Goldman Sachs Commodity Index

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3 Jul Goldman Sachs Commodity Index 31 Oct Feb Average yearly return = 23.8% Jul-94 Jul-95 Jul-96 Jul-97 Jul-98 Jul-99 Jul-00 Jul-01 Jul-02 Jul-03 Jul-04 Jul-05 Jul-06 Jul-07 Jul-93 Price index Jul-92

4 State-of-the-Art Commodities Investing Using commodities for strategic asset allocation Risk-return relationship Higher moment properties Inflation hedge Portfolio diversifiers and conditional correlations Using commodities for tactical asset allocation Term structure strategy Momentum strategy Economic-based strategy

5 Poor performance on a stand-alone basis Annualized mean return on comm odity and annualized excess mean return on US bond and stock indices 15% 10% 5% 0% -5% -10% US small caps US value Equal-weight S&P500 Platinum traditional assets US growth MSCI Europe US T-Bond Feeder cattle Live cattle US T-Bill Livestock MSCI Asia Pacific Equal-weight Metal commodities Gold Soybeans Agricultural Copper Soybean meal Soybean oil Corn MSCI LatinAmerica Silver Lean hogs Wheat Cotton Energy Crude oil Palladium Heating oil Sugar Oats Orange juice Cocoa Unleaded gas Frozen pork bellies Coffee Natural gas -15% Annualized standard deviation 0% 10% 20% 30% 40% 50% Individual commodities Commodity indices Traditional asset classes Sample = Oct 1990 Dec 2006

6 Poor performance on a stand-alone basis: Reward to risk ratios Reward to risk ratio = Annualized mean / Annualized standard deviation Cocoa Coffee Corn Cotton Oats Orange Juice Soybean Meal Soybean Oil Soybeans Sugar Wheat Copper Gold Palladium Platinum Silver Crude Oil Heating Oil Natural Gas Unleaded Gas Feeder Cattle Frozen Pork Be... Lean Hogs Live Cattle US T-Bill US T-Bond S&P500 US Small Caps US Value US Growth MSCI Europe MSCI Asia Pac... MSCI Latin Am Commodities Traditional Assets Agricultural Metal Energy Livestock Tradtional assets Equally-weighted portfolio

7 Higher moments properties: Average skewness slightly higher than that of stocks and bonds Skewness Cocoa Coffee Corn Cotton Oats Orange Juice Soybean Meal Soybean Oil Soybeans Sugar Wheat Copper Gold Palladium Platinum Silver Crude Oil Heating Oil Natural Gas Unleaded Gas Feeder Cattle Frozen Pork Be... Lean Hogs Live Cattle US T-Bill US T-Bond S&P500 US Small Caps US Value US Growth MSCI Europe MSCI Asia Pacific MSCI Latin Am Commodities Traditional Assets Agricultural Metal Energy Livestock Traditional assets Equally-weighted portfolio Underlined = Significant at 5%

8 Higher moments properties: Average excess kurtosis slightly lower than that of stocks and bonds Excess kurtosis Cocoa Coffee Corn Cotton Oats Orange Juice Soybean Meal Soybean Oil Soybeans Sugar Wheat Copper Gold Palladium Platinum Silver Crude Oil Heating Oil Natural Gas Unleaded Gas Feeder Cattle Frozen Pork Be... Lean Hogs Live Cattle US T-Bill US T-Bond S&P500 US Small Caps US Value US Growth MSCI Europe MSCI Asia Pac... MSCI Latin Am Commodities Traditional Assets Agricultural Metal Energy Livestock Traditional assets Equallyweighted tf li Underlined = Significant at 1%

9 GSCI is a good hedge against unexpected inflation GSCI return GSCI = x UI (4.49) Unexpected inflation = Year-on-year change in inflation Correlation between GSCI returns and unexpected inflation = 0.24

10 But not all commodities serve as a good hedge against unexpected inflation β UI t (β UI ) β UI t (β UI ) Agricultural Commodities Livestock Commodities Cocoa Feeder Cattle Coffee Frozen Pork Bellies Corn Lean Hogs Cotton Live Cattle Oats Livestock Index Orange Juice Soybean Meal Soybean Oil Metal Commodities Soybeans Copper Sugar Gold Wheat Palladium Agricultural Index Platinum Silver Energy Commodities Metal Index Crude Oil Heating Oil Natural Gas GSCI Unleaded Gas Energy Index Energy, livestock and metal are better hedges against unexpected inflation than agricultural commodities

11 Commodities have low correlations with US and global equity indices Metal Index Livestock Index Energy Index Agricultural Index S&P500 US Small Cap US Value US Growth MSCI Europe MSCI Asia Pacific MSCI Latin America -1 Average = 0.04 Sample = Oct 1990 Dec 2006

12 Even lower correlations with J.P. Morgan US and global fixed income indices JPM US T-Bond JPM US T-Bill JPM Global Asia JPM Global Africa JPM Global Europe Metal Index Livestock Index Energy Index Agricultural Index Average = -0.01

13 Low correlations with one another Metal Index -1 Agricultural Index Energy Index Livestock Index Livestock Index Energy Index Average = 0.10

14 And thus useful diversifiers for strategic asset allocation 30% 25% 20% Energy Average return 15% 10% JPM Asia JPM Africa US value MSCI Europe S&P500 JPM Europe US small cap US growth MSCI Latin America 5% US T-Bond Livestock Metal MSCI Asia Pacific 0% Agricultural 0% 5% 10% 15% 20% 25% 30% 35% -5% Standard deviation Traditional asset classes Traditional asset allocation Collaterized commodity indices Long commodities Long + 20% Short commodities Sample = Oct 1990 Dec 2006

15 What about the conditional correlations? Research thus far focused on the unconditional correlations between commodities and traditional asset classes Chong and Miffre (2006) use a bivariate GARCH(1,1) model to analyze how the conditional correlations between commodities and S&P500 returns evolve over time in periods of high market volatility

16 Unstable correlations over time: The case for corn and the S&P500 index Oct 13, 1982 Oct 21, 1987 Oct 28, 1987 Oct 16, Conditional correlation Conditional annualized volatility of S&P500 excess returns /16/1980 1/14/1981 1/13/1982 1/12/1983 1/11/1984 1/9/1985 1/8/1986 1/14/1987 1/13/1988 1/11/1989 1/10/1990 1/9/1991 1/8/1992 1/13/1993 1/12/ /14/1994 1/10/1996 1/8/1997 1/14/1998 1/13/1999 1/12/2000 1/10/2001 1/9/2002 1/8/2003 1/14/2004 Conditional correlation between S&P500 and corn futures returns Trend in correlation Conditional volatility of S&P500 excess returns Correlation between conditional correlation and conditional S&P500 volatility = %

17 Conditional correlations with the S&P500 tend to decrease in periods of high volatility in equity markets Regression of conditional correlations between commodity futures returns and S&P500 returns on the conditional volatility of the S&P500 index The table reports the slope coefficients and associated t-statistics S&P500 Volatility S&P500 Volatility β t (β ) β t (β ) Agricultural Commodities Livestock Commodities Cocoa Feeder Cattle Coffee Frozen Pork Bellies Corn Lean Hog Cotton Live Cattle Oats Orange Juice Metal and Other Commodities Soybean Meal Gold Soybean Oil Heating Oil Soybeans Lumber Sugar Palladium Wheat Platinum Silver Sample: Jan May 2004

18 Unstable correlations over time Excellent tools for diversification: Correlations between commodities and S&P500 index fall over time and in periods of high volatility in equity markets This is fortunate: When the volatility in equity markets is high, the benefits of diversification are the most appreciated Explanation 1: Flight-to-quality hypothesis Previous metals are refuge assets Stop-loss selling strategies of equity investors Explanation 2: Different impacts of major events on commodity and stock returns Oil shocks, Wars, Hurricane, Unexpected rise in inflation Positive (Negative) skewness in commodity (S&P500) returns

19 State-of-the-Art Commodities Investing Using commodities for strategic asset allocation Risk-return relationship Higher moment properties Inflation hedge Portfolio diversifiers and conditional correlations Using commodities for tactical asset allocation Term structure strategy Momentum strategy Economic-based strategy

20 Backwardation and contango Price Contango Short positions are profitable F 0,d > F 0,n Roll-return = F 0,n / F 0,d 1 < 0 F 0,d F 0,n F 0,n 0 n d time F 0,d Long positions are profitable Backwardation F 0,n > F 0,d Roll-return = F 0,n / F 0,d 1 > 0 n: Nearby contract d: Distant contract

21 Term structure of crude oil and gold futures prices on Aug, Settlement price of crude oil ($ / barrel) Crude Oil: Backwardation Positive roll-return Gold: Contango Negative roll-return Settlement price of gold ($ / Troy oz) Aug-07 Sep-07 Oct-07 Nov-07 Dec-07 Jan-08 Feb-08 Mar-08 Apr-08 May-08 Jun-08 Jul-08 Aug-08 Sep-08 Oct-08 Nov-08 Dec-08 Maturity of contract A backwardated market has a downward sloping term structure and positive roll-returns A contangoed market has an upward sloping term structure and negative roll-returns

22 Term structure strategy Rallis, Fuertes and Miffre (2007) At the end of each month we measure the roll-returns of 37 commodities as F 0,n / F 0,d 1 F 0,n = Price of nearby contract (contract with the nearest maturity) F 0,d = Price of distant contract (contract with the second nearest maturity) Sort all commodities into quintiles based on their roll-returns Q 1 = Quintile with the highest roll-returns (most backwardated contracts) Q 5 = Quintile with the lowest roll-returns (most contangoed contracts) Go long Q 1, short Q 5 and hold the position for a month Repeat the strategy over the sample Jan 1979 Jan 2007 Compare the performance of the active strategy to that of a long-only strategy

23 Future value of $1 when the roll-returns are measured relative to the 2 nd nearest contract 25 $22.33 Value of $1 invested in Jan $ $2.19 $0.13 Jan-79 Jan-81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Jan-93 Jan-95 Jan-97 Jan-99 Jan-01 Jan-03 Jan-05 Jan-07 Quintile 1 (Backwardated contracts) Long Q1 - Short Q5 Quintile 5 (Contangoed contracts) Equally-weighted long-only portfolio Source: Rallis, Fuertes and Miffre (2007)

24 What if the roll-returns are measured relative to the most distant contract? $3.94 $2.19 $1.74 Value of $1 invested in January $0.20 Jan-79 Jan-81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Jan-93 Jan-95 Jan-97 Jan-99 Jan-01 Jan-03 Jan-05 Jan-07 Quintile 1 (Backwardated contracts) Quintile 5 (Contangoed contracts) Long Q1 - Short Q5 Equally-weighted long-only portfolio

25 Summary statistics of performance TS 1 TS 2 Index Average monthly return * ** Standard deviation Reward/Risk ratio Skewness * * Excess kurtosis * * * JB normality test * * * Best month Worse month % VaR % VaR TS 1 : Roll-returns are measured relative to the 2 nd nearest contract TS 2 : Roll-returns are measured relative to the most distant contract Index: Long-only equally-weighted portfolio of commodity futures * and **: Significant at the 1% and 10% levels

26 Alphas and betas of term structure strategies Regression of the monthly returns on the long/short strategies on a constant, used as a measure of abnormal performance (α) the excess returns on the S&P500 index (β S&P500 ) the excess total returns on Lehman Aggregate US Bond Index (β LB ) the GSCI excess returns (β GSCI ) TS 1 TS 2 α * Annualised α β S&P β LB β GSCI ** * TS 1 : Roll-returns are measured relative to the 2 nd nearest contract TS 2 : Roll-returns are measured relative to the most distant contract * and **: Significant at the 1% and 5% levels

27 State-of-the-Art Commodities Investing Using commodities for strategic asset allocation Risk-return relationship Higher moment properties Inflation hedge Portfolio diversifiers and conditional correlations Using commodities for tactical asset allocation Term structure strategies Momentum strategies Economic-based strategies

28 Momentum means price continuation Price Ranking period = Past 1, 3, 6 or 12 months Holding period = Next 1, 3, 6 or 12 months 20% Winners Buy Winners Ignore the remaining 60% of commodities 20% Losers Sell 0 Losers Time Source: Miffre and Rallis, 2007, Journal of Banking and Finance, 31, 6,

29 13 momentum strategies are profitable in commodity futures markets 16% 14% 15% Average annualized return 12% 8% 4% 0% 10.9% 11.9% 10.5% 8.7% 9% 8.1% 8.4% 8% 7.6% 1% 5.3% 5.5% 2% -4% -3% Holding period of 1 month Holding period of 3 months Holding period of 6 months Holding period of 12 months Ranking period of 1 month Ranking period of 6 months Ranking period of 3 months Ranking period of 12 months Average return of 13 profitable momentum strategies = 9.4% Equally-weighted portfolio of 31 commodity futures lost 2.5%! Sample = Jan 1979 Oct 2004 Underlined = Significant at 10%

30 Momentum profits are not merely a compensation for market, interest rate and commodity risks Alpha = Momentum risk-adjusted return 16% 12% 8% 4% 0% -4% 10.9% 15% 12.9% 16% Holding period of 1 month 8.9% 11.4% 9.5% 9.8% Holding period of 3 months 8% 8.3% 9.5% 2.3% Holding period of 6 months 6.3% 5.8% 3.1% -1.9% Holding period of 12 months Ranking period of 1 month Ranking period of 6 months Ranking period of 3 months Ranking period of 12 months Average alpha of 13 profitable momentum strategies = 10.20% Underlined = Significant at 10%

31 Momentum strategies preserve diversification properties of commodities 1 12% 0.5-2% 4% 0 3% Correlation -0.5 Commodity S&P500 US T-Bond -1 US T-Bill H = 1 H = 3 H = 6 H = 12 H = 1 H = 3 H = 6 H = 12 H = 1 H = 3 H = 6 H = 1 H = 3 Average Ranking = 1 month Ranking = 3 months Ranking = 6 months Ranking = 12 months H = Holding period

32 Which contracts do the strategies recommend trading? Term structure of average futures prices Average prices of light crude oil futures Light Crude Oil: p (ω >0)=46.5% p (ω <0)=25% p (ω =0)=28.6% Cocoa: p (ω >0)=26% p (ω <0)=46.1% p (ω =0)=28.9% Contango Backwardation 1,675 1,650 1,625 1,600 1,575 Average prices of cocoa futures Months before contract expiration 1,550 p(ω>0): Percentage of buy recommendations p(ω<0): Percentage of sell recommendations p(ω=0): Percentage of neither buy / nor sell recommendations

33 To recap thus far Momentum strategies work well in commodity futures markets The strategies focus on commodity futures with steep upward or downward sloping term structures Like term structure strategies, momentum strategies buy commodity futures with downward sloping term structure: Backwardated markets sell commodity futures with upward sloping term structure: Contangoed markets

34 State-of-the-Art Commodities Investing Using commodities for strategic asset allocation Risk-return relationship Higher moment properties Inflation hedge Portfolio diversifiers and conditional correlations Using commodities for tactical asset allocation Term structure strategy Momentum strategy Economic-based strategy

35 Economic-based strategy Are economic indicators useful at predicting future commodity returns? Can we set up an active strategy in commodity futures markets that is based on business cycle variables and beat a longonly strategy? Weekly Wednesday prices on 25 commodity futures (agricultural, metal, gas, livestock) Lagged business cycle variables Dividend yield, DY Default spread, DS Slope of the term structure, TS Treasury-bill rate, TB Commodity returns Period: Sep, Dec,

36 Economic-based strategy Estimate a regression that relates each commodity returns R Comm,t to past values of the economic variables using 5 years of data R Comm, t = 0 + β1dyt 1 + β2dst 1 + β3tst 1 β + ε t Use the regression coefficients (β 0, β 1, β 2 and β 3 ) to forecast one step-ahead commodity returns If the forecast return is positive, buy the commodity If the forecast return is negative, sell the commodity Repeat the strategy over the whole sample: Sep 1990 Dec 2006 Compare the performance of the active strategy to that of a passive long-only strategy Test the sensitivity of the results to the set of business cycle variables used

37 Results for a contangoed commodity: Cotton (Average return = %) Reward to Risk Ratios of passive and 11 active strategies Reward to risk ratio = Annualized mean / Annualized standard deviation Passive DS, TS, TB DY, TS, TB Cotton, DS, TB Cotton, DS, TS 0.12 Cotton, DY, DS 0.51 Cotton, DY, DS, TS, TB Cotton, DY, TB Cotton, DY, TS Cotton, TS, TB DY, DS, TB DY, DS, TS Business cycle variables used in active strategy to forecast future commodity returns It is easy to beat a contangoed market

38 Results for a backwardated commodity: Unleaded gas (Average return = 21.21%) Reward to Risk Ratios of passive and 11 active strategies Reward/risk ratio = Annualized mean / Annualized standard deviation Passive DS, TS, TB DY, TS, TB Gas, DS, TB Gas, DS, TS Gas, DY, DS Gas, DY, DS, TS, TB Gas, DY, TB Gas, DY, TS Gas, TS, TB DY, DS, TB DY, DS, TS Business cycle variables used in active strategy to forecast future commodity returns It is impossible to beat a backwardated market

39 Economic-based strategy: Conclusions Economic-based strategies work well in contangoed markets but work poorly in backwardated markets This is possibly due to the low correlations between commodity returns and the returns of traditional asset classes. As a result, economic variables that predict stock and bond returns have no forecast power over commodity returns and economic-based strategies fail to consistently outperform long-only strategies

40 Transaction costs Transaction costs impact the profitability of active strategies. The results presented here overstate the performance by the amount of trading costs. However the latter should not be overstated Transaction costs Futures contracts: % to 0.033% Large-capitalization stocks: 0.5% Small-capitalization stocks: 2.3% Less problem of liquidity No restrictions on short-selling Small cross section of commodity futures on which the strategies are implemented (up to 37 contracts)

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