Q Group

Spring Seminar
03-05 April 2005
Key Largo

The Tactical and Strategic Value

of
Commodity Futures

Claude B. Erb Campbell R. Harvey

TCW, Los Angeles, CA USA Duke University, Durham, NC USA
NBER, Cambridge, MA USA
Commodity Futures: Summary Statistics

• Since 1969, the Goldman Sachs Commodity

Index (GSCI) has outperformed the S&P 500
• What does this imply about our asset allocation
decision to commodity futures?
• The critical question is whether the past will
repeat.
 Figure 1
Return and Risk
December 1969 to May 2004

14%

12% 50% S&P 500

50% GSCI GSCI Total
Return
S&P 500
10%
Compound annual return

8% Intermediate
Treasury
3-month
T-Bill
6%
Annualized Annualized
Compound Return Standard Deviation T-Stat*
Inflation U.S. Inflation 4.79% 1.15%
4%
Three Month Treasury Bill 6.33% 0.83%
Intermediate Government Bond 8.55% 5.82% 2.23
S&P 500 11.20% 15.64% 1.83
2% GSCI Total Return 12.24% 18.35% 1.89
50% S&P 500/50% GSCI 12.54% 11.86% 3.07
*Test of whether excess return is different from zero
0%
0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%
Annualized standard deviation
Note: GSCI inception date is December 1969. During this time period, the S&P 500 and the GSCI had a monthly return correlation of -0.03. GSCI is
collateralized with 3-month T-bill.
Commodity Futures: Different Indices

• GSCI – Production weighted

• Dow-Jones AIG – Production and liquidity
• Reuters-CRB – Equal weighted
 Figure 2
Market Value of Long Open Interest
As May, 2004

CRB Index
3.9%

DJ AIG Index
9.8%

GSCI Index
86.3%

Data Source: Bloomberg

 Figure 3
Return and Risk
January 1991 to May 2004

14% Average Standard Correlation

return deviation 1 2 3 4 5
1. GSCI 6.81% 17.53%
2. DJ AIG 7.83% 11.71% 0.89
12% 3. CRB 3.64% 8.30% 0.66 0.83
4. Wilshire 5000 11.60% 14.77% 0.06 0.13 0.18
5. EAFE 5.68% 15.53% 0.14 0.22 0.27 0.70 Wilshire
6. Lehman Aggregate 7.53% 3.92% 0.07 0.03 -0.02 0.07 0.03 5000
10%
Compound annualized return

8%
DJ AIG GSCI
Lehman US
Aggregate MSCI
6% EAFE

4%
3-month CRB
T-Bill

2%

0%
0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%
Annualized standard deviation of return

Comparison begins in January 1991 because this is the initiation date for the DJ AIG Commodity Index. Cash collateralized returns
 Table 1
The Composition of Commodity Indices
(as of May 2004)

P ortfolio Weights

C ommodity C RB GSC I DJ A IG C ommodity C RB GSC I DJ A IG

Aluminum - 0.029 0.071 Hogs 0.059 0.021 0.051
Cocoa 0.059 0.003 0.020 Live Cattle 0.059 0.036 0.067
Coffee 0.059 0.006 0.028 Natural Gas 0.059 0.095 0.099
Copper 0.059 0.023 0.067 Nickel - 0.008 0.019
Corn 0.059 0.031 0.051 Orange J uice 0.059 - -
Cotton 0.059 0.011 0.018 P latinum 0.059 0.000 -
Crude Oil 0.059 0.284 0.167 Silver 0.059 0.002 0.022
Brent Crude Oil - 0.131 - Soybeans 0.059 0.019 0.051
Feeder Cattle - 0.008 - Soybean Oil - 0.000 0.017
GasOil - 0.045 - Sugar 0.059 0.014 0.038
Gold 0.059 0.019 0.053 Unleaded Gas - 0.085 0.054
Heating Oil 0.059 0.081 0.047 Wheat 0.059 0.029 0.038
Lead - 0.003 - Red Wheat - 0.013 0.000
Zinc - 0.005 0.023
Total 1.000 1.000 1.000

# Contracts 17 24 20

Gini coefficient 0.00 0.65 0.32

Data Source: Goldman Sachs, Dow Jones AIG
Commodity Futures: Beware of Indexes

• GSCI – Traded since 1992

• But performance backfilled to 1969.
• 1969-1991, compound annual return=15.3%
beating the S&P 500 return of 11.6%
• 1992-2004, compound return of 7% while
S&P 500 was 10.4%
Commodity Futures: Beware of Indexes

• DJ-AIG – Traded since 1998

• But performance backfilled to 1991.
• 1991-1998, compound annual return=4.1%
beating the GSCI which only had 0.5%
Commodity Futures: Beware of Indexes

• CRB – Traded since 1986

• But performance backfilled to 1982.
Table 2
Historical Excess Returns
December 1982 to May 2004
Geometric A rithmetic Standard T- Sharpe A uto- Diffi cult
0 mean mean deviation statistic Skew Kurtosis ratio correlation storage

Overall
GSCI 4.49% 5.81% 16.97% 1.22 0.51 1.98 0.26 0.11
Sectors
Non-Energy -0.12% 0.36% 9.87% -0.06 0.09 -0.01 -0.01 0.01
Energy 7.06% 11.52% 31.23% 1.05 0.73 2.28 0.23 0.15
Livestock 2.45% 3.48% 14.51% 0.78 -0.19 0.93 0.17 0.05
Agriculture -3.13% -2.15% 14.35% -1.01 0.20 0.85 -0.22 -0.01
Industrial M etals 4.00% 6.41% 22.82% 0.81 1.27 5.92 0.18 0.06
Precious M etals -5.42% -4.46% 14.88% -1.69 0.29 2.21 -0.36 -0.18
Components
Heating Oil 5.53% 10.51% 32.55% 0.79 0.64 1.94 0.17 0.04 Y es
Live Cattle 5.07% 5.94% 13.98% 1.68 -0.51 2.74 0.36 0.02 Y es
Live Hogs -2.75% 0.17% 24.21% -0.53 -0.04 1.14 -0.11 -0.04 Y es
Wheat -5.39% -3.32% 21.05% -1.18 0.16 0.17 -0.26 -0.01 No
Corn -5.63% -3.32% 22.65% -1.15 1.37 9.16 -0.25 0.00 No
Soybeans -0.35% 1.92% 21.49% -0.08 0.44 1.86 -0.02 0.01 No
Sugar -3.12% 3.69% 38.65% -0.37 1.60 7.03 -0.08 0.03 No
Coffee -6.36% 0.85% 39.69% -0.74 1.12 3.09 -0.16 0.01 No
Cotton 0.10% 2.60% 22.64% 0.02 0.61 1.37 0.00 0.05 No
Gold -5.68% -4.81% 14.36% -1.83 0.30 2.33 -0.40 -0.14 No
Silver -8.09% -5.30% 25.03% -1.49 0.46 2.05 -0.32 -0.15 No
Copper 6.17% 9.15% 25.69% 1.11 1.03 3.92 0.24 0.06 Y es

Portfolios
EW Buy-and-Hold 0.70% 1.26% 10.61% 0.31 0.05 0.69 0.07 0.01
EW Rebalanced Portfolio 1.01% 1.51% 10.05% 0.46 0.01 0.37 0.10 -0.04
Average of 12 Commodities -1.71% 1.51% 8.17% -0.72 0.60 2.57 0.23 0.07

Rebalancing Impact 2.72% 0.00% 1.88% 0.78 -0.60 -2.20 -0.13 -0.11

Lehman Aggregate 3.45% 3.50% 4.65% 3.43 -0.20 0.48 0.74 0.12
S&P 500 7.35% 8.30% 15.30% 2.22 -0.76 2.70 0.48 -0.01
M SCI EAFE 5.84% 7.18% 17.29% 1.56 -0.22 0.38 0.34 0.05
Table 2
Historical Excess Returns
December 1982 to May 2004
Geometric Standard
0 mean deviation
Overall
GSCI 4.5% 17.0%
Sectors
Non-Energy -0.1% 9.9%
Energy 7.1% 31.2%
Livestock 2.4% 14.5%
Agriculture -3.1% 14.4%
Industrial M etals 4.0% 22.8%
Precious M etals -5.4% 14.9%
Components
Heating Oil 5.5% 32.5%
Live Cattle 5.1% 14.0%
Live Hogs -2.7% 24.2%
Wheat -5.4% 21.0%
Corn -5.6% 22.6%
Soybeans -0.4% 21.5%
Sugar -3.1% 38.7%
Coffee -6.4% 39.7%
Cotton 0.1% 22.6%
Gold -5.7% 14.4%
Silver -8.1% 25.0%
Copper 6.2% 25.7%
Table 2
Historical Excess Returns
December 1982 to May 2004

Geometric Standard
0 mean deviation

Overall
GSCI 4.5% 17.0%

Portfolios
EW Buy-and-Hold 0.7% 10.6%
EW Rebalanced Portfolio 1.0% 10.0%
Average of 12 Commodities -1.7% 8.2%

Rebalancing Impact 2.7% 1.9%

Lehman Aggregate 3.4% 4.7%

S&P 500 7.4% 15.3%
M SCI EAFE 5.8% 17.3%
Table 3
Excess Return Correlations
Monthly observations, December 1982 to May 2004

Non-Energy 0.36
Energy 0.91 0.06
Livestock 0.20 0.63 0.01
Agriculture 0.24 0.78 0.01 0.12
Industrial Metals 0.13 0.31 0.03 -0.02 0.17
Precious Metals 0.19 0.20 0.14 0.03 0.08 0.20

Heating Oil 0.87 0.08 0.94 0.04 0.00 0.05 0.13

Cattle 0.12 0.50 -0.03 0.84 0.07 0.03 0.01 0.00
Hogs 0.21 0.52 0.06 0.81 0.13 -0.06 0.05 0.06 0.37
Wheat 0.25 0.66 0.06 0.18 0.79 0.05 0.06 0.06 0.12 0.17
Corn 0.14 0.58 -0.03 0.10 0.78 0.12 -0.01 -0.04 0.05 0.11 0.52
Soybeans 0.20 0.58 0.02 0.11 0.72 0.18 0.14 0.05 0.03 0.14 0.43 0.70
Sugar 0.03 0.21 -0.06 -0.05 0.35 0.14 0.05 -0.04 0.02 -0.10 0.11 0.12 0.09
Coffee -0.01 0.15 -0.04 -0.07 0.23 0.07 0.01 -0.07 -0.06 -0.06 0.00 0.03 0.07 -0.01
Cotton 0.11 0.25 0.06 0.00 0.27 0.17 0.04 0.05 -0.06 0.06 0.05 0.11 0.18 -0.02 -0.01
Gold 0.20 0.16 0.16 0.01 0.07 0.18 0.97 0.15 -0.02 0.04 0.07 -0.01 0.14 0.02 0.00 0.03
Silver 0.08 0.19 0.02 0.02 0.10 0.19 0.77 0.02 -0.01 0.05 0.03 0.09 0.13 0.07 0.04 0.04 0.66
Copper 0.15 0.36 0.04 0.01 0.22 0.94 0.20 0.07 0.03 -0.02 0.08 0.16 0.23 0.14 0.11 0.19 0.18 0.21

Average Corre lations

GSCI with commodity sectors 0.33
GSCI with individual commodities 0.13
Heating oil with other commodities 0.03
Individual commodities -0.09
Figure 4
Term Structure of Commodity Prices
May 30, 2004

$41.50 $405
$41.00 $404
Crude Oil
$40.50 Backwardation
$403

Gold price ($/Troy ounce)

$40.00
$402
Oil price ($/barrel)

$39.50
$39.00 $401

$38.50 $400
$38.00
$399
$37.50
$398
$37.00
$36.50 Gold $397
Contango
$36.00 $396
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ir l- e-0 ts -0 r-0 r -0 r-0 y-0 ir l- y-0 l y-0
p Ju
n u be be be ar p a Ju
A ug e m em em ru A M
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S N D
Commodity Futures: Roll Returns

• The excess return consists of a spot return and a roll

return.
• The spot return is the change in the price of the nearby
futures contract.
• Since futures contracts have an expiration date
investors who want to maintain a commodity futures
position have to periodically sell an expiring futures
contract and buy the next to expire contract.
Commodity Futures: Roll Returns

• This is called rolling a futures position.

• If the term structure of futures prices is upward
sloping, an investor rolls from a lower priced expiring
contract into a higher priced next nearest futures
contract.
• If the term structure of futures prices is downward
sloping, an investor rolls from a higher priced expiring
contract into a lower priced next nearest futures
contract.
• This suggests that the term structure of futures prices
drives the roll return.
Commodity Futures: Roll Returns
• The excess return for gold futures was about -5.7% per annum,
the spot price return was -0.8% and the roll return was about -
4.8%.
• The roll return was negative because the gold futures market is
almost always in contango.
• The average spot return of heating oil and gold futures was
close to zero. The 11.2% excess return difference between
heating oil and gold was largely driven by a 9.5% difference in
roll returns.
• The 1.7% difference in spot returns was a relatively minor
source of the overall return difference between heating oil and
gold.
• This example illustrates that excess returns and spot returns
need not be the same if roll returns differ from zero
Figure 5
Excess and Spot Returns
December 1982 to May 2004

Excess Spot Roll

Return Return Return
Heating Oil Futures Excess Return
Heating Oil 5.53% 0.93% 4.60%
Heating Oil Spot Return
$3.50 Gold -5.68% -0.79% -4.90%
Gold Futures Excess Return
Difference 11.22% 1.72% 9.50% Gold Spot Return
$3.00

$2.50
Growth of $1

$2.00

$1.50

$1.00

$0.50

$0.00
Commodity Futures: Normal Backwardation?

• How important have roll returns been in explaining the

cross-section of individual commodity futures excess
returns?
• Long-only normal backwardation suggests that
commodity futures excess returns should be positive,
for both backwardated and contangoed commodity
futures.
• In fact, Gorton and Rouwenhorst (2004) suggest that
under normal backwardation there should be no
relationship between the term structure of commodity
futures prices and the returns from investing in
commodity futures.
Figure 6
Excess Returns and Roll Returns
December 1982 to May 2004
Intercept Roll Roll Adjusted
Intercept T-Stat Coefficient T-Stat R Square
Compound Annualized Excess Return 0.89% 1.84 1.20 10.97 91.57%

Excess Spot Roll

Return Return Return
Corn -5.63% 1.57% -7.19%
Wheat -5.39% 0.57% -5.96%
Silver -8.09% -2.54% -5.55%
Coffee -6.36% -1.24% -5.12%
8% Gold -5.68% -0.79% -4.90%
Sugar -3.12% 0.30% -3.42% Copper Heating
Hogs -2.75% 0.26% -3.01%
6% Soybeans -0.35% 1.80% -2.15% Oil
Cotton 0.10% -0.62% 0.72%
Compound Annualized Excess Return

Copper 6.17% 3.28% 2.89%

4%
Cattle 5.07% 1.97% 3.10% Live Cattle
Heating Oil 5.53% 0.93% 4.60%

Twelve Commodity Average -1.71% 0.46% -2.17%

2% Positive Roll Return Average
Negative Roll Return Average
4.22%
-4.67%
1.39%
-0.01%
2.83%
-4.66%

GSCI 4.49% 1.89% 2.59% Cotton

0%
Soybeans
-2%
Sugar Live Hogs
-4%
Wheat
Gold
-6% Corn
Coffee
-8%
Silver
-10%
-8% -6% -4% -2% 0% 2% 4% 6%
Compound Annualized Roll Return
 Figure 7
Consumer Price Index Composition, 2003

Other
Comm- Other goods Commodities
Food and
unication and services 22.3%
Education Beverages
3% 3.8%
2.8% 15.4%
Recreation
5.9%

Food
Commodities
Medical Care 14.4%
6.1%

Energy
Trans- Commodities
portation 3.5%
17% S ervices
Housing 59.9%
42.1%
Apparel
4.0%

Note:
Commodity Futures: Inflation Hedge?

• Inflation
• Unexpected Inflation
• Expected Inflation
• Change in Inflation
Figure 8
GSCI Excess Return and Unexpected Inflation
Annual Observations, 1969 to 2003

80%
Intermediate
GSCI S&P 500 Treasury

60% Geometric Average Excess Return When Inflation Rises 24.53% -3.60% -0.14%
Geometric Average Excess Return When Inflation Falls -8.36% 12.10% 4.42%
Geometric Average Excess Return 4.92% 4.88% 2.38%
40%
GSCI Excess Return

20%

0%

-20%

-40%
GSCI Excess Return = 0.083 + 6.50D Inflation Rate
2
R = 0.4322
-60%
-6% -4% -2% 0% 2% 4% 6%
Year-over-Year Change In Inflation Rate
Table 4
Commodity Excess Return And Change in Annual Inflation
Annual Observations, 1982 to 2003

Intercept Inflation Inflation D Inflation D Inflation Adjusted

Intercept T -Stat Coefficient T -Stat Coefficient T -Stat R Square

GSCI -5.27% -0.38 3.92 0.93 10.88 2.98 27.96%

Non-Energy -5.37% -0.64 1.84 0.71 3.94 1.77 5.95%

Energy -9.02% -0.36 7.50 0.97 18.80 2.81 24.54%
Livestock -11.90% -1.15 4.73 1.49 6.88 2.51 17.64%
Agriculture -7.60% -0.67 1.68 0.48 1.06 0.35 -9.64%
Industrial Metals 6.71% 0.26 1.20 0.15 17.44 2.59 26.73%
Precious Metals 20.93% 2.36 -8.02 -2.95 -2.78 -1.19 26.19%

Heating Oil -6.40% -0.26 6.07 0.81 17.76 2.73 23.89%

Cattle -7.07% -0.75 4.00 1.38 7.19 2.87 24.02%
Hog -20.39% -1.23 6.32 1.24 6.47 1.48 2.04%
Wheat -13.24% -0.87 3.09 0.67 -2.58 -0.64 -0.05%
Corn -23.02% -1.37 5.91 1.15 4.44 1.00 -2.57%
Soybeans 20.50% 1.17 -5.95 -1.11 -1.10 -0.24 -2.77%
Sugar 1.39% 0.06 -0.06 -0.01 3.56 0.61 -7.75%
Coffee 4.25% 0.11 -0.81 -0.07 0.24 0.02 -11.05%
Cotton 6.74% 0.31 -0.51 -0.08 0.30 0.05 -10.99%
Gold 19.16% 2.02 -7.50 -2.58 -2.38 -0.95 20.27%
Silver 24.83% 2.16 -10.18 -2.89 -4.45 -1.46 24.33%
Copper 7.15% 0.27 1.43 0.18 17.08 2.45 23.77%

EW T welve Commodities 1.16% 0.14 0.15 0.06 3.88 1.74 10.30%

Commodity Futures: Inflation Hedge?

• Variation across commodities

• Link to roll return
Figure 9
Unexpected Inflation Betas and Roll Returns Unexpected
Inflation Roll
December 1982 to December 2003 Beta Return
GSCI 10.88 2.52%
Non-Energy 3.94 -0.67%
Energy 18.80 5.19%
Livestock 6.88 1.46%
Agriculture 1.06 -3.64%
Industrial Metals 17.44 0.84%
Precious Metals -2.78 -4.64%

Heating Oil 17.76 4.20%

20 Live Cattle
Live Hogs
7.19
6.47
2.85%
-1.95%
Wheat -2.58 -5.89%
Copper Energy
Corn 4.44 -7.02%
Soybeans
Sugar
-1.10
3.56
-2.18%
-3.00% Industrial Heating
15 Coffee 0.24 -4.84%
Metals Oil
Cotton 0.30 1.05%
Gold -2.38 -4.97%
Silver -4.45 -5.61%
Unexpected Inflation Beta

Copper 17.08 2.74%

Twelve Commodity Average 3.88 -2.05% GSCI
10 Positive Roll Return Average
Negative Roll Return Average
10.58
0.53
2.71%
-4.43%

Live Hogs Live Cattle

Livestock
5 Sugar
Corn Non-Energy
Agriculture
Coffee Cotton
0
Gold Soybeans
Wheat
Precious Metals
-5 Silver

-10
-8% -6% -4% -2% 0% 2% 4% 6%
Compound Annualized Roll Return
Commodity Futures: What is the Risk?

Risk Factors
• Market
• Term
• Default
• SML
• HML
• Change in FX
Table 5
Unconditional Commodity Futures Betas
Monthly Observations, December 1982 to May 2004

S&P 500
Excess Term Default
Return Premium Premium SMB HML D Dollar

GSCI -0.05 -0.05 -0.25 0.07 -0.06 -0.57 **

Non-Energy 0.10 ** -0.11 -0.03 0.05 0.00 -0.05

Energy -0.14 -0.17 -0.07 0.04 -0.07 -1.05 **
Livestock 0.06 0.05 -0.23 0.05 0.04 0.09
Agriculture 0.09 -0.01 -0.12 0.06 -0.02 0.10
Industrial Metals 0.16 * -0.32 ** 1.18 *** 0.19 -0.05 -0.35
Precious Metals -0.08 -0.15 0.42 0.14 * -0.03 -0.83 **

Heating Oil -0.13 -0.22 -0.14 0.06 -0.16 -0.91 **

Cattle 0.07 0.01 -0.10 0.11 -0.01 0.21
Hogs 0.03 0.15 -0.45 -0.04 0.13 -0.08
Wheat 0.11 0.04 -0.42 0.19 * -0.12 -0.18
Corn 0.11 0.00 0.13 0.09 -0.01 0.55 *
Soybeans 0.04 -0.07 0.13 -0.02 0.08 -0.07
Sugar 0.05 -0.11 -0.43 * 0.16 -0.09 0.12
Coffee 0.13 -0.15 0.38 -0.25 * 0.16 -0.22
Cotton 0.18 -0.41 0.88 -0.08 0.03 0.46
Gold -0.15 ** -0.12 0.39 0.12 *** -0.04 -0.91 ***
Silver 0.08 -0.52 *** 1.16 *** 0.32 ** -0.02 -0.39
Copper 0.21 ** -0.31 * 1.15 *** 0.16 0.00 -0.42

Twelve Commodity Average 0.06 -0.14 ** 0.22 0.07 0.00 -0.15

Note: *, **, *** significant at the 10%, 5% and 1% levels.

Commodity Futures: Diversification Return

• Need to rebalance portfolio

• What is the return due to rebalancing?
Table 6
The mechanics of the diversification return

Equally Weighted
Heating Oil S&P 500 Portfolio
Excess Return Excess Return Excess Return
1994 19.96% -2.92% 8.52%
1995 7.73% 31.82% 19.78%
1996 67.37% 17.71% 42.54%
1997 -35.06% 28.11% -3.48%
1998 -50.51% 23.51% -13.50%
1999 73.92% 16.30% 45.11%
2000 66.71% -15.06% 25.82%
2001 -36.62% -15.97% -26.30%
2002 41.40% -23.80% 8.80%
2003 21.90% 27.62% 24.76%
Weighted Average
Portfolio Weight 50% 50%

Geometric Return 8.21% 6.76% 7.49% 10.95%

Variance 21.22% 4.44% 12.83% 5.34%
Beta (EW Portfolio) 1.79 0.21 1.00 1.00
Covariance 9.54% 1.14% 5.34% 5.34%

Diversification Return = EW Portfolio Return - Weighted Average Return = 10.95% - 7.49% = 3.46%

Approximate
Diversification Return = (Average Variance - Average Covariance)/2 = ( 12.83% - 5.34% ) /2 = 3.74%
 Figure 10
Commodity Futures Index Diversification Returns

4.5% 4.24%

4.0% 3.72%
Annualized Diversification Return

3.5%

3.0% 2.72% 2.80%

2.47%
2.5% 2.33%

2.0%

1.5% 1.20%

1.0%

0.5%

0.0%
Equally GSCI Above GSCI Below DJ AIG Chase Equally Equally
Weighted Median Median (1991-2001) Physical Weighted Weighted
GSCI Volatilty Volatilty Commodity CRB (1990- CRB (1990-
(1982-2004) (1970-1999) 2004) Monthly 2004)
Annually
Commodity Futures: Strategic Allocation

• Mean variance analysis

• What do you collateralize with?
Figure 11
Strategic Asset Allocation
December 1969 to May 2004
Sharpe Information
Composition Ratio Ratio
19% S&P 500 0% 0.37 -0.26 S&P 500 Collateralized
Intermediate Bond 59% 0.41 0.26
Commodity Futures
Cash Collateralized Commodity Future 0% 0.39 0.41
Bond Collateralized Commodity Futures 7% 0.50 0.47
17%
Compound Annualized Return

S&P 500 Collateralized Commodity Futures 34% 0.55 0.35 2

"Optimal" Portfolio 0.64 0.47

15% 60% Stocks/40% Bonds 0.44

Intermediate Bond Collateralized
Commodity Futures
13%
GSCI
(Cash Collateralized
11% Commodity Futures)
1 S&P 500

9% 60% S&P 500

40% Intermediate Treasury
Intermediate
Treasury
7%
5% 7% 9% 11% 13% 15% 17% 19% 21% 23% 25%
Annualized Standard Deviation of Return
 Asset Allocation Analysis Zephyr AllocationADVISOR: Trust Company of the West

Efficient Frontier
Return vs. Risk (Standard Deviation)
22

20

Stock CF

18

16
Bond CF
Return

14
GSCI

12 S&P 500

Current Portfolio
10

Bonds
8

6
0 5 10 15 20 25 30

Risk (Standard Deviation)

Asset Allocations - Current Portfolio Asset Allocations - Active Portfolio

Percent of Portfolio Percent of Portfolio

S&P 500 33.8% S&P 500

40.0%
Bonds Bonds
GSCI GSCI
60.0% Bond CF 58.9% Bond CF
Stock CF 7.3% Stock CF

Portfolio Return: 10.49% Portfolio Return: 12.54%

Portfolio Standard Deviation: 10.06% Portfolio Standard Deviation: 10.09%
Figure 11
Strategic Asset Allocation
December 1969 to May 2004

19% Mix 1 Mix 2

S&P 500 Collateralized
S&P 500 31% 0%
Commodity Futures
Intermediate Bond 27% 58%
17% Cash Collateralized Commodity Future 0% 0%
Compound Annualized Return

4
Bond Collateralized Commodity Futures 42% 33%
S&P 500 Collateralized Commodity Futures - 9%
15%
3
Intermediate Bond Collateralized
Commodity Futures
13% 2
GSCI
(Cash Collateralized Commodity Futures)
11%
1 S&P 500

9% 60% S&P 500

40% Intermediate Treasury
Intermediate
Treasury
7%
5% 7% 9% 11% 13% 15% 17% 19% 21% 23% 25%
Annualized Standard Deviation of Return
Table 7
Marginal Contribution To Portfolio Sharpe Ratio
Monthly Observations, December 1982 to May 2004

Stock Bond 60/40

Residual Information Residual Information Residual Information
Alpha Risk Ratio Alpha Risk Ratio Alpha Risk Ratio

GSCI 6.19% 16.99% 0.36 6.04% 17.00% 0.36 6.30% 16.99% 0.37

Non-Energy -0.49% 9.77% -0.05 0.60% 9.88% 0.06 -0.56% 9.79% -0.06
Energy 12.67% 31.22% 0.41 12.21% 31.28% 0.39 12.99% 31.21% 0.42
Livestock 2.93% 14.50% 0.20 3.10% 14.52% 0.21 2.77% 14.50% 0.19
Agriculture -2.87% 14.32% -0.20 -1.68% 14.36% -0.12 -2.89% 14.34% -0.20
Industrial Metals 5.08% 22.74% 0.22 8.70% 22.60% 0.39 5.35% 22.81% 0.23
Precious Metals -3.77% 14.86% -0.25 -3.87% 14.88% -0.26 -3.54% 14.84% -0.24

Heating Oil 11.64% 32.54% 0.36 11.70% 32.56% 0.36 12.06% 32.53% 0.37
Live Cattle 5.32% 13.96% 0.38 5.98% 14.01% 0.43 5.23% 13.97% 0.37
Live Hogs -0.05% 24.25% 0.00 -1.22% 24.16% -0.05 -0.36% 24.24% -0.01
Wheat -4.20% 21.03% -0.20 -3.72% 21.08% -0.18 -4.42% 21.02% -0.21
Corn -4.21% 22.63% -0.19 -2.61% 22.66% -0.12 -4.19% 22.65% -0.19
Soybeans 1.60% 21.53% 0.07 2.99% 21.47% 0.14 1.78% 21.53% 0.08
Sugar 3.25% 38.72% 0.08 4.97% 38.68% 0.13 3.45% 38.73% 0.09
Coffee -0.69% 39.67% -0.02 4.91% 39.28% 0.12 -0.08% 39.75% 0.00
Cotton 1.46% 22.59% 0.06 3.88% 22.59% 0.17 1.55% 22.62% 0.07
Gold -3.57% 14.21% -0.25 -4.48% 14.38% -0.31 -3.32% 14.21% -0.23
Silver -5.97% 25.05% -0.24 -2.71% 24.77% -0.11 -5.54% 25.08% -0.22
Copper 7.35% 25.53% 0.29 11.25% 25.54% 0.44 7.52% 25.62% 0.29

"Optimal" 0.75 0.86 0.75

Figure 12
One-Year Moving Average GSCI Excess and Roll Returns
December 1969 to May 2004

80% Excess Return Roll Return

60%
One-Year Moving Average Return

40%

20%

0%

-20%

-40%
70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 00 02 04
19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 20 20 20
Figure 13 Excess Return Excess Return

Long-Term Excess Return Persistence

December 1982 to October 1993 to
September 1993 May 2004
GSCI 5.20% 3.77%
December 1982 to May 2004
Non-Energy 3.45% -3.59%
Energy 6.43% 7.70%
Livestock 9.57% -4.26%
Agriculture -1.86% -4.40%
Industrial Metals 5.99% 2.04%
Precious Metals -9.05% -1.61%

Heating Oil 4.55% 6.53%

Live Cattle 11.00% -0.59%
Live Hogs 7.25% -11.88%
Wheat -0.13% -10.41%
Corn -4.47% -6.78%
10% Soybeans -3.73% 3.17%
Sugar -8.35% 2.45%
Coffee -10.70% -1.77%
Cotton
Gold
6.80%
-8.45%
-6.23%
-2.82%
Heating Energy
Compound Annualized Excess Return

Silver -15.79% 0.00

Copper 6.12% 6.22% Oil Copper
5% Correlation 0.03
GSCI
October 1993 to May 2004

Soybeans
Silver Sugar
Industrial Metals
0%
Live Cattle
Coffee Precious Metals

Gold Livestock
-5% Non-Energy
Agriculture

Corn Cotton

-10%
Wheat
Live Hogs

-15%
-20% -15% -10% -5% 0% 5% 10% 15%
Compound Annualized Excess Return
December 1982 to September 1993
Commodity Futures: Tactical Allocation

• Figure 14 shows the pay-off to a strategy of going long

the GSCI for one month if the previous one year excess
return has been positive or going long the GSCI if the
previous one year excess return has been negative.
• This result is stable over time.
• While the momentum effect is strongest in the first 13
years of the sample, the effect is robust in the more
recent period.
Figure 14
GSCI Momentum Returns
December 1982 to May 2004

Trailing Annual Excess Return > 0 Trailing Annual Excess Return < 0

20% 17.49%

15% 13.47%
11.34%
Compound Annualized Excess Return

10%

5%

0%

-5%
-4.07%
-5.49%
-10%
-9.89%
-15%
12/69 to 5/04 12/69 to 12/82 12/82 to 5/04
Commodity Futures: Tactical Allocation

• Table 8 illustrates the pay-off to an investment strategy

that invests 100% of portfolio assets in one of four
strategies: cash, bonds, cash collateralized commodity
futures or bond collateralized commodity futures.
• The decision rule is to invest in the strategy that has the
highest previous twelve month return.
Table 8
Momentum strategies based on: GSCI, bonds, cash, and equity
December 1969- May 2004

A. Cash, Bonds, GSCI B. Cash, bonds, stocks, GSCI

Compound Annualized Compound Annualized
Annualized Standard Sharpe Annualized Standard Sharpe
Return Deviation Ratio Return Deviation Ratio
Momentum Portfolio 17.32% 16.01% 0.70 20.55% 20.04% 0.72

Asset class returns

Cash + GSCI 12.16% 18.55% 0.32 12.16% 18.55% 0.32
Bond + GSCI 14.43% 19.19% 0.43 14.43% 19.19% 0.43
Stocks + GSCI 17.74% 23.83% 0.48
Cash 6.19% 0.83% 0.00 6.19% 0.83% 0.00
Bond 8.31% 5.81% 0.36 8.31% 5.81% 0.36
S&P 500 11.42% 15.51% 0.34
Trading strategy is to invest in the asset class with the highest previous 12-month return. In panel A, we consider
Cash collateralized GSCI, bond collateralized GSCI, bonds, and cash. In panel B, we add stock collateralized
GSCI and stocks.
Commodity Futures: Tactical Allocation

• Figure 15 examines the pay-off to investing in an

equally-weighted portfolio of the four commodity
futures with the highest prior twelve month returns, a
portfolio of the worst performing commodity futures,
and a long/short portfolio fashioned from these two
portfolios.
 Figure 15
Individual Commodity Momentum Portfolios
December 1982 to May 2004

Worst Four Commodities Equally Weighted Average

Best Four Commodities Long/Short

$12
Compound Annualized
Annualized Standard Sharpe
$10 Excess Return Deviation Ratio
Worst Four -3.42% 16.00% -0.21
Equally Weighted Average 0.80% 9.97% 0.08
$8 Best Four 7.02% 15.77% 0.45
Growth of $1

Long/Short 10.81% 19.63% 0.55

GSCI 4.39% 17.27% 0.25
$6

$4

$2

$0
83 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 000 001 002 003 004
19 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2

Trading strategy sorts each month the 12 categories of GSCI based on previous 12-month return. We then track the four
GSCI components with the highest (‘best four’) and lowest (‘worst four’) previous returns. The portfolios are rebalanced
monthly.
Commodity Futures: Tactical Allocation

• We now consider a variation of the strategy that uses

the sign of the previous 12-month’s return. We create
an “insurance providing” proxy portfolio by buying
commodities that have had a positive return over the
past 12 months and selling those that have had a
negative return.
• We use the insurance term because going long a
backwardated commodity provides price insurance as
does going short a contangoed commodity. It is
possible that in a particular month that all past returns
are positive or negative.
 Figure 16
Individual Commodity Momentum Portfolio Based on the Sign of the Previous Return
December 1982 to May 2004

"Providing Insurance" Equally Weighted Average GSCI

$4.5
Compound Annualized
Annualized Standard Sharpe
$4.0
Excess Return Deviation Ratio

$3.5 Providing Insurance 6.54% 7.65% 0.85

Equally Weighted Portfolio 0.80% 9.97% 0.08
$3.0 GSCI 4.39% 17.27% 0.25
Growth of $1

$2.5

$2.0

$1.5

$1.0

$0.5

$0.0

Trading strategy is an equally weighted portfolio of twelve components of the GSCI. The portfolio is rebalanced monthly.
The ‘Providing Insurance’ portfolio goes long those components that have had positive returns over the previous 12 months
and short those components that had negative returns over the previous period.
Commodity Futures: Tactical Allocation

• When the price of the nearby GSCI futures contract is

greater than the price of the next nearby futures
contract (when the GSCI is backwardated), we expect
that the long only excess return should, on average, be
positive.
• Table 9 uses the information in the term structure.
Table 9
Using the Information in the GSCI Term Structure for a Tactical Strategy
July 1992 to May 2004

Compound
Annualized Annualized Sharpe
Excess Standard
Return Deviation Ratio
GSCI Backwardated 11.25% 18.71% 0.60
GSCI Contangoed -5.01% 17.57% -0.29
Long if Backwardated, Short if Contangoed 8.18% 18.12% 0.45
Cash Collateralized GSCI 2.68% 18.23% 0.15
 Figure 17
Individual Commodity Term Structure Portfolio
December 1982 to May 2004

"Long/Short" Equally Weighted Average GSCI

$3.0

$2.5

$2.0
Growth of $1

$1.5

Compound Annualized
$1.0 Annualized Standard Sharpe
Excess Return Deviation Ratio
Long/Short 3.65% 7.79% 0.47
$0.5
Equally Weighted Portfolio 1.01% 10.05% 0.10
GSCI 4.49% 16.97% 0.26
$0.0

Trading strategy is an equally weighted portfolio of twelve components of the GSCI. The portfolio is rebalanced monthly.
The ‘Long/Short’ portfolio goes long those six components that each month have the highest ratio of nearby future price to
next nearby futures price, and the short portfolio goes short those six components that each month have the lowest ratio of
nearby futures price to next nearby futures price.
Commodity Futures: Conclusion

• Myths and Reality

Figure 11
Strategic Asset Allocation
December 1969 to May 2004

19% Mix 1 Mix 2

S&P 500 Collateralized
S&P 500 31% 0%
Commodity Futures
Intermediate Bond 27% 58%
17% Cash Collateralized Commodity Future 0% 0%
Compound Annualized Return

4
Bond Collateralized Commodity Futures 42% 33%
S&P 500 Collateralized Commodity Futures - 9%
15%
3
Intermediate Bond Collateralized
Commodity Futures
13% 2
GSCI
(Cash Collateralized Commodity Futures)
11%
1 S&P 500

9% 60% S&P 500

40% Intermediate Treasury
Intermediate
Treasury
7%
5% 7% 9% 11% 13% 15% 17% 19% 21% 23% 25%
Annualized Standard Deviation of Return
Table XXXXXX
Liability Betas and Hedging Credits
February 1997 to May 2004

Liability Betas Liability Hedging Credit

Active Active
Retired Active Future Future Retired Active Future Future
Lives Accrued Accruals Lives Lives Accrued Accruals Lives

Nominal Bonds 100% 50% 30% 10% 100.00% 50.00% 30.00% 10.00%
TIPs 50% 60% 70% 50.00% 60.00% 70.00%
Domestic Equities 5% 10% 5.00% 10.00%
Foreign Equities 5% 10% 5.00% 10.00%

GSCI 0.08 0.46 0.75 0.94 0.10% 0.33% 0.39% 0.45%

Non-Energy 0.06 0.16 0.34 0.50 0.08% 0.11% 0.18% 0.24%

Energy 0.00 0.54 0.91 1.16 0.00% 0.39% 0.47% 0.56%
Livestock 0.06 0.12 0.10 0.03 0.08% 0.09% 0.05% 0.02%
Agriculture 0.09 0.22 0.41 0.55 0.11% 0.16% 0.21% 0.27%
Industrial Metals -0.16 -0.22 0.20 0.75 -0.21% -0.16% 0.10% 0.36%
Precious Metals 0.30 0.56 0.79 0.87 0.39% 0.40% 0.41% 0.42%

Heating Oil 0.11 0.56 0.93 1.17 0.14% 0.40% 0.48% 0.57%
Live Cattle -0.06 -0.07 -0.09 -0.08 -0.07% -0.05% -0.05% -0.04%
Live Hogs 0.34 0.58 0.49 0.21 0.44% 0.41% 0.26% 0.10%
Wheat 0.04 0.24 0.45 0.62 0.05% 0.17% 0.23% 0.30%
Corn 0.16 0.44 0.70 0.85 0.21% 0.31% 0.36% 0.41%
Soybeans 0.57 0.82 1.15 1.26 0.74% 0.59% 0.60% 0.61%
Sugar -0.02 -0.20 -0.13 0.01 -0.02% -0.14% -0.07% 0.01%
Coffee -0.91 -1.30 -0.94 -0.09 -1.18% -0.93% -0.49% -0.04%
Cotton -0.17 -0.30 -0.19 0.05 -0.22% -0.22% -0.10% 0.02%
Gold 0.35 0.63 0.81 0.82 0.46% 0.45% 0.42% 0.40%
Silver -0.03 0.11 0.55 1.01 -0.04% 0.08% 0.28% 0.49%
Copper -0.29 -0.30 0.25 0.98 -0.38% -0.21% 0.13% 0.47%

Average 0.01 0.10 0.33 0.57 0.01% 0.07% 0.17% 0.27%

 Figure 4
Average Cross Correlations of Index Components
December 1993 to May 2004

1.0

0.9 0.88

0.8
0.74 0.73
0.69
0.7
Average correlation

0.6 0.56

0.5

0.4

0.3
0.24

0.2 0.16

0.1

0.0
Lehman Aggregate MSCI World Wilshire MSCI World MSCI World Equity CSFB/T remont GSCI
Components Currency Hedged Large/Mid/Small Unhedged Fixed Hedge Fund Index
Fixed Income Value/Growth Income
Table 4 Oct 25 2004 Revised
Commodity Excess Return and Change in Annual Inflation Non-overlapping
Annual Observations, 1982 to 2003 Bls dec-to-dec cpi

Intercept Inflation Inflation D Inflation D Inflation Adjusted

Intercept T -Stat Coefficient T -Stat Coefficient T -Stat R Square

GSCI -5.27% -0.38 3.92 0.93 10.88 2.98 27.96%

Non-Energy -5.37% -0.64 1.84 0.71 3.94 1.77 5.95%

Energy -9.02% -0.36 7.50 0.97 18.80 2.81 24.54%
Livestock -11.90% -1.15 4.73 1.49 6.88 2.51 17.64%
Agriculture -7.60% -0.67 1.68 0.48 1.06 0.35 -9.64%
Industrial Metals 6.71% 0.26 1.20 0.15 17.44 2.59 26.73%
Percious Metals 20.93% 2.36 -8.02 -2.95 -2.78 -1.19 26.19%

Heating Oil -6.40% -0.26 6.07 0.81 17.76 2.73 23.89%

Cattle -7.07% -0.75 4.00 1.38 7.19 2.87 24.02%
Hog -20.39% -1.23 6.32 1.24 6.47 1.48 2.04%
Wheat -13.24% -0.87 3.09 0.67 -2.58 -0.64 -0.05%
Corn -23.02% -1.37 5.91 1.15 4.44 1.00 -2.57%
Soybeans 20.50% 1.17 -5.95 -1.11 -1.10 -0.24 -2.77%
Sugar 1.39% 0.06 -0.06 -0.01 3.56 0.61 -7.75%
Coffee 4.25% 0.11 -0.81 -0.07 0.24 0.02 -11.05%
Cotton 6.74% 0.31 -0.51 -0.08 0.30 0.05 -10.99%
Gold 19.16% 2.02 -7.50 -2.58 -2.38 -0.95 20.27%
Silver 24.83% 2.16 -10.18 -2.89 -4.45 -1.46 24.33%
Copper 7.15% 0.27 1.43 0.18 17.08 2.45 23.77%

EW T welve Commodities 1.16% 0.14 0.15 0.06 3.88 1.74 10.30%

 Table X [No longer used]
Sensitivity to Inflation Linked Bond Returns
Monthly Excess Returns
February 1997 to May 2004
Annualized Intercept TIPs TIPs Adjusted
Intercept T-Stat Coefficient T-Stat R Square

GSC I 1.36% 0.17 1.03 2.40 5.25%

Non-Energy -8.18% -2.19 0.27 1.34 0.90%

Energy 9.20% 0.73 1.41 2.06 3.65%
Livestock -4.53% -0.78 0.17 0.54 -0.83%
Agriculture -12.49% -2.27 0.36 1.21 0.54%
Industrial M etals -0.38% -0.06 -0.18 -0.54 -0.84%
Precious M etals -2.80% -0.54 0.75 2.68 6.68%

Heating Oil 7.34% 0.54 1.21 1.66 2.01%

Natural Gas -2.93% -0.13 3.21 2.64 6.50%
C rude Oil 12.36% 0.93 1.43 2.00 3.36%
Unleaded Gas 20.15% 1.44 0.67 0.89 -0.23%
Live Cattle 1.03% 0.18 -0.06 -0.18 -1.14%
Live Hogs -14.51% -1.34 0.71 1.22 0.56%
Wheat -18.54% -2.12 0.52 1.11 0.27%
Corn -15.74% -1.99 0.76 1.79 2.49%
Soybeans 2.04% 0.23 0.80 1.64 1.91%
Sugar 4.07% 0.32 -0.47 -0.69 -0.61%
Coffee -6.14% -0.41 -1.26 -1.57 1.67%
Cocoa -0.42% -0.03 0.26 0.37 -1.01%
Cotton -12.25% -1.22 -0.40 -0.73 -0.54%
Copper 1.19% 0.14 -0.08 -0.19 -1.14%
Aluminum -1.53% -0.27 -0.30 -0.99 -0.03%
Nickel 10.74% 0.86 -0.06 -0.08 -1.17%
Zinc -3.42% -0.48 -0.40 -1.05 0.12%
Lead -0.32% -0.04 0.19 0.40 -0.98%
Gold -4.30% -0.82 0.82 2.88 7.82%
Platinum 16.17% 2.19 0.37 0.93 -0.16%
Silver 0.41% 0.04 0.37 0.72 -0.56%

Individual Commodity Average -0.22% -0.09 0.40 0.61 0.91%

S&P 500 Index 6.37% 0.97 -0.58 -1.65 1.96%
Lehman US Aggregate Bond Index 1.02% 1.08 0.54 10.65 56.65%
CSFB/Tremont Hedge Fund Index 5.85% 1.92 -0.02 -0.14 -1.15%
Citigroup Inflation-Linked Securities 0.00% - 1.00 - 100.00%
 Figure XX[No longer used]
The Economist Industrial Commodity Price Index

Nominal Return 0.79%

Inflation 2.11%

10 Real Return -1.30%

1.00
Nominal Price Correlation With Inflation Correlation Beta Alpha
One Year Time Horizon 48.33% 1.27 -1.50%
Five Year Time Horizon 60.98% 1.08 -1.13%
Ten Year Time Horizon 78.64% 1.10 -1.35%
0.80

Rolling Ten Year Correlation

0.60
Nominal/Real Price Index

Nominal Price-Inflation
0.40

1 0.20

0.00

-0.20

-0.40

0 -0.60

8 62 869 876 883 890 897 904 911 918 925 932 939 946 953 960 967 974 981 988 995
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Nominal Price Index Real Price Index Rolling Correlation

Cashin, P. and McDermott, C.J. (2002), 'The Long-Run Behavior of Commodity Prices: Small Trends and Big Variability', IMF Staff Papers 49, 175-99.