Lecture 2
Derivatives
Overview
• Futures contracts and exchanges; quote symbology
• Spread trades
• Delivery options
• Hedging with derivatives
• Tailing the hedge
• Basis risk and hedge scaling
• Minimum variance hedging
Most active futures contracts (by count)
An example futures complex
Expiration months and other codes
Why not start with A, B, C?
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A is for Ask
B is for Bid
C is for Corn
… (E is for Eggs; S is for Soybeans; W is for Wheat)
The typical futures ticker looks like GCH26 (Gold March 2026)
On Yahoo Finance, you can use GC=F for the current on-the-run
contract, or GCH26.CMX for a fully specified contract
CMX is the Comex division of CME
Futures spread trading
• Location spread: short WTI futures and long Brent futures. You just
bought (synthetic) oil transportation from Oklahoma to the coast
of Scotland
• Calendar spread: short March corn futures and long June corn
futures. You just rented (synthetic) corn storage for 6 months
• Crush spread: short soybean futures and long a suitable mix of
soybean oil futures and soy meal futures. That’s a synthetic
soybean crushing processor
• Crack spread: short crude oil and long gasoline, diesel and
heating oil futures. That is approximately a synthetic oil refinery
Delivery options
• The short party to a futures contracts may have some choice in
terms of:
• Exactly what to deliver (the quality option)
• When to deliver it, within the delivery window (the timing option).
• Delivery options arose out of practical necessities in agricultural
markets: both the quality and timing of the harvest will always be
somewhat uncertain months ahead of time
• Treasury bond futures inherited some delivery options from the
corn and bean markets: good (quality option – reduces the risk of
a short squeeze) and bad (timing options)
• The quality option comes with a schedule of price adjustments
Corporate hedging
• Hedging is generally defined as risk reducing transactions
• But what kind of risks?
• Systematic or idiosyncratic?
• Earnings or NPV?
• Risk of financial distress?
• Competitive position considerations of hedging costs
• Airlines locking in the price of jet fuel (major cost) may become
uncompetitive if others don’t and the spot price drops
• Take advantage of fixed income market segmentation by issuing
fixed and swapping to floating or vice versa, based on relative cost
Basis risk part I
• The only perfect hedge is in a…
• Trade-off between forwards and futures
• Liquidity vs specificity (in addition to counterparty credit risk)
• Basis is the difference between spot and futures price – “should” go to
zero at maturity of the futures contract, regardless of source
• Potential sources of the basis:
• Funding cost
• Storage cost
• Interim cash flows like dividends and coupons
• Convenience yield
• If you hedge a spot position with futures, you are exposed to basis risk,
even if your hedge is sized properly
Tailing the hedge
• The daily mark-to-market payments subtly changes futures vs
forward hedge ratios, even when the futures price equals the
forward price at each point in time
• Assume that the optimal hedge is one unit of a forward contract
• If interest rates were 0, the future value of the sum of the MTM
payments would exactly equal the P&L on the forward contract
• But with positive interest rates, the future value of the MTM
payments are magnified, suggesting that the proper futures hedge
should be smaller in magnitude than the forward hedge
Stack and roll
• How do you hedge long dated exposures with short dated futures?
• Let’s say you need to purchase 1,000 troy ounces of gold each of the
next 5 years and want to hedge your cost with futures now
• Gold has minimal storage cost and (at least in normal times)
convenience yield, so futures pricing is mostly driven by spot price and
funding cost
• Most of the liquidity is in near term futures maturities
• The stack and roll approach is to hedge with a near term maturity
contract and keep on rolling the position into longer maturities as they
become available, and reducing the position size with the hedging need
Basis risk part II
• Another use of the term basis is in the context of cross hedging,
hedging one asset with a position in another
• Classic example: hedge the returns on an equity portfolio with an
S&P500 futures contract
• The basis risk in this case is that the return on your portfolio and
the S&P500 may differ – perhaps by a lot
• How do you size the hedge in this case?
• What if you were forced to hedge with natural gas futures instead?
• Would your ”hedge” even reduce your risk in this case?
Minimum variance hedging
• Let’s say we define risk to be the variance of the value of the
hedged portfolio
• We need to estimate the variance of the price of the thing we want
to hedge, the variance of the futures price, and the correlation
between the two
• The optimal hedge ratio is the one that minimizes the variance of
the hedged portfolio – this is identical to the classic ordinary least
squares linear regression problem!