Futures Introduction
Futures

Usage



Hedgers
Speculators
Trading Environment


Open-Outcry Auction
CBOT, CME, NYMEX, NYBOT, Int’ls.
Marking-to-market &
Margin

Marking-to-market is daily settling up:
Assume delivery at day 5 for 50,000 units
Futures
Day
Price Profit/Loss
Proceeds
0
12.00
1
12.50
0.50 $
25,000
2
11.25
-1.25 $
(62,500)
3
10.00
-1.25 $
(62,500)
4
9.50
-0.50 $
(25,000)
5
11.00
1.50 $
75,000
$
(50,000)

Margin: Initial vs Maintenance Margin
Convergence of Futures to
Spot
Futures
Price
Spot Price
Spot Price
Futures
Price
Time
(a)
Time
(b)
Forwards


Specifications:
 Contract Size, delivery date, trading and
delivery location and timetables, pricing,
cash flows, and deposits
All aspects negotiable!
Pricing Relation with Futures:



Arbitrage Pricing as sequence of daily
“rolled” futures
If Interest Rates are known then Arbitrage holds
If Rates are unknown, then relation is floor
Pricing and Examples



Basis: Spot Price - Futures Price
Cash and Carry
(Reverse Cash and Carry)
Examples
Futures Pricing

Pricing is a result of convergence to the
future spot price and arbitrage relations.
In general:
F0 = S0 (1 + r)T
(Add Storage and Transportation for commodities!)
F0
S0
r
T
= Futures Price at time 0
= Spot Price at time 0
= cost of carry (risk-free)
= Time to expiration
Futures Pricing Example
Current Gold Price is $400 per ounce. Risk-free rate is 5%.
Time to expiration of futures contract is 3 months.
F0 = S0 (1 + r)T
F0 =
(3/12)
$400(1+.05)
F0 = $404.91
Cash and Carry



Back to Gold Example: Expected Futures was
$404.91. What if futures in market is $410, and gold
is still on spot market at $400? Assume r=5%, and
T=3 months.
Borrow $400. Buy Gold. Store it. Sell Futures at
$410.
Expiration:


Spot Gold is $425. Sell Gold, get $425. Pay
Loan:$400(1+.05)(3/12) = $404.91. Net $20.09 on Gold and
Loan. Short Futures Lost $15, Overall Net = $5.09.
Spot Gold is $375. Sell Gold, get $375. Pay
Loan:$400(1+.05)(3/12) = $404.91. Net Loss $29.91 on Gold
and Loan. Short Future Gains $35, Overall Net = $5.09
Reverse Cash and Carry



Again the Gold Example: Expected Futures was
$404.91. What if futures in market is $390, and gold
is still on spot market at $400? Assume r=5%, and
T=3 months.
Short Gold at $400. Buy $400 in T-Bills. Buy Futures
at 390.
Expiration:
 Spot Gold is $450. Short Gold lost $50, but T-Bills
returned $4.91 and Expiring Futures racked up
$60 marking-to-market. Net Gain $14.91.
 Spot Gold is $350. Short Gold gained $50 and TBills returned $4.91, but Expiring Futures lost $40
marking-to-market. Net Gain $14.91.
Other Futures

Pricing T-Bond Futures



Difference between 2 T-Bond Futures Prices should
be accrued interest and Cost-of-Carry
Cost of Carry = 3 month T-Bill = 5.25% (yrly)
June T-Bond Fut =
Mar T-Bond Fut *(1+CofC) - Accrued Interest =
120 14/32 * (1+.0525).25 - .075*100*1/4
= 120.12
Note: Quote was 120 3/32 Difference due to current
3 mo T-Bill and AI
Other Futures

Pricing Stock Index Futures:





Futures =
Current Index*(1+CofC) - Sum Disc’d Divs
Div Yield on S&P 500 is 1.5%
CofC is 5.25%
Current Index = 969.02
969.02*(1+.0525).33
- .015/3*969.02 /(1+.0525).33 = 980.76; 983.2