FinQuiz smart summary, commodity forwards and futures

Forward Contract If forward price is not known we will use instead of , 0, & forward price is then ,= Where r-d = represent commodity risk premium.. PRICING COMMODITY FORWARDS

“ COMMODITY FORWARDS AND FUTURES ”

1 INTRODUCTION TO COMMODITY FORWARDS

Forward price on a financial asset 
, = 
  +   where


= spot price

r = continuously compounded interest rate

 = continuously compounded dividend yield

Forward curve or forward strip ⇒ set of prices for a given commodity for different maturity dates

If forward curve is upward (downward) sloping ⇒ contango (backwardation)

2 EQUILIBRIUM PRICING OF COMMODITY FORWARDS

Synthetic commodity can be created by combining a long forward contract with

a long position in zero coupon bond that pay F0,T at time T

Forward Contract

If forward price is not known we will use
   instead of  , 0,  &

forward price is then 
,=
    Where

r-d = represent commodity risk premium

 = expected spot price at time T

If commodity can’t be physically stored ⇒ no arbitrage principal can’t be used (as in above bullet point formula)

 & is difficult to estimate

3 NONSTORABILTY: ELECTRICITY

Electricity has distinguishing characteristics from financial assets as well as from other commodities as:

Difficult to store

Maximum supply is fixed at any point in time

Demand varies by season, day of the week & by time of the day

Large electricity price swings over the day reflect changes in  , which in turn reflect ∆ in demand over the day (these swings are not occur with financial assets)

Electricity forward market provides price discovery (information not otherwise obtainable)

IR = Interest Rate

CY = Convenience Yield

4 PRICING COMMODITY FORWARDS BY ARBITRAGE: AN EXAMPLE

Apparent reverse cash-and-carry arbitrage for a pencil These calculations appear to demonstrate that there is an arbitrage opportunity if the pencil forward price is below $0.221 However, there is a logical error in the table

Cash Flows

Lend short-sale proceeds @ 10%

An Apparent Arbitrage and Resolution

Example of pencils which are:

Storable

Supply is perfectly elastic (price

is expected to stay the same)

Reverse cash-and-carry arbitrage for a pencil This table demonstrates that there is an arbitrage opportunity if the pencil forward price is below $0.20 it differs from table 3 in properly accounting for lease payments

Cash Flows

Short-sell pencil @ lease rate of 10%

Lend short-sale proceeds @ 10%

Pencils Have a Positive Lease Rate

Cash-and-carry arbitrage with pencil lending When the pencil is loaned, interest is earned and the no-arbitrage price is $0.20

Cash Flows

Lender of the pencils will require to pay interest & situation will be like this:

Reference: Level III Curriculum, Volume 5, Reading 33, Page 177

Reference: Level III Curriculum, Volume 5, Reading 33, Page 178

Reference: Level III Curriculum, Volume 5, Reading 33, Page 178

5 THE COMMODITY LEASE RATE

Commodity lender is effectively making an investment of S0 in order to receive an expected amount of ST

Lease rate is the difference b/w commodity discount rate (α) & expected growth rate of commodity price (g) = − 

With this lease rate, the NPV of a commodity loan:

The Lease Market for a Commodity


, = 
(  ೟ 

Forward price with a lease rate (lease payment is like a dividend)

Annualized lease rate  = −  
,   Cash-and –carry arbitrage with a commodity for which the lease rate is  the implied non-arbitrage restriction is ,≤ 

 ࢋ൫࢘షࢾ࢒൯ࢀ Cash Flows

Buy ࢒commodity units and lend @ 

೐൫ೝషഃ೗൯೅

೐൫ೝషഃ೗൯೅

Reference: Level III Curriculum, Volume 5, Reading 33, Page 181

Cash-and –carry arbitrage with a commodity for which the lease rate is  the implied no-arbitrage restriction is ,≥ ࢋ൫࢘షࢾ࢒൯ࢀ

Cash Flows

Short ࢒ commodity units with lease rate

Reference: Level III Curriculum, Volume 5, Reading 33, Page 182

Effective annual lease rate  = ()

 బ,೅



 భൗ೅

− 1

Contango (backwardation) when lease rate < Rf (lease rate > Rf)

Forward Prices and the Lease Rate

Carry market ⇒ market of storable commodities

Reason for storage ⇒ seasonal variation in either supply or demand

Storage Costs & Forward Prices


 = 
, ! "−(0, )


, ≥ 
+ (0, )


,= 
(()

If storage is feasible, then it is almost always costly & affect forward price

Cash & carry logic with storage costs⇒ store only if the PV of selling at time T is at least as great as that of selling today

Where

(0, ) = Future value of storage cost

So the forward price should at least:

if continuous storage cost:

With storage costs, the forward curve
faster than the IR

Storage costs are considered negative dividend yield (negative CF for holding the assets)

Storage costs will be considered only when storage will occur

Storage Costs and the Lease Rate

Storage costs can be saved by lending the commodity

If lender is making a payment to borrower ⇒ negative dividend

The Convenience Yield


(≤ 
,≤ 
(()

CY ⇒ nonmonetary return from a commodity

Commodity lender saves λ-C by not storing the commodity & borrower pays δ = C-λ (where c = convenience yield)

No arbitrage price range of an arbitrage (reverse cost & carry)

An average investor (not a commodity user) can’t earn CY when performing a cash & carry because borrowers will already hold the optimal amount of the commodity

CY is hard to observe & serve two purposes:

Explain patterns in storage

Additional parameter to explain forward curve

7 GOLD FUTURES

Gold often trades in certificate form as a claim to physical gold at a particular location

Exchange traded gold futures are available at New York Mercantile Exchange

Gold Investments

Storage cost

Forgo lease rate if lease rate is positive & gold

is not lended

Lease rate can be earned if convenience yield

is attached

Holding T-bill & going long gold futures

Preferable way to obtain gold price exposure

Evaluation of Gold Production

! ೔
,!೔− + ())
,!!

) Where

!೔ = ounces of gold to be extracted

+ ()) = extraction cost


,!೔ = set of n forward prices

Assumption ⇒operation certainty & quantity of production

is known

8 SEASONALITY: THE CORN FORWARD MARKET

Corn is produced at one time of the year & consumed throughout the year

Corn storability & carry markets have an impact on forward curve

9 NATURAL GAS

Asset underlying one contract ⇒ one month worth of gas, delivered at a specific location

Several characteristics:

Costly to transport internationally

Costly to store

Demand is highly seasonal

10 OIL

Oil forward curve is very much different from gas forward curve

Oil is easier to transport & store than gas

11 COMMODITY SPREADS

Commodity spread ⇒ spread that arise because some commodities are inputs in the creation of other commodities

Crush spread ⇒ trader with a position in soybeans & same quantity opposite position in soybean meal & oil

Crack spread ⇒ difference in price b/w crude oil & equivalent amounts of heating oil & gasoline

12 HEDGING STRATEGIES

Complications when using commodity futures to hedge commodity price exposure:

Uncertain quality

Commodities are heterogeneous & costly to transport or store

Basis risk

Basis Risk

Basis Risk ⇒ price of commodity you are hedging may move differently than the price of commodity underlying the futures contract

Strip hedge ⇒ hedge a stream of obligations by offsetting each obligation with a futures contract (maturity & quantity matched)

Stack hedge ⇒ futures contracts with a single maturity with the no

of contracts selected so that ∆ in the PV of future obligations are offset by ∆ in the value of this stack of future contracts

Stack & roll ⇒ process of stacking futures contacts in near term contract & rolling into the new near term contract

Reasons to use stack hedge

More liquidity & trading volume in near-term contracts

Speculation on the shape of forward curve

Weather Derivative

Weather derivative ⇒ contracts that make payments based upon realized characteristics of weather (to cross hedge their specific risk)

Weather derivatives are example of cross hedging


(≤ 
,≤ 
(()

CY ⇒ nonmonetary return from a commodity

Commodity lender saves λ-C by not storing the commodity & borrower pays δ = C-λ (where c = convenience yield)... oil & gasoline

12 HEDGING STRATEGIES

Complications when using commodity futures to hedge commodity price exposure:

Uncertain quality

Commodities are heterogeneous... risk

Basis Risk

Basis Risk ⇒ price of commodity you are hedging may move differently than the price of commodity underlying the futures contract

Strip hedge ⇒ hedge a stream