy-related products substantially improve the stocks and bonds portfolio performance.On the other hand, agricultural commodities provide substantial diversification benefits to the stocks and bonds portfolio.A major reason for these results is the low correlation between the returns of equity/bond and agricultural commodities and a high average return on agricultural commodities.Including gold futures in one's equity portfolio improves performance due to a low correlation between gold and equity/bond returns.Still, this improvement is much less than that shown by the agricultural commodities because of their higher returns.Adding specific equity sectors to the traditional portfolio also somewhat improves performance.As portfolio constituents, the desirability of agricultural commodities and gold may also be ascribed to the low volatility and positive skewness of their returns.However, to some extent, the benefits of diversification depend on the strategy followed for portfolio construction (the MV strategy of portfolio construction shows some divergent results for specific measures).One can expect to improve the performance of equity and bond portfolios by adding futures contracts based on agricultural commodities or gold.The results of this study broadly demonstrate the diversification benefits of commodities for bonds and stocks portfolio in the Indian market.However, the effect of the individual commodity is studied only for gold.The effect of other commodities is studied with aggregate commodity futures index and sectoral commodity futures indi-ces.Given the data availability, this approach was adopted to increase the scope.As the commodities differ in their properties, a study of the diversification benefits of individual commodities may shed more light on the nature and causes of these diversification benefits.Agricultural commodities hold a special promise in this area.

CONCLUSION
This study investigates the benefit of adding commodities/commodity futures as asset classes in a portfolio of equities and bonds in the Indian market.
The results of this study support the evidence that the behavior of different commodity groups is quite different.In general, the volatility of commodity groups (represented by their futures index) is lower than that of the stocks (represented by the composite equity index Nifty and sectoral equity indices), except for the energy-based commodity group.In the Indian market, commodities would generally not Note: This table provides the performance measures for the out of sample performance of gold, gold futures, and sectoral equity indices with different asset allocation strategies.The portfolios are rebalanced with a monthly frequency.VaR is the modified value at risk at the 95% confidence level.
be beneficial as standalone investments, as their long-run return is lower than that of the stock market, except for agricultural commodities.More importantly, no significant correlation exists between the aggregate commodity index (or sectoral commodity indices) returns with the equity and bond returns.Out of these, the agricultural commodities have a low correlation with the other commodity groups (energy and metal, in our study) and an insignificant correlation with the bond and equity indices.The agricultural commodities and gold provide the highest and second-highest performance enhancement, whereas the aggregated commodities, energy, and metal-related commodities provide much lower diversification benefits.Gold also benefits from a low correlation with equity and bond returns, but its returns are not sufficiently high, which reduces the overall diversification benefits.
Contrary to the results of the more developed commodity markets, this study finds that the aggregate commodity basket, industrial and precious metals, and energy-related products do not improve the stocks and bonds portfolio performance.On the other hand, agricultural commodities provide substantial diversification benefits to the stocks and bonds portfolio.Gold also offers a good amount of diversification benefits.The addition of specific equity sectors to the traditional portfolio also improves the performance somewhat.
Another issue is that most studies of commodity diversification use a commodity index as the investment vehicle.In reality, the futures based on different commodities have different properties.The data consists of monthly returns of the stock, bond, and commodity futures indices from October 2005 to March 2017, except for the Dhaanya index.The data for the Dhaanya index is from January 2007 to March 2017, as January 1 st , 2007 is the base date for this index.CCIL (Clearing Corporation of India Ltd. The use of commodities, commodity futures, and commodity indices are studied for hedging and diversification benefit(Abanomey & Mathur, 1999b; Abid et al., 2020; Gagnon et al., 2020; Shah & Dar, 2021; Stoll & Whaley, 2011; Tiwari et al., 2022; Willenbrock, 2011; You & Daigler, 2010).However, some recent research has cast doubts on these findings.One major source of concern is the growing link between commodity and equities returns as a result of commodity financialization.(Tang&Xiong,2012; Adams & Glück, 2015).Tang and Xiong (2012) attributed it to index traders who invest in equity and commodity markets by investing in commodity index futures.Adams http://dx.doi.org/10.21511/imfi.20(4).2023.04isdue to the infrequent rise in commodity prices.versification.They conclude that commodities do not add value to the portfolios of investors.On the other hand, both Bessler and Wolff (2015) and You and Daigler (2013) conclude that commodities add value to the portfolio, but the outof-sample performance of portfolios, including commodities, is worse than their in-sample performance.Agyei-Ampomah et al. (2014) examine the impact of gold on investors' wealth during economic turmoil.The results show that palladium and industrial metals, particularly ) The T-bill index is used for determining the risk-free rate.This index consists of the T-bills with less than 365 days of maturity.The CCIL T-bill Index data are taken from the CCIL website.Gold and gold futures data are sourced from MCX.All the prices are denominated in INR and are extracted from the Bloomberg database.

Table 1
(4)sents the descriptive statistics of the monthly return series for all the assets (gold and http://dx.doi.org/10.21511/imfi.20(4).2023.04indices) from October 2005 to March 2017 (other than Dhaanya), consisting of 138 observations.volatility and VaR than the commodity futures indices but are comparable to Nifty.The annualized standard deviations of T-bills and Gsec are 0.6% and 7.5%.All the return series are lep-tokurtic.The stock indices' returns are negatively skewed (-0.72), whereas those of the agriculture index and gold are positively skewed (0.52 & 0.08).This suggests that these two commodities have less downside risk than stock indices.This result is also corroborated by values at risk.The monthly VaR of the agriculture index and gold is a low of 5.4 % and 6.2%.

Table 4
least Omega and Sharpe ratios are provided by the portfolios comprising the futures index of energy, Nifty, and Gsec; and with the MV strategy (-0.023 and 1.087, respectively).

Table 2 .
Correlation matrix of asset returns for the full period Note: This table provides the correlation matrix for asset returns for the full period.* indicates that the value is not significantly different from 0 at 5% level.

Table 3 .
Risk and returns of portfolios with different commodity groups (4)e: This table provides the summary results for different portfolios under different asset allocation strategies, for the outof-sample period.MAD is mean absolute deviation.http://dx.doi.org/10.21511/imfi.20(4).2023.04

Table 4 .
Performance measures of portfolios with different commodity groups This table provides the performance measures for the out of sample performance of different commodity group portfolios with different assets allocation strategies.The portfolios are rebalanced with a monthly frequency.VaR is the modified value at risk at the 95% confidence level.

Table 5 .
Risk and returns of portfolio with gold, gold futures and equity sectors Note: This table provides the summary results for different portfolios under different asset allocation strategies, for the outof-sample period.MAD is mean absolute deviation.

Table 6 .
Performance measures of portfolios with gold, gold futures, and sectoral equity indices