Chapter 13 of 22 · Unit 5 · Real assets and currencies · 14 min read
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The overview article placed commodities and gold among the eleven asset classes and gave each a short paragraph. This chapter goes one step down. We start with what moves the price of a barrel of oil or a bushel of wheat, then look at how investors hold these things (almost always through futures contracts), and why the futures route can earn a very different return from the price you see on the news. Gold gets its own thread, since it behaves less like a raw material and more like a currency with no central bank. We end with three episodes worked through with the math.
For every reader: the idea in plain words, no formulas.
A commodity is a raw material that is the same whichever producer sells it: crude oil of a given grade, copper, wheat, natural gas, cattle. Because one barrel is as good as another, these goods trade on exchanges with standard terms.
Few investors want a tank of oil in the garage. So they buy a futures contract instead, a promise to buy the commodity at a set price on a set date. Before that date arrives, the fund sells the contract and buys the next one out. Commodity index funds and most commodity ETFs work this way. Their return depends on three things: how the price moves, what it costs to swap the old contract for the new one, and the interest earned on the cash they hold while they wait.
Supply and demand set the price, as in any market, yet in commodities both sides react slowly. A new copper mine takes years to open. A drought cuts this year's wheat crop and nothing can replace it until the next harvest. On the demand side, people keep driving to work when petrol costs more, at least for a while.
When neither side can adjust fast, a small shortfall needs a large price change to clear the market. That is why oil can double or halve within a year. The forces that push supply and demand around are familiar:
Gold sits apart. Nearly all the gold ever mined still exists in vaults and jewellery, so a year's mine output adds only a small fraction to the stock. A shortage of new gold moves the price very little. What moves it is how much people want to hold the metal they already have.
Gold pays no interest and no dividend. Holding it means giving up what a bond or a bank deposit would pay. When safe assets pay a good return after inflation, that sacrifice is large and gold tends to lose favour. When they pay little or nothing after inflation, holding gold costs little, and the price tends to rise. Fear helps too: in a crisis, people buy the one asset that is nobody's debt.
| Months out | Contango ($) | Backwardation ($) |
|---|---|---|
| 0 | 80 | 80 |
| 3 | 83 | 77.3 |
| 6 | 86 | 74.6 |
| 9 | 89 | 71.9 |
| 12 | 92 | 69.2 |
Source: computed: illustrative curves: +$1.00 and −$0.90 a month from $80, as of 2026-10-28.
For readers who want the mechanism, with the diagrams.
Beginner path stops here
The spot price is what a buyer pays for delivery now. A futures price is what a buyer agrees today to pay for delivery on a later date. Spot and futures are linked, since a trader can buy now and store the good, or agree now to buy it later. If the futures price were far above spot plus the cost of storing and financing, traders would buy spot, store it and sell futures. That trade pins the futures price to spot plus the cost of carry.
Each futures contract has an expiry month. A list of prices for the coming months, plotted against the delivery date, is the futures curve. The curve tells you what the market will pay today to lock in a price for each future month. It is a price for delivery, and the market sets it with storage costs, interest and the benefits of holding the physical good all in mind.
When later months cost more than near ones, the curve slopes upward and traders call it contango. Contango is normal when inventories are high: storage is plentiful, nobody needs the barrel urgently, and the futures price covers the cost of keeping it until delivery.
When later months cost less than near ones, the curve slopes downward: backwardation. This happens when inventories are tight. Refiners and manufacturers will pay up for a barrel today because running short would halt a plant. The extra value of having the good on hand now is the convenience yield.
The slope of the curve carries information. A steep contango says the world has more oil than it needs right now. A deep backwardation says the opposite.
A fund that holds futures has to sell each contract before it expires and buy the next one. That swap is the roll. In contango, the fund sells the cheaper expiring contract and buys a dearer one, so each roll leaves it with fewer barrels for the same money. If spot prices stay flat, the fund loses a little every month. In backwardation the roll works the other way: the fund sells high and buys low, and gains barrels.
The gain or loss from rolling is the roll yield. Over long periods it has been one of the largest parts of a commodity fund's return, and it explains why an oil fund can fall in a year when the spot price of oil ends where it started.
| Roll | Barrels, contango | Barrels, backwardation |
|---|---|---|
| 0 | 1,000 | 1,000 |
| 1 | 987.7 | 1,012.7 |
| 2 | 975.5 | 1,025.5 |
| 3 | 963.4 | 1,038.5 |
| 4 | 951.5 | 1,051.6 |
| 5 | 939.8 | 1,064.9 |
| 6 | 928.2 | 1,078.4 |
| 7 | 916.7 | 1,092 |
| 8 | 905.4 | 1,105.9 |
| 9 | 894.2 | 1,119.9 |
| 10 | 883.2 | 1,134 |
| 11 | 872.3 | 1,148.4 |
| 12 | 861.5 | 1,162.9 |
Source: computed: barrels x 80 / 81 (or 80 / 79) at each monthly roll, spot flat at $80, as of 2026-10-28.
Three things decide how far futures sit above or below spot:
When interest plus storage exceeds the convenience yield, the market is in contango. When the convenience yield is larger, it is in backwardation. Gold, which costs little to store and never runs scarce in the vault, almost always trades in a mild contango that reflects interest rates. Crude oil swings between the two states.
| Case | Spot ($) | Futures ($) |
|---|---|---|
| Gold, one year | 2000 | 2,092.06 |
| Oil, six months | 80 | 78.42 |
Source: computed: F = S x e^((r + u - y) T); gold r 4 %, u 0.5 %, y 0, T 1; oil r 4 %, u 2 %, y 10 %, T 0.5, as of 2026-10-28.
A fully collateralised futures fund holds the futures and keeps the full value of the position in Treasury bills. Its return splits into three parts:
| Part | What it is | Can it be negative? |
|---|---|---|
| Spot return | the change in the price of the physical good | yes |
| Roll yield | the gain or loss from swapping expiring contracts for later ones | yes, in contango |
| Collateral yield | the interest on the Treasury bills behind the position | only if bill rates turn negative |
Say spot prices rise 3 % in a year, the roll costs 5 % and bills pay 4 %. The fund's return is about +2.0 %, far less than the 3 % spot gain plus 4 % interest a casual reader might expect. Gary Gorton and Geert Rouwenhorst found that a collateralised basket earned returns similar to stocks from 1959 to 2004, as the overview article reports. Much of that came from roll and collateral yield in periods of backwardation and high bill rates. When contango became common in the 2000s and 2010s, the same funds did much worse.
A broad commodity index mixes groups that respond to different news, which is why their prices often diverge.
Energy. Crude oil trades worldwide and responds to OPEC decisions, inventories, refinery demand and wars in producing regions. Natural gas is more local, because moving it across oceans needs liquefaction plants and special ships, so a cold winter in Europe or a hot summer in Texas can move one region's price without touching another's.
Industrial metals. Copper, aluminium, nickel and zinc follow factory output and construction, and China has been the largest buyer of most of them for two decades. Traders sometimes call copper the metal with a doctorate in economics because its price tracks world industry so closely. Supply responds slowly, since a new mine takes a decade from discovery to output.
Agriculture. Wheat, corn and soybeans move with weather and the harvest calendar, and supply resets once a year. Government policy matters too: biofuel mandates tie corn and sugar to energy prices, and export bans by large producers can lift world prices overnight. Prices also carry a seasonal pattern, highest before a harvest and lowest after it.
Livestock. Cattle and hog prices depend on feed costs (mostly corn), herd cycles that take years to turn, and disease outbreaks that close export markets.
Precious metals. Silver and platinum have large industrial uses and behave partly like industrial metals. Gold behaves mostly like a monetary asset, as the next sections explain.
| Driver | How it moves prices | An episode |
|---|---|---|
| World demand | growth raises use of energy and metals | metal prices through China's 2000s building boom |
| Supply shock | a sudden cut, with slow responses on both sides | the 1973 embargo |
| Producer policy | output targets change supply on purpose | OPEC's no-cut decision of 27 November 2014 |
| Inventories and storage | full tanks push near prices down and steepen contango | April 2020, WTI below zero |
| The dollar | a weaker dollar raises dollar prices | commodity strength in the weak-dollar years of the 2000s |
| Interest rates | higher rates raise carrying costs and lower inventory demand | the early 1980s slump in many prices |
| Roll and curve shape | contango drains a futures fund month after month | oil funds in 2009 and 2020 |
The real yield on a ten-year Treasury inflation-protected bond (TIPS) is the return a holder earns after inflation. FRED publishes it daily as series DFII10. Because gold pays nothing, the real yield is what an investor gives up by holding gold instead of TIPS. Through the 2000s and 2010s the two moved in opposite directions most of the time: gold rose as real yields fell toward and below zero, and fell when they climbed.
The link is a tendency, and it has broken for long stretches. Central bank buying, sanctions risk and demand from Asian households have all moved gold in ways real yields cannot explain, as we show in Level 4.
| Month | Gold ($/oz) | 10-year real yield (%) |
|---|---|---|
| 2003-12 | 406.95 | 1.98 |
| 2004-12 | 442.08 | 1.67 |
| 2005-12 | 510.1 | 2.12 |
| 2006-12 | 629.79 | 2.25 |
| 2007-12 | 803.2 | 1.79 |
| 2008-12 | 816.09 | 2.17 |
| 2009-12 | 1,134.72 | 1.36 |
| 2010-12 | 1,390.55 | 1.04 |
| 2011-12 | 1,639.97 | -0.03 |
| 2012-12 | 1,684.76 | -0.76 |
| 2013-12 | 1,221.51 | 0.74 |
| 2014-12 | 1,200.62 | 0.51 |
| 2015-12 | 1,075.74 | 0.73 |
| 2016-12 | 1,157.36 | 0.56 |
| 2017-12 | 1,264.45 | 0.5 |
| 2018-12 | 1,250.4 | 1.02 |
| 2019-12 | 1,479.13 | 0.14 |
| 2020-12 | 1,858.42 | -0.98 |
| 2021-12 | 1,790.43 | -0.99 |
| 2022-12 | 1,797.55 | 1.36 |
| 2023-12 | 2,026.18 | 1.84 |
| 2024-12 | 2,648.01 | 2.09 |
Source: World Bank Commodity Price Data (the Pink Sheet), monthly gold price, US dollars per troy ounce; Federal Reserve Bank of St. Louis, FRED, series DFII10 (10-year TIPS yield (real), percent; monthly mean of daily values), as of 2024-12, 2026-10-26.
Monthly gold averages from the World Bank; monthly means of the daily real yield; the table shows each December and the last month both series cover.
For Series 65 and CFA readers: formulas and worked examples.
Series 65 path stops here
With continuous compounding, a risk-free rate , a storage cost and a convenience yield , all as yearly rates, the futures price for delivery in years is:
In words, the futures price equals the spot price grown at the interest rate plus the storage cost, less the benefit of holding the good, over the time to delivery.
If the exponent is positive and the curve is in contango. If it is negative and the curve is in backwardation.
Worked example Gold one year out
Take gold at $2,000 an ounce, a 4 % interest rate and storage and insurance of 0.5 % a year. Gold is never scarce in the vault, so we set the convenience yield to zero. The one-year futures price comes to $2,092.06, which is $92.06 of carry above spot. A trader who sees the futures quoted higher than that can buy gold, store it and sell the futures for a riskless profit; one who sees it lower can do the reverse.
Worked example Oil in a tight market
Take crude at $80, a 4 % interest rate, 2 % storage and a 10 % convenience yield, because refiners are short of barrels. The exponent is −4.0 % a year, and the six-month futures price comes to $78.42, below spot. The curve is in backwardation.
The same formula run backwards gives the convenience yield the market is paying. Solving for :
In words, the convenience yield equals the carrying costs minus the yearly log gap between the futures and spot prices.
Worked example Backing out the convenience yield
Spot crude is $80 and the six-month futures trades at $76, with interest at 4 % and storage at 2 %. The implied convenience yield is 16.3 % a year. A number that high says inventories are very short.
A fund holds the front-month contract at $80 and must roll into the next month at $81. If the spot price does not move, each $80 of old contract buys only 80/81 of a new one. The monthly roll yield is:
In words, the roll yield is the gap between the expiring price and the next contract's price, as a share of the expiring price.
Worked example Rolling at 80 and 81
The roll costs −1.25 % each month. If the curve keeps that slope all year and spot stays flat, twelve rolls compound to about −14.0 %. A spot price that ends the year unchanged still leaves the fund down by about that much before collateral interest.
When the curve is in backwardation, the same arithmetic gives a positive number, and a fund can earn money in a year when spot falls.
Write for the price elasticity of demand (as a positive number) and for the elasticity of supply. If a shock removes a share of supply, the price has to rise until demand falls and other supply rises enough to fill the hole:
In words, the percent price change needed to clear a supply loss is the size of the loss divided by how strongly buyers and sellers respond to price.
Worked example A two percent supply cut
Take a 2 % cut in world oil supply. If demand and supply together respond with a short-run elasticity of 0.1, the price must rise by about 20 %. If the combined elasticity were 0.2, the rise would be about 10 %. We use these elasticities as round illustrations; Chapter 5 discusses the estimates.
The same division explains the crash side. When demand falls by a few percent in a recession and producers keep pumping, the price falls by many times that.
If a ten-year TIPS pays a real yield , the extra purchasing power a TIPS holder ends with, compared with a gold holder whose metal merely keeps pace with inflation, is:
In words, the gap equals one plus the real yield compounded over the holding period, minus one.
Worked example A 1.5 % real yield over ten years
At a 1.5 % real yield, a TIPS holder ends ten years with 16.1 % more purchasing power than a gold holder whose metal only matched inflation. For gold to keep up, its real price must rise by that much. At a real yield of zero, the gap disappears, which is why gold did well when real yields went negative.
For readers who want past episodes run through the Level 3 math.
2008 Oil above $145, then near $30
West Texas Intermediate crude rose above $145 a barrel in July 2008 and fell to about $30 by late December 2008 (EIA, FRED series DCOILWTICO). The rise came on years of strong demand from emerging economies with little spare capacity; the fall came as the financial crisis cut demand.
Run the elasticity arithmetic from Level 3 on the fall. World oil demand fell by a few percent between mid-2008 and early 2009. With a short-run combined elasticity near 0.1, a demand drop of that size calls for a price fall of tens of percent, and the market delivered a fall of −79.3 % from $145 to $30. The scale of the move fits a market where neither side can adjust quickly.
The Bloomberg Commodity index lost about 36 % in 2008, as the overview article reports. Diversification across metals, grains and energy did not help in a year when one force, collapsing world demand, hit them all.
| Month | Average ($) | Lowest daily close ($) |
|---|---|---|
| 1986-12 | 15.93 | 14.93 |
| 1987-12 | 17.09 | 15.12 |
| 1988-12 | 16.38 | 15.36 |
| 1989-12 | 21.06 | 20.22 |
| 1990-12 | 27.28 | 25.3 |
| 1991-12 | 19.48 | 18.28 |
| 1992-12 | 19.41 | 18.69 |
| 1993-12 | 14.57 | 14.09 |
| 1994-12 | 17.13 | 16.6 |
| 1995-12 | 19.02 | 18.43 |
| 1996-12 | 25.27 | 23.4 |
| 1997-12 | 18.33 | 17.6 |
| 1998-12 | 11.34 | 10.82 |
| 1999-12 | 26.12 | 25.01 |
| 2000-12 | 28.64 | 25.82 |
| 2001-12 | 19.45 | 18.04 |
| 2002-12 | 29.52 | 26.8 |
| 2003-12 | 32.2 | 30.61 |
| 2004-12 | 43.15 | 40.71 |
| 2005-12 | 59.37 | 57.31 |
| 2006-12 | 61.96 | 60.31 |
| 2007-12 | 91.69 | 87.45 |
| 2008-07 | 133.37 | 122.21 |
| 2008-12 | 41.12 | 30.28 |
| 2009-12 | 74.47 | 69.48 |
| 2010-12 | 89.15 | 86.75 |
| 2011-12 | 98.56 | 93.55 |
| 2012-12 | 87.86 | 85.14 |
| 2013-12 | 97.59 | 93.61 |
| 2014-12 | 59.07 | 53.45 |
| 2015-12 | 37.19 | 34.55 |
| 2016-12 | 51.97 | 49.85 |
| 2017-12 | 57.88 | 55.79 |
| 2018-12 | 49.52 | 44.48 |
| 2019-12 | 59.82 | 55.97 |
| 2020-04 | 16.55 | -36.98 |
| 2020-12 | 47.02 | 44.54 |
| 2021-12 | 71.71 | 65.44 |
| 2022-12 | 76.44 | 71.05 |
| 2023-12 | 71.9 | 68.27 |
| 2024-12 | 70.12 | 68.35 |
| 2025-12 | 57.97 | 55.44 |
Source: Federal Reserve Bank of St. Louis, FRED, series DCOILWTICO (WTI crude oil, Cushing, dollars a barrel; monthly mean of daily values, with the month's lowest daily value), as of 2026-10-27.
2020 WTI settles at minus $37.63
On 20 April 2020 the May 2020 WTI futures contract settled at −$37.63 a barrel on CME's NYMEX, the day before it expired. Lockdowns had cut fuel demand so fast that storage at Cushing, Oklahoma, the contract's delivery point, was close to full.
A negative price looks absurd until we use the cost-of-carry formula. A holder of the May contract had to take delivery of 1,000 barrels in Cushing within days. With tanks nearly full, the storage cost for anyone without a tank was close to infinite. In the formula, a huge makes the next month's contract worth far more than the expiring one. Seen from the expiring side, a buyer with no place to put the oil would pay someone to take the barrels away. Traders who held the contract with no storage paid to be released.
The roll did the rest of the damage for funds. Oil funds that rolled into later months that spring sold cheap near contracts and bought far dearer later ones. A stylised version shows the size of the hit. Put $100 in a front-month contract at $20, which buys 5.00 barrels. Roll into the next month at $28 and the same $100 buys 3.57 barrels, a loss of −28.6 % of the barrels held, with the spot price unchanged. The largest US oil fund changed its rolling rules in April 2020 and spread its holdings further out the curve; we leave the details to its filings (see Gaps).
1980 Gold at $850, then a 28-year wait
The LBMA gold price reached $850 an ounce on 21 January 1980, after a decade of high inflation, the Iranian revolution and the Soviet invasion of Afghanistan. Gold did not pass that level again in nominal terms until January 2008.
A nominal price that ends where it started still hides a loss, because prices of everything else rose. The CPI-U index from the Bureau of Labor Statistics stood at 77.8 in January 1980 and 211.08 in January 2008, so the cost of living rose 2.71 times. A gold holder who bought at the peak and sold at the same nominal price 28 years later lost −63.1 % of purchasing power, about −3.5 % a year.
The real-yield story explains much of the path. In 1980, real rates on Treasury bills were negative, so gold cost nothing to hold. Then Paul Volcker's Federal Reserve pushed real rates far above zero (see Chapter 7), and bonds paid investors well for two decades. Gold had to compete with that, and lost.
Gold rose to near $1,900 an ounce in September 2011 (LBMA), with ten-year TIPS real yields near zero and falling below zero by 2012. When real yields jumped in the 2013 "taper tantrum", gold fell about 28 % in the calendar year, its largest fall since 1981, as the overview article reports. Those two moves fit the opportunity-cost math above.
In 2022 the link broke. The ten-year real yield on FRED's DFII10 went from about −1.0 % at the start of the year to about +1.5 % at the end. By the Level 3 math, a jump of that size in the real yield should have hurt gold badly. Gold ended 2022 close to where it began. Central banks bought gold in large amounts that year and kept buying, and from 2023 gold rose strongly while real yields stayed positive.
Claude Erb and Campbell Harvey studied this in "The Golden Dilemma" (Financial Analysts Journal, 2013). They found that gold's real price swings far more than inflation does, so it works poorly as an inflation hedge over horizons that matter to most investors, and that the real price had been high by historical standards. Their warning applies to any single story about gold: real yields explain a lot of its moves, central bank demand and fear explain others, and no simple model has predicted it well for long.
Educational only. Not investment, tax, or legal advice, and not an offer of advisory services. InnovationStrat Wealth, LLC is not yet registered as an investment adviser.