Introduction to FINANCIAL FUTURES from myths to truths

1
Introduction to FINANCIAL FUTURESfrom myths
to truths

• S. J. Chang, Ph.D.
• College of Business
• Illinois State University

2
What Are Derivatives?

• Sophisticated, Dynamic Risk Management
  Instruments
• Forward A customized, risk-exposed contract
  for a future trade
• Futures A standardized, exchange-traded,
  daily-settled forward
• Swap A multiple of forwards with
  periodic settlements
• Option A forward synthesized with a
  riskfree asset
• Derivative, Dependent, Contingent, Conditional,
  Synthetic, Hybrid, Interstitial, ..., Fuzzy!
• Flexible, Dynamic, Adaptive, Proactive,
  Versatile, ...

3
Why Derivatives?

• Growing Diversity and Volatility in Risk
  Sources
• Diversification/Sophistication in Corporate
  Financial
• Management and Investment Needs
• Global Local gt Glocalization
• Integration - Segmentation
• Regulation - Deregulation - Liberalization
• Intermediation - Disintermediation -
  Reintermediation
• Securitization - Financial Engineering

4
Derivatives - - -

• Volatility gt Hedging Need and Speculation
  Opportunity
• Since when? Commodity Futures (CBOT-1848)
• Financial Futures 1972
• Expanding Scope and Scale
• CME's Daily Trading Value 20 x NYSE's
• Free-hand Estimate of World Derivatives
  30-100 tril.

5
Key Concepts in Derivatives

• Volatility "Derivatives feed on volatility!"
• Liquidity Derivatives markets cannot function
  properly
• w/o sufficient liquidity - easy entry and easy
  exit
• Hedging Risk-avoiding strategy to protect
  position values
• Speculation Risk-taking, dynamic investing
  strategy to
• generate high returns
• Arbitrage Riskfree, profit-seeking strategy
  from temporary
• price distortion
• Symmetry Long vs Short - A Zero-sum Game!
• Leverage Small Commitment - Large Consequence
• Fungibility Substitutability of
  assets/contracts (Money - Live Cattle)

6
First Definitions

• Forward A forward contract calls for the
  delivery of an asset (real or financial) at a
  future date for a predetermined price.
• - informal, , private, customized, and
• risk-exposed (because of inherent, strong
• incentives to default)
• Futures A formal, standardized,
  exchange-traded contract in which the
  underlying asset will be delivered on a future
  date at a specified price.

7
Futures Markets Cover Almost Everything
Commodities

• Grains Oilseeds wheat, corn, oats, soybeans,
  red beans, rye,
• rice, barley, rapeseed, flaxseed, blackseed,.
  
• Foods Fibers cocoa, coffee, frozen OJ, sugar,
  cheese, flour, peanuts, potatoes, copra, dry
  milk, ...
• Livestock Meat live cattle, feeder cattle,
  hogs, piglets,
• port bellies, lamb, chicken, ...
• Metals copper, gold, silver, zinc, platinum,
  lead,
• tin, nickel, palladium, aluminum alloy, ...
• Oil Gas crude oil, heating oil, unleaded
  gasoline,
• natural gas, gas oil, propane, ...
• Other Materials cotton, wool, lumber, rubber,
  yarn, raw
• silk, dry cocoon, scrap metals,
  fertilizers,...

8
Financials

• Interest Rates Fed Funds, TBills/Notes/Bonds,
  BA, E,
• LIBOR, FIBOR, PIBOR, HIBOR, Zeroes,
• Muni Bond Index, EM, EY, ESFr, Gilt,
  Bund, JGB, CGB, Notional Bonds, Brady
  Bonds, yield spreads, ...
• Currencies USDX, Euro, DM, JY, BP, SF, FF, CD,
  AD, IL, Rolling/Deferred Spot, Cross
  Rate,..
• Stock Indexes DJIA, SP500, NYSE, VLI, SP
  Midcap400,
• Russell 2000, DAX, FT-SE 100, CAC 40,
  Eurotop100, TOPIX, Nikkei225/300, Hang
  Seng Index, MSCI, KOSPI 200,
• ... CRB Index, GSCI, Freight Index, inflation
  rates, crop yield insurances, catastrophe
  insurances, tax liability, waste/ pollution
  allowance, electricity, water, air, recyclables,
  ...

9
Futures Exchanges

• Futures contracts are traded on exchanges
• U.S.
• CBOT, MidAm ComEx, CME, IMM, CRCE, NYCE, FINEX,
  NYSE (NYFE), PHLX (PBOT), NYMEX, CSCE, COMEX,
  CSCE, KCBT, MGE
• Overseas
• Australia (SFE), Austria, Belgium, Brazil
  (BMF), Canada (TFE, ME, WCE), China, Denmark,
  Finland, France (MATIF), Germany (EUREX, DTB),
  Hong Kong (HKFE), Hungary, Ireland, Italy, Japan
  (TSE, TIFFE, OSE), Malaysia, Netherlands (EOE),
  New Zealand, Norway, Philippines, Singapore
  (SIMEX), South Africa, S. Korea, Spain, Sweden,
  Switzerland, U.K. (LIFFE, LME, IPE)

10
..., Clearinghouse, CFTC, NFA, ...

• Pit Trading Traders get together in exchange
  pits and make offers by open outcry (US) vs
  Electronic Trading
• Clearinghouse Steps between the buyer and
  seller (as counterparty and trade guarantor). -
  CBOTCC
• Each trader must deposit margin with the
  exchange. Through daily settlement procedure
  called marking-to-market, all traders realize
  gains and losses each day.
• In the US, futures trading (all commodity and
  financial futures plus options on futures) is
  regulated by the CFTC (1974), while all spot
  security trading (stocks, bonds, etc., plus spot
  options) is governed by the SEC (1934).
• NFA - National Futures Association

11
Reminder The main purposes of futures trading
are hedging and speculation.
The key to success of hedging and
speculation is liquidity.

• Devices to Increase Liquidity
• Standardization (size, tick, cycle, delivery,
  margins, ...)
• Cash Settlement without Physical Delivery
• Marking-to-Market Daily recognition of profits
  and losses -gt flexible, dynamic risk management!
• Low Margins Leverage
• Clearinghouse Guaranteed Settlement

12
Open Interest

• A measure of futures market liquidity
• Number of futures contracts that are
  outstanding for future delivery or settlement.
• One matched case of long (A) and short (B)
  trades constitutes one unit of open interest.
• If (A) reverses her initial position with (C)
  while (B) holds his position, the open interest
  does not change.
• When both (A) and (B) eventually unwind their
  positions, the open interest reduces by one unit.

13
Futures Trading Matchups

• 1. Short Hedger vs. Long Hedger
• (corn grower vs. cereal maker)
• (corporate bond issuer vs. bond investor)
• 2. Short Speculator vs. Long Speculator
• (speculates corn price to fall) (... rise)
• (speculates bond price to fall, (... rise,
  
• or interest rate to rise) or ...
  fall)
• 3. Short Hedger vs. Long Speculator
• 4. Short Speculator vs. Long Hedger

14
Futures Margins

• A good-faith deposit (earnest money) made by
  the traders to ensure the completion of the
  contract.
• (In stock trading, margins are down payment of
  the trade.)
• Exchanges set the initial and maintenance
  margin requirements upon which brokerage houses
  set their own margins.
• Typically small (2-5 of contract amount) ---
• Leverage!

15
Marking-To-Market

• Daily Profit/Loss Recognition
• As the day's trades are completed, all futures
  contracts are marked to the market at the
  settlement price.
• (futures a series of one-day forwards)
• While the credited profits are withdrawable,
  the trader must replenish the account if it falls
  below the maintenance margin.
• Margin call When the market moves against the
  position by Initial Margin - Maintenance Margin
  1 tick

16
Marking-to-Market An Example

• Short (sell) 1 Sep T-Bond futures at 93-00
• Initial margin 3,250, Maintenance margin
  3,000
• 1 tick 1/32 of 1,000 31.25
• Date Price Change Account Value
  Total Payment
• --------------------------------------------------
  ------------------------------------
• May 12 93-00 3,250 3,250
• May 13 93-04 -125 3,125
  3,250
• May 14 93-08 -125 3,000
  3,250
• May 15 94-00 -750 2,250
  3,250
• (deposit 1,000) 3,250 4,250
• May 16 93-16 500 3,750
  4,250

17
Cost-of-Carry Relationship

• The theoretical relationship between St and
  Ft,T for any futures contract is essentially
  governed by the cost-of-carry relationship.
• A futures trade necessitates storing and
  carrying the underlying asset until the delivery
  date. This entails costs, benefits, or both to
  the potential deliverer. "Cost of Carry"
  includes storage costs, transportation costs,
  insurance costs, interest costs, other
  opportunity costs as well as interest/dividend
  receipts and other opportunity benefits
  (commodities vs. financials).
• Ft,T St C
• Futures Price Spot (Cash) Price Cost of
  Carry

18
BASIS

• Theoretically, for most commodities (and some
  financials like stock index futures), Ft,TgtSt
• (Distant futures contracts priced higher than
  nearby contracts.)
• For interest rate futures, Ft,TltSt (Distant lt
  Nearby)
• Basis Actual, observed difference between
  Ft,T and St
• B Ft,T - St or St - Ft,T or Ft,T -
  St
• A positive basis Ft,T - St gt 0 for storable
  commodities Contango A positive expected basis
  E(Ft,T - ST) Ft,T - E(ST) gt 0 vs.
  (Normal) Backwardation Ft,T lt E(ST)
• Ft,T and St generally move in the same
  direction. In fact, as a price of a derived
  asset that is contingent/conditional on the
  underlying asset, Ft,T should closely reflect St.
  
• Conceptually, Ft,T can be viewed as the
  expected spot price (net of cost of carry) Ft,T
  ? E(ST)

19
Convergence The basis for a particular
contract may narrow or widen over a certain
(short) period (initial basis ? cover basis
basis risk). However, it eventually narrows
down to zero as the futures delivery date
draws near. Over the contract's life, basis
gradually disappears (FT,TgtST). It is the
strong positive correlation and the convergence
property between FT,T and ST that makes
hedging possible. Hedging A conservative
portfolio strategy where the investor attempts to
cover the potential losses from a spot
position with the potential gains from an
opposite futures position.
20
Short Hedge Create a short futures position to
cover a long spot. Farmers or potential
security sellers can preserve value by
locking in selling price. Long Hedge Create a
long futures position to cover a short spot.
Grain processors or potential security buyers can
limit opportunity loss by locking in
purchase price. Hedge Ratio Number of futures
contracts needed for hedging is set where the
variability of the total hedged position value is
minimized. Min Var(VH) Min Var(S-?F) Min
Var(?s2 ?2?f2-2? ?s ?f r) ??/?? ? 0 ?
(?s/?f)r (? ? ?) ? QF QS.? Perfect
hedge is impossible due to imprecise matches in
assets, quantities, time horizons, and the
correlation between S and F. (... can only be
found in ???) (nedrag esenapaJ
a ni)
21
Hedge Outcome When the basis widens, the
short hedger will suffer an imperfect
hedging loss when the basis narrows, the short
hedger will gain due to the imperfect hedging.
Spot Futures Basis --------------------------
------------------------ 100 L 105 S
5 105 S 111 L 6 ------- -------- ------
- 5 (gain) -6 (loss) 1 (widens) net
-1 100 L 105 S 5 95 S 101 L
6 ------- -------- ------- -5 (loss) 4
(gain) 1 (widens) net -1
22
(Contd) A short hedger loses when the basis
narrows Spot Futures Basis ----------------
--------------------------------- 100 L 105 S
5 105 S 109 L 4 ------- -------- --
----- 5 (gain) -4 (loss) -1 (narrows) net
1 100 L 105 S 5 95 S 99 L
4 ------- -------- ------- -5 (gain) 6
(gain) -1 (narrows) net 1 A long hedger
will gain when the basis widens and suffer a loss
when the basis narrows. (Symmetry)
23
Stock Index Futures The underlying asset is
undeliverable stock market index. DJIA
(CBOT) x 10 SP500 (CME) x 250 MINI SP
(CME) x 50 SP MIDCAP400 (CME) x 500
Russell2000 (CME) x 500 NASDAQ100 (CME) x
100 NYSE CI (NYFE) x 500 GSCI (CME) x
250 VLCI (KCBT) x 500 (since
1982) FT-SE100 (LIFFE) x 10 CAC-40
(MATIF) x E10 DAX-30 (EUREX,DTB) x
E25 Nikkei225 (OSE) x 1,000 (CME x
5) KOSPI200 (KSE) x W500,000
24
Stock futures can be used for both hedging and
speculation. Reminder Futures market is
typically net short ---gt Speculators pick
up the slack ---gt They assume the risk
the hedgers pass on. Intramarket Spread (Time
Spread) e.g., Buy a March SP futures and
sell a June SP futures. Intermarket Spread Take
opposite positions between two different
indices with the same T (e.g., NYSE and SP).
Short Hedging with Stock Futures - An Example
Diversified portfolio worth W175 mil. with ?1.13
KOSPI 200 Spot 100.50, Futures 102.00
Sell 4 contracts (175,000,000x1.13)/(100.50x500,0
00)3.94 Later Spot-gt97.75 Futures-gt99.50
(Basis -1.50 ? -1.75) S (97.75-100.50)/100
.50(1.13)(175 mil.)-W5,411,070 F
(102.00-99.50)500,000(4)W5,000,000 Net
-W411,070!
25
Arbitrage Pricing of Stock Index Futures Cost
of Carry FSC (CSr) gt FS(1r)t gt
FS.ert When dividends are paid, however, the
effective cost of carrying the stocks
reduces. FS(1r-d)t gt FS.e(r-d)t
Example t T At
t --------------------------------------------
-- Borrow _at_ r St Buy Spot
Portfolio -St Sell Index Futures
Ft,T At T Repay the Loan
-St(1r) Sell Spot Portfolio ST Cover
the Hedge (Buy Index Futures) -FT,T Collect
Dividends DT --------------------------
--------------------- Total Cash Flow
0 Ft,T-St(1r)DT Then,
Ft,TSt(1r)-DT gt Ft,TSt(1r-d) gt
Ft,TSt.e(r-d)t
26
Index Arbitrage Efforts to exploit
discrepancies between stock index futures
prices and the spot stock prices. Often
involves computer-based Program Trading
---gt Use of computer programs to initiate trades
in spot and futures markets (based
on arbitrage pricing mechanisms) Portfolio
Insurance Dynamic Hedging with Index
Futures Lower transactions costs, Greater
liquidity, and Leverage effect Separation of
stock management and insurance strategy, ...
27
T-Bill Futures T-Bills Pure discount
(zero-coupon) securities T-Bill futures
IMM-CME, 1 mil., 90-day bills 1 tick 1 basis
point (1/100) of a point 25.00 Prices are
quoted in annual discount yield (percentage) -gt
Effective discount percentage -gt value e.g.,
T-Bill contract quoted 94.45 (discount 5.55)
(.0555)(90/360).013875 -gt .986125
-gt986,125 1,000,0001-(.0555)(90/360)
986,125 Annualized Return on T-Bills
(Discount Yield 5.55) Daily compounding (1,00
0,000/986,125)(365/90) - 1.0 .0583
5.83 Continuous compounding (13,875/986,125
.0140702) exp(.0140702)(365/90) - 1.0 .0587
5.87
28
Eurodollar Futures E -denominated deposits
in banks outside the U.S.(since 60s) Euro-mark,
Euro-franc, Euro-yen, ... (LIBOR, P/F/M/S/H..)
E rate gt T-Bill rate E futures Most
active, 3-month Euro deposits, IMM/LIFFE,
Cash-settled, 1 million, 1 tick25 Quoted
rate is a quarterly compounded 90-day yield. E
futures price is determined in the same
manner as in T-Bill futures e.g., With a quoted
E price of 93.64, 1,000,0001-(.0636)(9
0/360) 984,100 Hedging with Eurodollar
Futures E futures hedging swap dealers (3
months -gt 1, 2, ..., 10 years) Stack Hedging
Rolling (nearby) contracts over a hedging period
Strip Hedging Hedging with a series of
different maturity contracts at the
same time Rolling Strip Hedging a strip a
(distant) stack
29
E Futures Pricing and Implied Forward Rate
What should be the price of the DEC E futures
below? 11/14 12/19

3/20 -------- 35 days ---------------------
--- 91 days ----------------
------LIBOR8------------------------- ?
------------------- -----------------------
--LIBOR8.0625------------------------
1(.080625)(126/360) 1(.08)(35/360)1DEC(91/
360) DEC8.02 gt 91.98 ltdeciphering
forward rates from the term structure
ltdiscounting/compounding with varying periodic
rates (1r1)(1r2)(1r3)...(1rn)
(1r)n
30
Strip Rate Implied Long-term Rate in a E
Strip e.g. For a one-year strip from 1/22/99
to 1/21/00 Spot 2-month LIBOR
gt 8.3125 -gt MAR 56 days Futures
MAR 91.69 gt 8.31 -gt JUN 91
days JUN 91.65 gt 8.35 -gt SEP 91
days SEP 91.59 gt 8.41 -gt DEC 91
days DEC 91.37 gt 8.63 -gt 1/21 36
days 1(.083125)(56/360) x 1(.0831)(91/360)
x 1(.0835)(91/360) x 1(0.0841)(91/360) x
1(0.0863)(36/360) 1.0878 gt
8.78 8.78(365/360)8.66!
31
Duration (D) Length of time needed to
recover the initial bond investment An average
(PV-weighted) date of cash flow from a bond A
measure of interest rate sensitivity of bond
price Ratio of time-weighted cash flow (PV) to
the bond price M, for zero coupon securities
DltM, for coupon securities ?
t.CFt(1y)-t/P (or D? t.CFt.e-yt/P) It
can be shown that ?P/?y -DP/(1y) Further,
?P/P -D.?y/(1y) or ?P/P
-Dm.?y, where Dm D/(1y) gt The percentage
change in the bond price for a
particular small change in yield is proportional
to D!
32
Duration Matching and Immunization Match the
average duration between cash inflows and
outflows (betw. assets and liabilities), then a
small change in interest rate will have
no/little effect on the portfolio.
Convexity C(1/P)(?2P/?y2) With moderate or
large rate changes, the bond's sensitivity is
further examined by convexity (degree of
curvature). ?P/P -D.?y/(1y)
(1/2).C.(?y)2 With the same D, a high convexity
is preferred to a low C. Duration-Based
Hedge Ratio S (spot) - F (futures) N
?(?s/?f), ?S -S.Ds.?y/(1y), ?F
-F.Df.?y/(1y), and ?1 (between S and F)
N?(?s/?f)?s/?f ??S/?FSDs/FDf
33
E Hedging - An Example 4/29 A company has
just borrowed 15 mil. for 3 months at 1-month
LIBOR 100 b.p. 1-mon LIBOR 8.00 -gt 8.8
(5/29) -gt 9.4 (6/29) JUN E futures 91.88
-gt 91.12 (5/29) SEP E futures 91.44 -gt
-gt -gt 90.16 (6/29) Short Hedge?
First month interest is known 15mil.x(.08100bp)
/12112,500 Second month can be hedged by
shorting JUN E futures Contract Price
1mil. x 100-(.25)(100-91.88) 979,700 With
Ds1/120.8333 and Df3/120.25, the D-based
hedge ratio is NSDs/FDf15,000,000(0.08333)/97
9,700(0.25)5.10 Likewise, third month
interest is hedged by SEP E futures Contract
Price 1mil. x 100-(.25)(100-91.44)978,600
NSDs/FDf15,000,000(0.08333)/978,600(0.25)5.11
gt Short 5 JUN contracts and 5 SEP
contracts. Close out the JUN contracts on 5/29
and the SEP contracts on 6/29. LIBOR
increases sharply and E futures price declines!
5/29 Gain in futures (25x76bp) x 5
contracts 9,500 Loss in spot 15mil. x
(.088-0.80)(1/12) 10,000 6/29 Gain in
futures (25x128bp) x 5 contracts
16,000 Loss in spot 15mil. x
(.094-.080)(1/12) 17,500
34
T-Bond Futures Face 100,000 Maturity 15
or more years (not callable) Coupon 8
equivalent 1 point 1/32 100,000(1/32)(1/10
0) 31.25 Quoted price in thirty-seconds of
a dollar 90-05 90 and 5/32 100,000 x
.9015625 90,156.25 Cash Price Quoted Price
Accrued Interest since last coupon date Since
deliverable bonds are not precisely defined, CBOT
provides conversion factors to adjust for
coupon/maturity differences. But, there will
always be bonds which are cheapest to deliver.
35
Invoice Price Actual price the long pays at
delivery Quoted Futures Price x
Conversion Factor A.I. A.I.(Half-year
Interest)x(DaysElapsed/TotalDays in 6-mon pd.)
e.g., An 8-7/8 bond's last coupon was paid on
8/15. The bond is delivered on
9/30. 8/15-9/3046 days 8/15-2/15184
days A.I.100,000(.08875)(1/2)x(46/184)1,109.
375 Conversion Factor value adjustment for
deliverable bonds Value of a 1 bond
discounted at 8. gt 1 for bonds with a coupon gt
8. lt 1 for bonds with a coupon lt 8. C.T.D.
one with the lowest theoretical futures price
among deliverable bonds Actual futures
price is lower than theoretical price because of
the value of options available to the shorter
Quality option right to deliver the CTD bond
Timing option right to choose any day of the
delivery month Wild Card flexibility between
2pm close and 8pm notice
36
Theoretical Price of T-Bond Futures FPt,T
(CashPrice of CTD/ConvF) (Net Cost of
Carry) Cost of Carry opportunity cost
incurred due to carry/storage less any
opportunity gain from carrying the asset
(prevailing borrowing rate - coupon rate
on CTD) FS(1r-d)t gt FS.e(r-d)t
(1/CF)(CPtAI)Rt(t/360)-Y(t/365) From FPt,T
(CPt/CF) (1/CF)(CPtAI)Rt(t/360)-Y(t/365),
(CPtAI)Rt(t/360)-Y(t/365) FPt,T(CF) -
CPt Rt (360/t) x FPt,T(CF)-CPtY(t/365
)/(CPtAI) gt With FPactual futures price, a
repo rate can be inferred. When the shorter
buys the bond in the cash market and holds it
until delivery, purchase price CPtAI
and net expected proceeds price change
coupon FP(CF)-CPt Y(t/365). So, the
(annualized) holding-period return is
R(360/t) x FP(CF)-CPtY(t/365)/(CPtAI)
Implied Repo Rate (IRR)
37
T-Bond Futures (contd) CTD one with the lowest
theoretical futures price (FP) gt one with the
highest cost of carry gt one with the highest
opportunity (borrowing) cost gt one with the
highest (implied) repo rate gt one with the
highest yield when boughtheld till delivery If
IRR gt actual repo rate, buy cash bonds and short
futures. (IRR is based on the actual futures
price) The higher the actual futures price,
the higher the IRR. So, if IRR is higher than
the actual rate, this means the futures is
overpriced. If IRR lt actual repo rate, buy
futures and short cash bonds.
38
Currency Futures Example 3/1 - A U.S. company
expects to receive Y50 mil. at the end of
July. (IMM Yen futures - M, J, S, D) A good
rule of thumb for the choice of delivery
month Choose a delivery month that is as close
as possible to, but later than, the planned
hedge unwinding. (SEP!) 3/1 Yen futures
0.7800 cents per Yen 7/31 "
0.7250 " Yen spot 0.7200 cents per
Yen (Yen depreciates) Short 4 contracts
of SEP Yen futures. Close out the position on
7/31. Then, Cover Basis 0.7200-0.7250
-.0050 Gain on futures 0.7800-0.7250
0.0550 Effective price at 7/31
0.72000.05500.7750
0.7800-0.00500.7750 Total at
7/31 (0.007750) x 50mil. 387,500 ( gain on
futures(0.000550)x50mil.27,500)
39
Interest Rate Parity Borrow W1 at the rate of rw
and buy dollars at a spot exchange rate of S
(W/). Deposit the dollars at rus for t. What
is the forward exchange rate F (W/) that should
apply when the won fund is repaid? Principal
Interest in deposit (1/S)(1rust)
Principal Interest in W loan (1rwt) gt
(1/F)(1rwt) (1/S)(1rust) (1/F)(1rwt) gt
F(1rust) S(1rwt) gt F S(1rwt)/(1rust)
S S(rw-rus)t/(1rust) gt F S.e(rw-rus)t
Cost of carry borrowing cost(rw) - benefit
(rus)