# 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
**σ**^{2}_{S(t)-F(t) }= σ^{2}_{S(t) }+ σ^{2}_{f(t) }- 2σ_{S(t)}σ_{f(t)}ρ_{s,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 S
_{0}today, and will get back S_{t} - If loan is fairly priced, its NPV = 0
- NPV = E
_{0}(S_{t})e^{-αT}– S_{0} - Where α is required return on the commodity
- Now, suppose commodity price grows at rate g, E
_{0}(ST)= S_{0}egT - Then, NPV = S
_{0}e^{(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,****F**_{0,T}= S_{0}e^{(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

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?

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 = -15,000S
_{T}+ 15*1000*(S_{T}– 105) - Payoff = -$1,575,000, at any future oil S
_{T}

**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