Forecasting Commodity Returns

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1 Strategic thinking Forecasting Commodity Returns A Look at the Drivers of Long-Term Performance Commodities as an asset class have performed extremely well in the recent past, outpacing the returns of most equity and bond markets. Recent strong performance has led to significant investor interest in commodities an interest heightened by a historically low correlation between commodities and most other asset classes. By Andrei Belov, CFA Senior Research Analyst Citi Global Wealth Management By Holly Cao, CFA Senior Research Analyst Citi Global Wealth Management However, while historic volatility levels and correlations reasonably can be expected to persist, returns are a different story. Historical returns are extremely sensitive to the measurement period, and future returns will be similar only by coincidence or if prevailing economic conditions are like those that have been present historically. This being the case, it is imperative that investors understand the sources of asset returns and form realistic expectations prior to making an investment especially a long-term one. In this study, we explore the underlying factors that we believe drive performance in commodity markets and identify and analyze the various components of spot and futures returns. In the process, we demonstrate that spot or physical commodities generally make poor strategic investments and why most futures-based commodity investments historically have outperformed their spot counterparts. OCTOBER 27

2 Figure 1: Cumulative Real Performance of Spot Commodities & Cash (197 to 27) 12% GSCI Spot-Commodities Basket To facilitate asset-allocation decisions, we develop fundamental models to forecast forward-looking returns for five major commodity subgroups. Consistent with our methodology for forecasting the returns of other asset classes, we start with long-term steady-state return expectations and then adjust these expectations to a 1-year strategic time horizon. These return forecasts then can be used as inputs in the Whole Net Worth asset-allocation methodology to construct and analyze portfolios with commodity allocations US Three-Month T-Bill 1988 Data Source: Goldman Sachs, Federal Reserve as of 1 September Overview of Commodity Markets While most other asset classes familiar to investors are financial in nature, commodities are hard assets. Financial assets are expected to generate future cash flows, which provide a basis for their valuation. Accordingly, factors that impact future cash flows will be the primary drivers of financial-asset performance. Hard assets, on the other hand, do not have any future cash flows associated with them, and their performance primarily is driven by supply-and-demand factors. Therefore, the framework generally used to evaluate and forecast the performance of a traditional asset class, such as stocks or bonds, cannot be readily applied to commodities. This makes it particularly important to understand the sources of long-term commodities performance. Investors may gain exposure to commodities either through spot markets or futures markets. We will examine both in some detail. Spot Commodities. The spot markets are markets for physical commodities (barrels of oil, bushels of wheat, etc.) where goods are bought and sold for cash and for immediate delivery. These markets are sometimes referred to also as physical or cash markets. Commodities producers and consumers are the predominant players in spot markets. Investors typically do not transact in physical commodities because they don t hold them in their portfolios (with gold perhaps being the exception). The difficulty and cost of storing physical commodities may seem like the primary reason for investors absence from the spot market. However, a more fundamental factor is also at work. While spot-commodity prices have experienced significant short-term appreciation and depreciation, over the long run they essentially only have kept pace with inflation. Figure 1 shows the cumulative performance of a basket of physical commodities in real (or inflation-adjusted) terms over the past 37 years, ending in August 27. While recent returns have been positive in real terms, the experience of the 198s and 199s demonstrates that spot-commodity returns also can lag inflation for extended periods of time. 1 The implication is that, historically, spot commodities have underperformed cash. However, unlike cash, investments in spot commodities can be accompanied by significant volatility. Considering that holding physical commodities also is quite burdensome, it s no surprise that investors typically turn to futures markets to gain exposure to commodities. Commodity Futures. While spot commodities are bought and sold for immediate delivery, futures contracts are agreements to buy or sell a set quantity of a commodity at a predetermined price and date in the future. Futures contracts have expiration dates when the contracts are settled, at which point the holder may accept physical delivery of the underlying commodity. Investors holding long futures positions who do not want to take delivery will roll their positions forward selling contracts before they expire and purchasing longer-dated ones. Rolling futures positions forward would have no impact on returns if futures prices were equal to spot prices. /OCTOBER 27

3 However, typically this is not the case. Not only do futures prices differ from spot prices, but this difference also may vary across contracts with different maturities, creating a curve, or term structure, of futures prices. Figure 2 illustrates the three general term structures that can prevail in futures markets. Whenever futures prices are above or below the spot price, they will converge, or roll, towards the spot price over the life of the contract. This means investors will earn a return, known as the roll yield, on their positions. If a contract is priced at a premium to the spot market (a term structure known as contango) the futures price will depreciate towards the spot price, producing a negative roll yield. The opposite holds true when contracts are priced at a discount to the spot price (a term structure known as backwardation), producing a positive roll yield. Price (USD) Figure 2: Term Structure of Futures Prices $ Spot Price Flat Negative Roll Yield Positive Roll Yield Contango Delivery Date (DD) Data Source: Citi Global Wealth Management Backwardation If spot prices were to remain unchanged over the life of the contract (the simplifying assumption used in Figure 2) then futures investors would simply earn the roll yield. However, in the real world spot prices do change, and these changes also impact futures prices. Thus, investors purchasing commodity futures are exposed to both changes in the spot price and the roll yield. Futures Return = Spot Return + Roll Yield When investors purchase futures contracts, they are not required to put up the entire notional value of the underlying commodity in cash. Instead, they post a margin requirement set by the exchange typically a small percentage of the notional value. Returns on such leveraged positions are not comparable to returns on spot commodities unless futures investors collateralize their positions. To do this, they have to set aside cash or other collateral equal to the notional value of the contracts. Collateralizedfutures positions have an additional source of return because their collateral earns a yield typically a cash rate such as the return on short-term US Treasury bills. Spot investors, on the other hand, forego this collateral yield, which means the cash rate also can be viewed as the financing cost of carrying spot positions. Collateralized-Futures Return = Spot Return + Roll Yield + Collateral Yield Investors typically would expect to earn returns on collateralized-futures contracts similar to those on the underlying assets purchased in the spot market. For example, futures contracts on financial assets such as Treasury notes or the stocks in the Standard & Poor s 5 Index normally produce returns that virtually are identical to the underlying securities. These contracts have a term structure that is upward sloping or in contango, leading to a negative roll yield. As contracts mature and converge towards the spot price, the negative roll yield offsets the carrying cost on the underlying spot securities. This includes the financing cost, which equals the collateral yield that would be earned on an equivalent futures position. As a result, returns on the two investments are equalized. 2 As noted previously, long-term historical returns on spot commodities roughly have equaled the rate of inflation. If commodities behaved like financial assets, we also would expect returns on futures contracts to be similar to inflation. However, this has not been the case historically. Figure 3 compares the cumulative nominal returns on a basket of the spot commodities in the Goldman Sachs Commodity Index with those for a comparable basket of futures over the 37 years ending in August 27. We see that futures have outperformed the spot market by a considerable margin. Two factors explain why term structures of commodities prices and thus roll yields historically OCTOBER 27/

4 Figure 3: Cumulative Performance of Commodities (197-27) 8% GSCI Collateralized-Futures-Commodities Basket 7 GSCI Spot-Commodities Basket result is a flatter or backwardated term structure relative to what s normally observed in financial markets and, subsequently, a convenience yield earned by longfutures holders. Because of the insurance premium and the convenience yield, the roll yield on commodity futures is not simply a function of offsetting the carrying costs of the underlying spot assets. Instead the following relationship holds: Roll Yield = (Insurance Premium + Convenience Yield) - Spot Cost of Carry Figure 4 summarizes our overview of the commodity markets and illustrates the various components of spot-futures-commodity returns. Data Source: Goldman Sachs as of 1 September 27 Figure 4: Composition of Commodities Returns have resulted in futures contracts providing higher returns for investors than the spot market. They are the insurance premium and the convenience yield. The logic behind the insurance premium is that at any point in time there will be commodity producers who want to hedge their future profits against price volatility. To do this, they have to sell futures contracts against their expected output, locking in current prices. For this to work, though, there have to be speculators willing to go long futures. These speculators essentially sell insurance to the producers by transferring the price risk to themselves. But unless they expect commodity prices to appreciate, speculators won t assume this risk unless they are compensated for it. Producers provide this compensation by selling futures contracts at a discount to spot prices, so that the speculators on the other side can expect, on average, to earn a positive return. This premium creates a backwardated term structure and a positive roll yield. The convenience yield, by contrast, is driven by the desire of industrial consumers of raw commodities to hedge against supply disruptions. In order to ensure against shortages, consumers often have a strong preference for keeping physical commodities on hand. While this preference causes spot prices to rise relative to futures prices, consumers are willing to pay the premium for the convenience of having a secure supply on hand. The Spot Return Inflation Futures Return Roll Yield Inflation Collateralized- Futures Return Collateral Yield Roll Yield Inflation Expected Future Performance So far we have identified the different components of spot and futures returns. Next we need to analyze the fundamental factors that drive long-run returns and develop forward-looking forecasts. Consistent with the framework we use for other asset classes, we start with the concept of equilibrium returns. These are steady-state expectations that have a long-term time horizon and are unaffected by current market pricing. We then translate these forecasts into strategic return expectations over a finite time horizon, which we define as a 1-year investment period. /OCTOBER 27

5 In the case of collateralized commodity futures, we need to estimate the three sources of return shown in Figure 4: inflation, roll yield and collateral yield (i.e., the cash rate). We can use our inflation and cash-rate forecasts to estimate the spot return and the collateral yield. Here our analysis is focused on understanding the fundamental drivers and forecasting for the roll yield. In commodity futures markets, the insurance premium and convenience yield are the main drivers of roll-yield volatility. Thus, in order to forecast returns, we need to understand the factors that influence these two components. The insurance premium is driven by the desire of commodity producers to hedge against price uncertainty, while the convenience yield stems from the desire of industrial consumers to hedge against supply shocks. In both cases, the amount of hedging activity should depend primarily on the level of demand for a commodity relative to its supply. Other things being equal, an increase in demand relative to supply (or a decrease in supply relative to demand) should result in: higher price volatility, causing producers to increase their hedging activity and speculators to demand higher insurance premiums a higher probability of supply disruptions, causing consumers to increase their spot-commodity buying and a rise in the convenience yield Both responses will contribute to a higher roll yield. The opposite will be true if demand decreases relative to supply (or if supply increases relative to demand), leading to a lower roll yield. Figure 5 illustrates that changes in demand relative to supply historically have explained a significant portion of roll-yield variability in energy markets. Armed with these insights, we can begin to develop a forecasting approach. Equilibrium Forecasts To forecast the equilibrium roll yield, we need to have expectations for the long-term supply-and-demand relationship for the underlying commodity. Because these characteristics differ across various commodities, we have divided commodity markets into five major subgroups energy, industrial metals, precious metals, agricultural crops and livestock. Based on our analysis, we have developed three fundamental models for forecasting equilibrium roll yields. Figure 5: Energy Roll Yield and Supply/Demand Relationship (1983 to 27) Roll Yield 4% Correlation= 6% Rolling Annual Roll Yield Year-Over-Year Change in Average Annual Consumption as % of Stocks Data Source: Goldman Sachs, US Energy Information Administration as of 1 September 27 Precious Metals. The relationship between spot and futures prices for precious metals is akin to financial assets in that collateralized-futures returns typically equal spot returns. Several factors contribute to this result. First, the supply of precious metals is almost infinite compared to the relatively small amounts used for industrial purposes, so neither spot nor futures prices are affected significantly by changes in industrial demand. This means industrial consumers typically do not maintain large stockpiles as a hedge against supply shocks, eliminating the convenience yield. Precious metals also are nonperishable and relatively inexpensive to store. This gives producers less incentive to hedge against short-term price fluctuations, eliminating the insurance premium. Finally, low carrying costs make it economical for some investors to hold spot precious metals in their portfolios. This allows them to take advantage of arbitrage opportunities between spot and futures markets, which tends to keep prices in the two markets in line with each other. Due to these factors, spot and futures returns for precious metals historically have been fairly similar, indicating a negative roll yield that roughly offsets spot carrying costs, as seen in Figure 6. Because these costs primarily consist of the costs of financing, we can use our cash-rate forecast as a proxy for the equilibrium roll yield. 8% Consumption as % of Stocks OCTOBER 27/

6 Livestock. In the case of livestock, supply-and-demand dynamics historically have remained fairly stable over the long term. Figure 7 shows the growth rate of livestock consumption relative to available supply over the 37 years ending in August 27. While the short-term growth rate has been volatile, over the long term it has remained close to zero. Because livestock are both perishable and renewable, supply can be adjusted relatively quickly to bring it in line with demand. This makes it reasonable to expect that, in equilibrium, consumption growth relative to supply will remain close to zero going forward. Given our expectation that supply will equal demand in equilibrium, and the fact that the level of demand relative to supply has a direct impact on both the insurance premium and the convenience yield, we can forecast the equilibrium roll yield for livestock commodities based on year-over-year changes in average annual consumption as a percentage of available stocks. Energy, Industrial Metals and Agricultural Crops. Demand levels relative to supply for these three commodity subgroups have shown substantial variation over the long term. Thus, in order to forecast roll yield based directly on supply and demand, we first would need to estimate their future levels. However, forecasting supply and demand over the long term is difficult at best due to the multitude of factors that can affect them, such as changes Figure 6: Cumulative Performance of Precious Metals (1973 to 27) 12% Collateralized Futures Data Source: Goldman Sachs as of 1 September 27 Spot Figure 7: Average Annual Livestock Consumption as % of Available Stocks (197 to 27) 3% Year-Over-Year Change Rolling 1-Year Average of Year-Over-Year Changes Data Source: US Department of Agriculture as of 1 September 27 in consumer preferences, depletion rates, geopolitical events, etc. This led us to search for proxies that could be used to forecast roll yields indirectly. We identified two factors that we believe explain the historical roll-yield variability within the subgroups: spot returns and the real-cash-rate level. Other things being equal, an increase in demand for a commodity relative to the available supply or a decrease in supply relative to demand should result in higher spot prices. Lower relative demand or higher relative supply should have the opposite effect. As a result, the relationship between underlying spot-price changes (or returns) and the roll yield should be indicative of the impact of relative changes in supply and demand on both the insurance premium and the convenience yield. Using a statistical tool known as regression analysis, we examined whether this relationship had held historically. We found that underlying spot returns were a good predictor of future roll yields, implying that spot prices tend to adjust more quickly than roll yields to changes in supply and demand. The real cash rate should directly impact the insurance premium. The risk-free rate serves as the market s base interest rate the minimum expected return investors are willing to accept. As such, it also impacts the returns demanded on riskier assets. Given that the insurance premium compensates investors for the price risk of holding /OCTOBER 27

7 long futures contracts, it should in part be a function of the real cash rate. All else being equal, a higher rate should prompt investors to demand a larger insurance premium, while a lower rate should lead producers to pay a smaller premium. We also tested the historical prevalence of this relationship and verified that real-cash-rate levels were a good predictor of roll yields. Based on this analysis, we created predictive models that use underlying spot returns and real-cash-rate levels to forecast roll yields for the three commodity subgroups. These incorporated our equilibrium real-cash-rate forecast, as well as our expectation that long-term spot prices will continue to appreciate in line with inflation. Figure 8 compares the forecast for industrial metals to the actual roll yield. Expected Equilibrium Returns. Now that we have developed roll-yield forecasts for various commodity subgroups, we use a long-term inflation-rate forecast to estimate an expected spot return and our forecasted cash rate to estimate the expected collateral yield. Adding these to the roll-yield forecasts gives us our expected collateralized-futures returns. From Equilibrium to Strategic Forecasts Equilibrium forecasts are fairly stable in nature and we expect them to be realized over the very long term. Our equilibrium forecasts for the five major commodity subgroups as well as for two broad commodities baskets as of July 27 are shown in Figure 9. However, while equilibrium forecasts have an infinite time horizon, most investors make their decisions based on a finite investment horizon. As a result, we adjust our equilibrium forecasts to a shorter 1-year strategic time frame. We assume current market pricing to be the point of origin, while the strategic return is the return investors can expect to earn as current prices converge toward equilibrium levels over a 1-year horizon. 3 Thus, unlike equilibrium forecasts, strategic returns take into account prevailing market valuations and their impact on returns. Strategic Return = Equilibrium Return + Capital Gains/Losses Due to Current Market Valuation Once we have adjusted our roll-yield estimates for current market conditions, we add our inflation and cash-rate estimates to arrive at our strategic return forecasts. Figure 8: Industrial Metals Roll Yield and Spot Returns/Real Cash Rate Relationship (1977 to 27) Correlation=65% 6% Actual Rolling Annual Roll Yield Data Source: Goldman Sachs, Federal Reserve as of 1 September 27 Figure 1 shows our nominal and real forecasts for the same commodity subgroups and commodities baskets. These return forecasts are subject to change over time because they depend on prevailing market valuations and may change significantly given the volatile nature of commodities. Using strategic forecasts in Figure 1 as inputs in the Whole Net Worth asset-allocation methodology, we can construct and analyze portfolios with commodity allocations. Despite our extensive research of commodities markets, we have a lower degree of confidence in our forecasting capabilities for commodities than for traditional asset classes such as stocks and bonds. This is primarily due to the roll-yield variability across different commodities and inconsistency over time, as well as the possibility of permanent changes in market dynamics. 4 As a result of these factors and depressed return forecast, due to current market overvaluation (i.e., extremely contango price term structure), we chose not to include commodities in the Whole Net Worth strategic model portfolios. While this might change going forward, investors who would like to include commodities can still use the Whole Net Worth methodology to make opportunistic allocations to commodities within their portfolios. 5 Forecasted Rolling Annual Roll Yield OCTOBER 27/

8 Figure 9: Collateralized-Commodity-Futures Equilibrium Forecast as of July 27 *Historical risk and return since inception of each index. Data Source: Goldman Sachs, Dow Jones as of 1 September 27 Annualized Total Return Forecast Annualized Real Return Forecast Energy 9.9% 7.7% 11.5% 31.2% Industrial Metals 7.6% 5.4% 1.4% 23.6% Precious Metals 2.5%.3% 6.6% 23.% Agriculture 4.4% 2.2% 5.3% 19.4% Livestock 6.9% 4.7% 1.1% 18.2% GSCI Commodities Basket 8.6% 6.4% 11.5% 18.7% DJ-AIG Commodities Basket 6.9% 4.7% 7.3% 12.1% Figure 1: Collateralized-Commodity-Futures Strategic Forecasts as of July 27 Historical* Annualized Total Return Historical* Risk (Volatility) Annualized Total Return Forecast Annualized Real Return Forecast Historical* Annualized Total Return Historical* Risk (Volatility) Over/ Undervaluation vs. Equilibrium Energy 7.8% 5.6% 11.5% 31.2% -2.1% Industrial Metals 8.7% 6.5% 1.4% 23.6% 1.1% Precious Metals 2.8%.6% 6.6% 23.%.3% Agriculture 3.9% 1.7% 5.3% 19.4% -.5% Livestock 5.7% 3.5% 1.1% 18.4% -1.2% GSCI Commodities Basket 7.2% 5.% 11.5% 18.7% -1.5% DJ-AIG Commodities Basket 6.1% 3.9% 7.3% 12.1% -.7% *Historical risk and return since inception of each index. Data Source: Goldman Sachs, Dow Jones as of 1 September 27 /OCTOBER 27

9 Conclusions When investing in commodities, investors have a choice of spot and futures markets. Spot commodities make poor strategic investments because over the long term they produce returns roughly equal to the rate of inflation. Commodity futures historically have performed significantly better. This extra return has come in the form of a roll yield, which results from the backwardated term structure of many commodity-futures prices. However, the size of this roll yield may vary significantly. When assessing the attractiveness of commodities, it is imperative that investors form forward-looking return expectations rather than rely solely on historical performance. To that end, we have developed fundamental models for forecasting the collateralized-futures returns of five major commodity subgroups. Using these forecasts as inputs in the Whole Net Worth asset-allocation framework, we can construct and analyze portfolios with commodity allocations. n 1 For a discussion of the economic forces that influence spot-commodity prices and that tend to keep spot returns in line with inflation please see Appendix A, page 1. 2 If returns on collateralized-futures contracts and the underlying assets purchased in the spot market were not equalized, an arbitrage opportunity would exist between the spot and futures markets and investors would exploit it, forcing an adjustment of prices. Appendix B, page 1, describes this process in more detail and addresses why such arbitrage opportunities may not be exploited in the case of commodities. 3 The expected strategic return equals the average annual return over the 1-year convergence period. A hypothetical example is illustrated in Appendix C, page The dynamics of commodity-futures markets have begun to change with more investors making long strategic allocations to commodities and hedge funds increasing their trading activity in these markets (taking both long and short positions). The increasing number of investors is reducing the need of commodity producers to offer an insurance premium when hedging against price volatility, which is decreasing the roll yield earned on long positions. 5 For more information on Whole Net Worth, please read Whole Net Worth Asset Allocation: An Overview by Rui de Figueiredo, Ph.D., and Paul Goldwhite, CFA, published by Citi Private Bank in October 23, and Building on Whole Net Worth: Casting a Wider Net to Capture an Expanding Set of Investment Options by Parul Gupta, CFA, and Nicolas Richard, CFA, published by Citi Private Bank in April 27. OCTOBER 27/

10 APPENDIX A: Economic Factors Influencing Spot- Commodity Returns Why have spot-commodity returns roughly equaled the rate of inflation over the long term? In order to answer this question, we need to understand the major factors that drive spot-commodity prices: Inflation. Buying and holding a commodity does not generate any additional value outside of the use value of the commodity itself and thus does not produce a real return. As a result, all else being equal, commodity prices should keep up with the general level of prices in the economy. Productivity increases. Over time, technological advances have made the production of commodities more efficient and less costly relative to other goods. This has tended to put downward pressure on prices. Depletion effect. Supplies of some commodities (e.g., oil, natural gas, copper, etc.) are finite. As more resources are extracted and used, less remains for future consumption. Over time, supplies will tend to decrease and become more expensive to exploit, putting upward pressure on prices. Substitution effect. When a commodity becomes scarce and/or expensive, consumers will look for lower-cost substitutes replacing petroleum products with natural gas, electricity or ethanol, for example. This tends to have a negative impact on prices. Given these four factors, we can express the long-term return of spot commodities as follows: Spot Return = Inflation - Productivity Increases + Depletion Effect - Substitution Effect For many commodities, the impact of depletion largely will be offset by productivity increases and the substitution effect. Because many commodities are used as inputs in the production of other goods, sustainable changes in commodity prices also will flow through into the overall price level. So, in the long term we can expect spotcommodity returns to roughly equal the rate of inflation. APPENDIX B: Term Structures of Financial- and Commodity- Futures Prices In the case of financial assets, collateralized-futures contracts have to provide investors with returns that almost are identical to those of underlying securities. If this was not the case, arbitrage opportunities would exist between the futures and spot markets, allowing investors to earn a risk-free return by exploiting them. Investors would take advantage of the mispricings between the markets until prices adjusted, eliminating arbitrage opportunities. Consider, for example, an investor who wishes to invest in the S&P 5 Index. He or she can do so via the spot market by buying the S&P 5 stocks in the index or by purchasing a futures contract on the index. If the return from holding the individual stocks does not equal the return from the collateralized-futures contract, it should be possible to lock in a profit by buying the cheaper of the two investments and selling the more expensive one. These transactions will tend to cause prices to adjust, eliminating the return differential. Buying and holding S&P 5 stocks, either directly or through a commingled vehicle, is a more expensive proposition than maintaining an index-futures position in part because of higher transaction and storage costs, but also because investors must either pay cash for stocks (foregoing the collateral yield earned on futures positions) or use borrowed funds to finance their investments. The result is a return advantage for futures. This being the case, investors would be expected to buy futures contracts and sell stocks until futures prices have been pushed high enough to eliminate any return advantage. The result should be a contango term structure and a negative roll yield, which offsets the higher costs of holding the underlying stocks. Roll Yield = -(Cost of Carry) = -(Financing Cost + Transaction Cost + Storage Cost) By contrast, commodity-futures contracts historically have had a return advantage over spot commodities, which reflects the special characteristics of spot commodities. While arbitrage opportunities can and do exist between spot- and futures-commodities markets, investors often have limited ability to exploit them. For example, 1 /OCTOBER 27

11 if futures are expected to outperform, investors need to short the spot market and go long futures. However, because commodities typically are held for production and consumption purposes and not investment, investors largely are unable to borrow them to sell short. By the same token, investors who expect spot commodities to outperform need to go long the spot market while shorting futures. While this theoretically is possible, the logistics and costs of holding spot commodities can be prohibitive. Figure 11: Strategic Convergence From Current to Equilibrium Conditions Contango Backwardation APPENDIX C: Adjusting Equilibrium Forecasts In developing strategic return forecasts for commodity futures we assume the current price term structure will converge to the structure implied by our equilibrium roll- yield forecasts. Figures 11 and 12 illustrate a hypothetical convergence and its impact on returns over a 1-year strategic time horizon. In Figure 11, futures prices adjust from a contango term structure to backwardation in equilibrium. This implies a negative roll yield in years one through four, a zero roll yield in year five and a positive roll yield thereafter. When forecasting spot returns we assume a straightforward linear interpolation between current and equilibrium pricing. For the term structure of commodity-futures prices, however, we use an accelerated or logarithmic interpolation. We chose to use an accelerated interpolation for commodity futures to account for the fact that historically term-structure cycles in commodity-futures markets have been shorter in duration than the 1-year strategic horizon and to align the volatility of commodities forecasts with those of other asset classes by lowering their sensitivity to changes in the term structure. n Current Equilibrium Year Data Source: Citi Global Wealth Management Futures Price Spot Price Figure 12: Returns During Strategic Convergence Spot Return Collateral Yield Roll Yield Collateralized-Futures Return Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 1 Data Source: Citi Global Wealth Management OCTOBER 27/1 1

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