# Derivatives Forwards

Pages: 5 (781 words) Published: May 1, 2013
Commodity Forwards: with some focus on crude oil

6-1

Same concept applies…
• In general, commodity forward prices can be found using the same economic principles used for financial forward prices:

F0,T = S0 e

(r − δ )T

but the details will be different
6-2

Dirty details
• 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 • http://www.kitco.com/market/LFrate.html

• More typically, lease rates can only be estimated by observing forward prices

6-3

Think about 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 • if NPV=0, α is the “__________”

6-4

Commodity loan (cont)
• Now, suppose commodity price grows at rate g, E0(ST)= S0egT • Then, NPV = S0e(g-α)T - S0, • But now if g 0.5% 6-21

More oil characteristics
• Viscosity is a measure of how well if flows or the “friction” in the liquid  

water is very low viscosity, mayonnaise would be high!

Pour point • The lowest temperature at which crude or other refined product flows as a liquid 

Higher pour points can be more expensive to store and transport, because they may need heated

  

“Paraffinic” = low-viscosity and high flammability “Napthenic” = high-viscosity, but not highly flammable “Intermediate” = in between paraffinic and napthenic

6-22

Common oil types
• “Light and sweet”

API gravity between 33 and 45 degrees
• West Texas Intermediate (39.6) • Brent (North West European crude, 38.06) • Dubai (31) • Saudi Ghawar Field (33-40)

• “Heavy and sour”

API gravity between 10 and 33 degrees
• Urals (Eastern European crude)

APIs greater than 10 float on water

http://en.wikipedia.org/wiki/API_gravity
6-23

Most valuable company on Earth?
• http://en.wikipedia.org/ wiki/Saudi_Aramco • Approximately 6.25% of world production comes from their Ghawar Field 

Largest field in their portfolio

6-24

Current WTI strip
As of 14:11 02/27/12 9-mo lease rate is approximately 17 bp per annum, given current treasury rates

6-25

Many oil-based strategies
• Refiners are worried about spread between cost of oil (input) and refined products (output) • Pg 173 – long oil futures and short appropriate quantities of gasoline and heating oil futures  

For example, use a 5-3-2 ratio There are options traded on the crack spread on NYMEX

GS is currently recommending clients to long WTI and short Brent 

6-26

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 = -15000ST + 15*1000*(ST – 105) Payoff = -\$1,575,000, at any future oil ST. 6-27

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 =.072*40 = \$2.88 mill • Payoff from forwards = 274.28*1000(118-105)=\$2.88 mill

• Note, we now have...

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