Futures market Forwards Forward contract - an agreement between two parties involving the future delivery of a particular quantity of an asset at a price agreed upon today. Buyers and sellers are obliged to deliver or take delivery. No money is exchanged until settlement.
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futures contract specifications can be found on:
Trading Unit': 40,000 lbs. USDA-inspected 12-14, 14-16 pound or 16-18 pound (at a 21/2c discount) Pork Bellies
Price Quote: $ per hundred pounds (or cents/pound)
Min Price Fluct: $.025 $10.00/tick
Daily Price Limit: $2.00 $800.00/contract
Contract Months: Feb, Mar, May, Jul, Aug
Trading Hours: 9:10 am-1:00 pm (Chicago Time)
Last day: 9:10 am-12:00 pm
Last Day of Trading: The business day immediately preceding the last 5 business days of the contract month.
Delivery Days: Any business day of the contract month.
Delivery Points: The CME Clearing House or a current list of approved warehouses.
Long = future spot price minus futures price
Short = futures price minus future spot price
1) futures prices move so dramatically that the amount required to mark to market is larger than the balance of an individual's margin account, and
2) the individual defaults on payment of the balance.
At the close of trading on June 6, the futures price has fallen to 2290 (what causes futures prices to move is discussed below).
Underlying one futures contract is $25 x Index, so the buyer's position has changed by $25(2290-2300)=-$250.
Since the buyer has bought the futures contract and the price has gone down, he has lost money on the day and his broker will immediately take $250 out of his account. This immediate reflection of the gain or loss is known as marking to market.
Delivery must be made at approved warehouses in the major wool selling centres throughout Australia.
For wool to be deliverable, it must possess the relevant measurement certificates issued by the Australian Wool Testing Authority (AWTA) and appraisal certificates issued by the Australian Wool Exchange Limited (AWEX).
In particular, it must be good topmaking merino fleece with average fibre diameter of 21.0 microns, with measured mean staple strength of 35 n/ktx, mean staple length of 90mm, of good colour with less than 1.0% vegetable matter.
(.2)(10×5000)(2.26 1/4) = $22,625 in a margin account.
Suppliers are natural hedgers
F < E[PT]
Purchasers are the natural hedgers => F > E[PT]
P0 = E[PT]/(1+k)T
P0 = F/(1+Rf)T
E[PT]/(1+k)T = F/(1+Rf)T
E[PT]* (1+Rf)T /(1+k)T = F
If beta > 0,
then k > Rf
F < E[PT]
F0=S0(1+rf -d)as follows.
For example, if F0=1055, this strategy would yield 1055+26-1000(1.076) = 5.
For example, if F0=1045, this strategy would yield 1000(1.076)-1045-26 = 5.
A US firm wants to protect against a decline in profit that would result from a decline in the pound:
Interest rate parity theorem
Developed using the US Dollar and British Pound
F0 is the forward price
E0 is the current exchange rate
rus = 5% ruk = 6% E0 = $1.60 per pound T = 1 yr
If the futures price varies from $1.58 per pound arbitrage opportunities will be present.
Hedge Ratio in pounds
=ch. in value of unprotected position / profit on 1 futures position
$200,000 per $.10 change in the pound/dollar exchange rate
$.10 profit per pound delivered per $.10 in exchange rate
= 2,000,000 pounds to be delivered
Hedge Ratio in contacts
Each contract is for 62,500 pounds or $6,250 per a $.10 change
$200,000 / $6,250 = 32 contracts
Portfolio value = $10 million
Modified duration = 9 years
If rates rise by 10 basis points (.1%)
Change in value = ( 9 ) ( .1%) = .9% or $90,000
Present value of a basis point (PVBP) = $90,000 / 10 = $9,000 per basis point
PVBP for the portfolio
PVBP for the hedge vehicle (contract size is 1000)
= 100 contracts
General principles that apply to stock apply to commodities.
Carrying costs are more for commodities.
Spoilage is a concern.
Where; F0 = futures price P0 = cash price of the asset
C = Carrying cost c = C/P0
0 Purchase 1 share at $50
1 Purchase 1 share at $53
Stock pays a dividend of $2 per share
2 Stock pays a dividend of $2 per share
Stock is sold at $108 per share
Period Cash Flow
0 -50 share purchase
1 +2 dividend -53 share purchase
2 +4 dividend + 108 shares sold
Internal Rate of Return:
Simple Average Return:
(10% + 5.66%) / 2 = 7.83%
Text Example Average:
(.10 + .0566) / 2 = 7.83%
Text Example Average:
[ (1.1) (1.0566) ]1/2 - 1
What is abnormal?
Abnormal performance is measured:
E (rp-rf) / p
Managed Portfolio: return = 35% standard deviation = 42%
Market Portfolio: return = 28% standard deviation = 30% T-bill return = 6%
30/42 = .714 in P (1-.714) or .286 in T-bills
(.714) (.35) + (.286) (.06) = 26.7%
How do we get the weights?
Since this return is less than the market, the managed portfolio underperformed
3) Jensen’s Measure
= rp - [ rf + ßp ( rm - rf) ]
= Alpha for the portfolio
rp = Average return on the portfolio
ßp = Weighted average Beta
rf = Average risk free rate
rm = Avg. return on market index port.
Appraisal Ratio = ap / s(ep)
It depends on investment assumptions
1) If the portfolio represents the entire investment for an individual, Sharpe Index compared to the Sharpe Index for the market.
2) If many alternatives are possible, use the Jensen or the Treynor measure
The Treynor measure is more complete because it adjusts for risk
Adjusting portfolio for up and down movements in the market
rp - rf
rm - rf
Steadily Increasing the Beta
Set up a ‘Benchmark’ or ‘Bogey’ portfolio
Where B is the bogey portfolio and p is the managed portfolio
Contribution for asset allocation (wpi - wBi) rBi
+ Contribution for security selection wpi (rpi - rBi)
= Total Contribution from asset class wpirpi -wBirBi