Futures market

1
Futures market
2
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.
• This may introduce default risk for some forward
  contracts.

3
Example

• Example You buy a forward contract to receive
  delivery of Euros at an exchange rate of 1 / in
  three months.
• If in three months the spot rate is 1.2 /, you
  gain, since you get 1 Euro for each dollar
  through your forward contract, but the Euros are
  currently worth more 1.2 dollars for each Euro.
• To think about it another way, you get one Euro
  for each dollar, whereas if you had waited, your
  dollar would have bought only 0.83 Euros.

4
Futures

• Futures contract - similar to a forward contract
  but it is entered into on an organized exchange
  and has standardized features (contract size,
  delivery date, acceptable grade of the commodity,
  etc.)
• They have very low transactions costs.
  Commissions can run as low as .05 of the value
  of the contract.

5
History

• Rice contracts - 17th Century Japan
• 1848 CBOT established
• Financial Futures
• 1972 foreign currencies at CME
• 1975 interest rate futures at CBOT
• 1982 stock index futures at KBT, CME, NYFE

6
Foreign Exchange Futures

• Futures markets
• Chicago Mercantile (International Monetary
  Market)
• London International Financial Futures Exchange
• MidAmerica Commodity Exchange
• Active forward market

7
Types of Contracts

• Agricultural commodities
• Metals and minerals (including energy contracts)
• Foreign currencies
• Financial futures
• Interest rate futures
• Stock index futures
• futures contract specifications can be found on
• http//www.duke.edu/charvey/options/futures/f_idx
  .htm

8

• Frozen Pork Bellies Futures Ticker Symbol PB
• 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 910 am-100 pm (Chicago Time)
• Last day 910 am-1200 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.

9
Key Terms for Futures Contracts

• Futures price - agreed-upon price at maturity
• Note that this is different than the price of a
  security, which is the price paid today for the
  security. A futures contract involves no exchange
  of money at the outset.
• Long position - agree to purchase
• Short position - agree to sell
• Profits on positions at maturity
• Long future spot price minus futures price
• Short futures price minus future spot price

10
Key Difference in Futures

• Secondary trading - liquidity.
• Standardized contract units.
• Clearinghouse warrants performance.
• Unlike forwards, there is no default risk with
  futures.
• Sellers do not have to be concerned about
  evaluating the credit risk of every different
  buyer, since the clearing house guarantees all
  transactions.

11
Trading Mechanics

• Clearinghouse - acts as the counterparty to all
  buyers and sellers.
• Obligated to deliver or supply delivery
• Stands in the middle of the transaction between
  the long and short position

Long Position
Short Position
Clearinghouse
commodity ?
commodity ?
12
Margin Accounts

• When buying a contract, the buyer must post a
  performance bond that is, deposit money in a
  margin account, usually 20 percent of the value
  of the contract.
• Note that this margin account is NOT the same as
  a stock margin account in which a buyer is making
  a down payment and borrowing funds from the
  broker to complete the sale.
• Since the account earns interest, there is no
  cost to you, the buyer, of posting the
  performance bond.

13
Margin and Trading Arrangements

• Initial Margin - funds deposited to provide
  capital to absorb losses (more than one-day price
  moves)
• Marking to Market - each day the profits or
  losses from the new futures price are reflected
  in the account (daily settlement.). This is
  calculated by taking the difference between the
  closing futures price at the end of the day minus
  the previous closing price.
• Maintenance or variation margin - an established
  value below which a traders margin may not fall.

14
Clearinghouse

• Bears any residual credit risk, that exists
  because
• 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.

15
Daily Settlement - an example

• Suppose that the current futures price of gold
  for delivery 4 days from now is 293.50 per
  ounce.
• Over the next 3 days, the price evolves as
  follows, and the daily settlements are calculated
  accordingly for a long positionDay
  Futures Price Profit (loss)/ounce 1
  295.20 1.70 2 294.60 -0.60 3
  293.00 -1.60Net Profit -0.50

16

• Suppose an Australian futures speculator buys one
  SPI (share price index) futures contract on the
  Sydney Futures Exchange (SFE) at 1100am on June
  6. At that time, the futures price is 2300.
• 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.

17

• Where does the 250 go?
• On the opposite side of the buyer's buy order,
  there was a seller, who has made a gain of 250
  (note that futures trading is a zero-sum game -
  whatever one party loses, the counterparty
  gains).
• The 250 is credited to the seller's account.
• Suppose that at the close of trading the
  following day, the futures price is 2310. Since
  the buyer has bought the futures and the price
  has gone up, he makes money.
• In particular, 25(2310-2290)500 is credited
  to his account. This money, of course, comes from
  the seller's account.

18
Forwards and FuturesProfits and Losses

• A futures contract can be considered a series of
  one-day forward contracts.
• Its as if you close out your position each day
  and then open up a new position.
• The price of a futures contract will approach the
  spot price as the futures contract nears its
  maturity date.
• The capital gains and losses on the futures
  contract are realized over the life of the
  contract rather than at the end, which is the
  case with a forward.

19
Closing out Positions

• Option One You can reverse the trade
• Go long (enter into a contract to buy) if closing
  out a short position.
• Go short (enter into a contract to sell) if
  closing out a long position.
• The difference in the prices in the two contracts
  will be your profit.
• Example you have been long corn futures for 5
  days. You want out. You enter into a short
  contract for the same amount. The long and short
  positions cancel at the clearinghouse.

20
Closing out Positions

• Option Two You can take or make delivery.
• Financial futures though are cash settled.
• Most trades are reversed and do not involve
  actual delivery.

21

• Deliverable quality Greasy wool futures.
• 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.

22

• Because any particular bale of wool is unlikely
  to exactly match these specifications, wool
  within some prespecified tolerance is
  deliverable.
• In particular, 2,400 to 2,600 clean weight
  kilograms of merino fleece wool, of good
  topmaking style or better, good colour, with
  average micron between 19.6 and 22.5 micron,
  measured staple length between 80mm and 100mm,
  measured staple strength greater than 30 n/ktx,
  less than 2.0 vegetable matter is deliverable.
• Premiums and discounts for delivery that does not
  match the exact specifications of the underlying
  contract are fixed on the Friday prior to the
  last day of trading for all deliverable wools
  above and below the standard, quoted in cents per
  kilogram clean.

23
Trading Strategies

• Speculation -
• You go short if you believe price will fall.
• You go long if you believe price will rise.
• Hedging -
• long hedge - protecting against a rise in price
• e.g. for an input to production
• short hedge - protecting against a fall in price
• e.g. for an output commodity

24
Corn Example

• You are a farmer who wants to sell your corn
  harvest in September. You would like to lock into
  a price now.
• The current futures price is 2.26 ¼ per bushel,
  and you think that this is an acceptable lock-in
  price.
• Contract size is 5000 bushels.
• You go short 10 contracts and deposit
• (.2)(105000)(2.26 1/4) 22,625 in a margin
  account.
• This means you agree to sell 50,000 bushels of
  corn to the CBOT on September for 2.26 ¼ per
  bushel.

25
Corn Example

• September comes around and the current corn price
  is 1.
• You sell your corn to a buyer for 1.
• But you make money on your futures contract.
• Since the futures price equals the spot price
  when the contract comes due, the futures price is
  also 1.
• At this point your margin account will have
  gained value by the amount (2.26 1/4 -
  1)(50,000).
• So at this point you enter into a long contract.
  The two contracts (one long and one short) cancel
  out, you dont have to deliver any corn to the
  CBOT, and you pocket the gain to your margin
  account.

26
Forward and Futures Pricing

• There are two ways to acquire an asset for some
  date in the future
• Purchase it now and store it
• Take a long position in futures
• These two strategies must have the same market
  determined costs.
• Otherwise we could do arbitrage.

27
Determining Forward Prices

• Consider a perfect hedge
• Hold an underlying asset and short a forward
  contract on that asset.
• This combined position has no risk!
• You knew the terms of the contract from the
  start.
• At the maturity date, you deliver the underlying
  asset in exchange for the forward price.
• Therefore, a perfect hedge should return the
  riskless rate of return.
• This idea can be used to develop a relationship
  between forward (or futures) prices and spot
  prices.

28
Basis Convergence Property

• On the delivery date, the futures price spot
  price or FT PT or FT - PT 0
• gain or loss (marking to market) on a long
  position FT - FT-1
• the sum of all daily settlements FT - F0
• given convergence, this means sum of all daily
  settlements PT - F0

29
Futures prices versus expected future spot price
30
Futures Prices vs. Expected Spot

• Expectations Hypothesis
• Normal Backwardation
• Contango
• Modern Portfolio Theory

Suppliers are natural hedgers F lt EPT
Purchasers are the natural hedgers gt F gt EPT
P0 EPT/(1k)T P0 F/(1Rf)T EPT/(1k)T
F/(1Rf)T EPT (1Rf)T /(1k)T F
If beta gt 0, then k gt Rf F lt EPT
31
Are forward and future prices the same?

• Marking to market complicates valuation for
  futures
• However if interest rats do not change then
  forwards and futures should have the same price
• We are going to assume that interest rates do not
  change.

32
Hedge Example

• An investor owns an SP 500 fund that has a
  current value equal to the index level of 1000.
• Assume dividends of 26 will be paid on the index
  at the end of the year.
• Assume that the futures price for a contract that
  calls for delivery in one year is 1050.
• The investor hedges by shorting one futures
  contract.

33
Rate of Return for the Hedge

• If we denote the one-year futures price today in
  the market by F0, the dividend by D, and the spot
  price by S0, we can write the return on the
  strategy as
• The way to understand this is to think about in
  and out.
• He gets F0 when he delivers his SP fund. He gets
  D in dividends, and he pays S0 for the fund.
• Plugging in the numbers from the example we get.

34
General Spot-Futures Parity

• Since this strategy is risk-free, its return must
  be equal to the risk free rate.
• Rearranging terms, we get
• Continues compounding should be usedhow would
  the formula look then?

35
Intuition behind the Pricing Formula

• One can interpret the formula
• F0S0(1rf -d) as follows.
• If the futures contract is priced correctly, you
  should be indifferent between
• arranging today to buy the underlying asset at a
  cost of F0 one year from now and,
• paying S0 to buy the asset today, foregoing
  interest of rfS0 on your money (over the next
  year), but receiving dS0 (at the end of the year)
  as a benefit to holding on to the asset for the
  year.

36
Arbitrage Opportunities

• If spot-futures parity is not observed, then
  arbitrage is possible.
• If the futures price is too high
• Short the futures
• Borrow the cost of the stocks at the risk free
  rate
• Buy the index
• For example, if F01055, this strategy would
  yield 105526-1000(1.076) 5.

37
Arbitrage Opportunities

• If the futures price is too low, the reverse is
  true
• Go long futures
• Short the index
• Invest the proceeds at the risk free rate.
• For example, if F01045, this strategy would
  yield 1000(1.076)-1045-26 5.

38
Stock Index Contracts

• Available on both domestic and international
  indexes.
• Advantages over direct stock purchase
• lower transaction costs
• better for timing or allocation strategies
• takes less time to acquire the portfolio

39
Using Stock Index Contracts to Create Synthetic
Positions

• We have seen how to create a synthetic lending
  strategy by holding the index and taking a short
  position in index futures.
• By playing with this relationship, we can see how
  to create a synthetic index purchase
• Go long the index future and lend.
• Also, we can see that being long a forward or
  futures contract is equivalent to buying the
  underlying stocks in the index and borrowing to
  finance this purchase.

40
Using Stock Index Futures as a Partial Hedge

• We saw how to create a completely riskless
  portfolio by combining a long position in stocks
  with a short position in index futures.
• A portfolio manager may also want to take a short
  position in an index futures contract to reduce
  temporarily the portfolio's exposure to the
  market (but not eliminate all exposure).
• This allows the manager to take advantage of her
  superior stock-picking ability, and avoids the
  triggering of high transaction costs (from
  selling off stock and buying it again later) and
  of capital gains taxes.

41
Using Stock Index Futures as a Partial Hedge

• The number of futures contracts to go long or
  short is determined by how much you want to
  change the portfolios level of risk.
• You can measure the change in risk by the amount
  you want to change the portfolios beta or by the
  amount you want to change the portfolios level
  of total investment.
• These two approaches are equivalent.

42
Using Stock Index Futures as a Partial Hedge

• Changing beta
• Changing value

43
Example

• A portfolio manager whose 450 million portfolio
  currently has a beta of 1.2 believes that the
  market may fall in the next couple of months and
  wants to reduce the portfolio beta to 0.8.
• How many contracts should she short?
• Assume that the SP 500 is now at 1000.
• If the market falls by 1, the SP index will
  fall by 10 points.

44
Example

• Since SP futures contracts come in multiples of
  500 (per point), the drop translates into a
  change of 5,000 per contract.
• The manager's portfolio would fall by
• 5.4 million (1.24501) if the beta stayed at
  1.2,
• 3.6 million (0.84501) if beta falls to 0.8.
• Thus, to reduce the loss by 1.8 million (
  5.4-3.6), the manager should short 360 contracts
  (1,800,000/5,000).

45
Hedging Foreign Exchange Risk

• A US firm wants to protect against a decline in
  profit that would result from a decline in the
  pound
• Estimated profit loss of 200,000 if the pound
  declines by .10.
• Short or sell pounds for future delivery to avoid
  the exposure.

46
Pricing on Foreign Exchange Futures
Interest rate parity theorem Developed using the
US Dollar and British Pound
where F0 is the forward price E0 is the current
exchange rate
47
Text Pricing Example
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.
48
Hedge Ratio for Foreign Exchange Example
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
49
Interest Rate Futures

• Idea to separate security-specific decisions
  from bets on movements in the entire structure of
  interest rates
• Domestic interest rate contracts
• T-bills, notes and bonds
• municipal bonds
• International contracts
• Eurodollar
• Hedging
• Underwriters
• Firms issuing debt

50
Uses of Interest Rate Hedges

• Owners of fixed-income portfolios protecting
  against a rise in rates.
• Corporations planning to issue debt securities
  protecting against a rise in rates.
• Investor hedging against a decline in rates for a
  planned future investment.
• Exposure for a fixed-income portfolio is
  proportional to modified duration.

51
Hedging Interest Rate Risk Text Example
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
52
Hedge Ratio Text Example
PVBP for the portfolio PVBP for the hedge
vehicle (contract size is 1000) 9,000
90
H
100 contracts
53
Commodity Futures Pricing
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
54
Swaps

• Interest rate swap
• Variable for fixed
• Foreign exchange swap
• One currency for another
• Credit risk on swaps
• Exists but not very problematic
• Why not?
• Swap Variations
• Interest rate cap
• Interest rate floor
• Collars combines caps and floors
• Swaptions- an option on a swap

55
Pricing on Swap Contracts

• Swaps are essentially a series of forward
  contracts.
• One difference is that the swap is usually
  structured with the same payment each period
  while the forward rate would be different each
  period.
• Using a foreign exchange swap as an example, the
  swap pricing would be described by the following
  formula.

56
Portfolio performance evaluation
57
Introduction

• Complicated subject
• Theoretically correct measures are difficult to
  construct
• Different statistics or measures are appropriate
  for different types of investment decisions or
  portfolios
• The nature of active management leads to
  measurement problems

58
Dollar- and Time-Weighted Returns

• Dollar-weighted returns
• Internal rate of return considering the cash flow
  from or to investment
• Returns are weighted by the amount invested in
  each stock
• Time-weighted returns
• Not weighted by investment amount
• Equal weighting

59
Text Example of Multiperiod Returns

• Period Action
• 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

60
Dollar-Weighted Return
Period Cash Flow 0 -50 share purchase 1 2
dividend -53 share purchase 2 4 dividend
108 shares sold
Internal Rate of Return
61
Time-Weighted Return
Simple Average Return (10 5.66) / 2 7.83
62
Averaging Returns
Arithmetic Mean
Text Example Average (.10 .0566) / 2 7.83
Geometric Mean
Text Example Average
(1.1) (1.0566) 1/2 - 1 7.81
63
Comparison of Geometric and Arithmetic Means

• Past Performance - generally the geometric mean
  is preferable to arithmetic
• Predicting Future Returns- generally the
  arithmetic average is preferable to geometric
• Geometric has downward bias

64
Abnormal Performance

• What is abnormal?
• Abnormal performance is measured
• Benchmark portfolio
• Market adjusted
• Market model / index model adjusted
• Reward to risk measures such as the Sharpe
  Measure
• E (rp-rf) / ?p

65
Factors That Lead to Abnormal Performance

• Market timing
• Superior selection
• Sectors or industries
• Individual companies

66
Risk Adjusted Performance Sharpe

• 1) Sharpe Index

rp - rf
?
p
?
67
M2 Measure

• Developed by Modigliani and Modigliani
• Equates the volatility of the managed portfolio
  with the market by creating a hypothetical
  portfolio made up of T-bills and the managed
  portfolio

68
M2 Measure Example
Managed Portfolio return 35 standard
deviation 42 Market Portfolio return
28 standard deviation 30 T-bill return
6 Hypothetical Portfolio 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
69
Risk Adjusted Performance Treynor

• 2) Treynor Measure

rp - rf ßp
70
Risk Adjusted Performance Jensen
3) Jensens Measure
rp - rf ßp ( rm - rf)
?
p
?
Alpha for the portfolio
p
rp Average return on the portfolio ßp
Weighted average Beta rf Average risk free
rate rm Avg. return on market index port.

71
Appraisal Ratio
Appraisal Ratio ap / s(ep)

• Appraisal Ratio divides the alpha of the
  portfolio by the nonsystematic risk
• Nonsystematic risk could, in theory, be
  eliminated by diversification

72
Which Measure is Appropriate?

• 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

73
Limitations

• Assumptions underlying measures limit their
  usefulness
• When the portfolio is being actively managed,
  basic stability requirements are not met
• Practitioners often use benchmark portfolio
  comparisons to measure performance

74
Market Timing

• Adjusting portfolio for up and down movements in
  the market
• Low Market Return - low ßeta
• High Market Return - high ßeta

75
Example of Market Timing
rp - rf




















rm - rf



Steadily Increasing the Beta
76
Performance Attribution

• Decomposing overall performance into components
• Components are related to specific elements of
  performance
• Example components
• Broad Allocation
• Industry
• Security Choice
• Up and Down Markets

77
Process of Attributing Performance to Components

• Set up a Benchmark or Bogey portfolio
• Use indexes for each component (equity, fixed
  income, etc)
• Use target weight structure

78
Process of Attributing Performance to Components

• Calculate the return on the Bogey and on the
  managed portfolio
• Explain the difference in return based on
  component weights or selection
• Summarize the performance differences into
  appropriate categories

79
Formula for Attribution
Where B is the bogey portfolio and p is the
managed portfolio
80
Contributions for Performance
Contribution for asset allocation (wpi -
wBi) rBi Contribution for security selection
wpi (rpi - rBi) Total Contribution
from asset class wpirpi -wBirBi
81
Complications to Measuring Performance

• Two major problems
• Need many observations even when portfolio mean
  and variance are constant
• Active management leads to shifts in parameters
  making measurement more difficult
• To measure well
• You need a lot of short intervals
• For each period you need to specify the makeup of
  the portfolio