# Introduction commodity spot and futures markets

• Bill of lading is a document that mentions the commodity owner and acknowledges that the goods have been received as cargo and are ready for delivery
• The major risks involved with commodity transactions are:
• Price risk:  Risk of downward movement in price. Futures/Forward contracts reduce this      risk
• Transportation risk: Consists of two risks:
• Ordinary: Deterioration, spoilage, accident etc.
• Extraordinary: wars, riots, strike etc.
• Delivery risk: Parties may withdraw from delivery. This risk has been greatly decreased by robust practises by clearing houses
• Credit risk: Counter party risk which is mainly an issue in spot market
• Commodity markets also, like financial markets consists Hedgers, Speculators and Arbitrageurs
• Hedgers are generally farmers/ranchers who want to lock in a price

Basis risk in commodity futures

• Basis is the difference between spot price and the price of commodity’s future contract at any given time
• Changes in basis is due to changes in cost of carry of the asset. Basis risk is generally represented by the volatility / variance of the basis over time
• σ2S(t)-F(t) = σ2S(t) + σ2f(t) - 2σS(t)σf(t) ρs,f
• Hedge effectiveness =

Commodity Forwards

• Commodity forward prices can be described using the same formula as used for financial forward prices
• For financial assets, δ is the dividend yield
• For commodities, δ is the commodity lease rate
• The lease rate is the return that makes an investor willing to buy and lend a commodity
• Some commodities (metals) have an active leasing market
• Lease rates can typically only be estimated by observing forward prices

Futures term structure

• The set of prices for different expiration dates for a given commodity is called the forward curve (or the forward strip) for that date
• If on a given date the forward curve is upward-sloping, then the market is in contango
• If the forward curve is downward sloping, the market is in backwardation
• Note that forward curves can have portions in backwardation and portions in contango

• Since r is always positive, assets with δ =0 display upward sloping (contango) futures term structure
• With δ >0, term structures could be upward or downward sloping

A commodity loan

• If you loan a commodity, you are giving up S0 today, and will get back St
• If loan is fairly priced, its NPV = 0
• NPV = E0(St)e-αT – S0
• Where α is required return on the commodity
• Now, suppose commodity price grows at rate g, E0(ST)= S0egT
• Then, NPV = S0e(g-α)T – S
• If g<α, NPV<0
• this is common for commodities (supply with near-perfect elasticity)
• Therefore, to make loan feasible, you would require lender to pay you the α-g difference
• This would get NPV back to zero
• If 1 unit is loaned, you receive a lease payment of e(α-g)T units, and NPV = 0

The Commodity Lease Rate

• The lease rate (δ) is the difference between the commodity discount rate, α, and the expected growth rate of the commodity price, g
• For a commodity owner who lends the commodity, the lease rate is like a dividend
• With the stock, the dividend yield, δ, is an observable characteristic of the stock
• With a commodity, the lease rate, δ l, is income earned only if the commodity is loaned. It is not directly observable unless there is an active lease market

• With the addition of the lease payment, NPV of loaning the commodity is 0
• The lease payment is like the dividend payment that has to be paid by the person who borrowed
• a stock
• Therefore:

Forward Prices and the Lease Rate

• The lease rate has to be consistent with the forward price
• Therefore, when we observe the forward price, we can infer what the lease rate would have to be if a lease market existed
• The annualized lease rate
• The effective annual lease rate

Storage and Carry Markets

• A commodity that may be stored is said to be in a carry market
• Reasons for storage
• There is seasonal variation in either supply or demand (e.g., some agricultural products)
• There is a constant rate of production, but there are seasonal fluctuations in demand (e.g., natural gas)

Storage Costs and Forward Prices

• One will only store a commodity if the PV of selling it at time T is at least as great as that of
• selling it today
• Whether a commodity is stored is peculiar to each commodity
• If storage is to occur, the forward price is at least
• Where λ(0,T) is the future value of storage costs for one unit of the commodity from time 0 to T

Storage Costs and Forward Prices (cont’d)

• When there are storage costs, the forward price is higher. Why?
• The forward price must compensate a commodity holder for both the financial cost of carry (interest) and the physical cost of carry (storage)
• With storage costs, the forward term structure can be steeper than the interest term structure
• Convenience Yield
• Some holders of a commodity receive benefits from physical ownership (e.g., a commercial user)
• This benefit is called the commodity’s convenience yield
• The convenience yield creates different returns to ownership for different investors, and may or may not be reflected in the forward price
• Convenience and leasing
• If someone lends the commodity they save storage costs, but lose the ‘convenience’
• Stated as (λ –c)
• Therefore, commodity borrower pays a lease rate that covers the lost convenience less the storage costs:
• δ = c – λ

Pricing with convenience

• So, if:

• And if, δ = c – λ
• Then,  F0,T  = S0e(r+ λ -c)T

No-Arbitrage with Convenience

• From the perspective of an arbitrageur, the price range within which there is no arbitrage is:

• Where c is the continuously compounded convenience yield
• The convenience yield produces a no-arbitrage range rather than a no-arbitrage price. Why?
• There may be no way for an average investor to earn the convenience yield when engaging in arbitrage

Example

Suppose that the price of corn is $2.20/bushel, the effective annual interest rate is 4.6%, and effective annual priced storage costs are 10% of the current price/bushel. What is the 6-month forward price? Solution F = 2.2e (.046 + 0.1) 0.5 =$2.37
Now suppose the holder of the asset realizes a convenience yield of 2%. What is the price?
F = 2.2e (.046 + 0.1 - 0.02) 0.5 = $2.34 The futures price dropped because the cost of carrying corn dropped Hedging oil costs? • Suppose we are scheduled to purchase 15,000 bbls of oil in July 2008. The current futures price is$105/bbl, and each contract covers 1,000 bbls.  If we hedge, what is our cost of oil if the spot price of oil in July 2008 is $70/bbl or$120/bbl?
• Our natural exposure is short, therefore hedge long
• Direct hedge, β = 1.  N=15/1*1 = 15 contracts
• Payoff = -15,000ST + 15*1000*(ST – 105)
• Payoff = -$1,575,000, at any future oil ST Hedging production costs • Suppose oil is a major component of our total production costs which equal$40 million, but it is not the only component.  In general, our production costs rise/fall with sensitivity of 0.72 (beta=0.72) to oil.  Each crude oil contract is on 1,000bbls. Suppose S0=108 and F=105.
• Now, how many contracts do we use to hedge?
• Cross hedge, β = 0.72.  N = 40m/105,000*0.72 = 274.28 contracts
• Suppose oil goes up by 10% from 108 to 118
• Increase in production costs = 0.072*40 = $2.88 million • Payoff from forwards = 274.28*1,000 (118-105) =$2.88 million
• Note, we now have basis risk – the basis for our hedge does not match the hedging instrument perfectly – what if our relation is not 0.72?

Strip and Stack Hedges

• In the last example, we bought 450K bbls forward
• This might be one component of a “strip hedge” if we are selling forward in other periods as well
• In a “stack hedge”, we enter near-term contracts sufficient to cover the present value of future obligations
• We then “roll the hedge” into new contracts as the near-term contracts expire