The slides provides basic conception of financial markets and exemplify the financial derivatives, arbitrage and arbitrage position

1. Sako Mwakalobo
INTERNATIONAL BOND MARKET
• The international bond market
encompasses two basic market segment
• Foreign bonds
• Eurobonds
• A foreign bond issue is one offered by
foreign borrower to the investor in a
national capital market and denominated
in that nation’s currency. e.g. a Germany
MNC issuing dollar denominated bonds to
US investor.

2. Sako Mwakalobo
EUROBOND
• Eurobond issue is one denominated in a
particular currency but sold to investors in
national capital markets other than the
country that issued the denominating
currency. e.g. a Dutch borrower issuing a
dollar denominated bonds to investors in
the U.K, Switzerland, and the Netherlands.
• The market for foreign bonds and
Eurobonds operate in parallel with the
domestic national bond markets, and all
three market groups compete with one
another

3. Sako Mwakalobo
EUROBOND
• Eurobonds are known by the currency ibn which
they are denominated, for example, U.S. dollar
Eurobonds, yen Eurobonds and Swiss franc
Eurobonds or correspondingly, Eurodollar bonds,
Euroyen bonds, and EuroSF bonds
• The Foreign bonds frequently have colorful
names that designate the country in which they
are issued. e.g. Yankee bonds are dollar –
denominated foreign bonds originally sold to US
investor, Samurai bonds are yen denominated
foreign bonds, sold in Japan, and Bulldogs are
pound sterling denominated foreign bonds sold
in the UK

4. Sako Mwakalobo
BEARER BONDS AND REGISTERED BONDS
• Eurobond, Bearer bond, possession is evidence
of ownership. The issue does not keep any
records indicating who is the current owner of a
bond.
• Registered bonds, the owner’s name is on the
bond and it is also recorded by the issuer, or
else the owner’s name is assigned toe the bond
serial number recorded by the issuer. When a
registered bond is sold, a new bond certificate
is issued with the new owner’s name, or the
new owner’s name is assigned to the bond
serial number.
• Which one would you like and why?

5. Sako Mwakalobo
FOREIGN BONDS
• The foreign bonds must meet the security
regulations of the country in which they
are issued. These may include
• Prospectus disclosing the financial
information about the issuer and should
be available to the would be investors
• They may be required to meet all
conditions as local bonds.
• They may not be sold to the residents of
the country concerned.

6. Sako Mwakalobo
GLOBAL BONDS
• It is a very larger international bond offering by
a single borrower that is simultaneously sold in
North America, Europe and Asia
• They follow the bond registration requirements
of domestic bonds, but have the fee structure of
Eurobonds.
• They enlarge the borrower’s opportunities for
financing at reduced costs. Purchasers mainly
institutional investors to date, desire the
increased liquidity of the issue and have been
willing to accept lower yields.

7. Sako Mwakalobo
GLOBAL BOND
• The largest corporate bond issue is the
$14.6 billion Deutsch Telecom
multicurrency offering. The issue
includes three US dollar tranches with 5,
10 and 30 year maturities totaling $9.5
billion, two euro tranches with 5,10 year
maturities totalling €3 billion, two British
pound sterling tranches with 5 and 30
year maturities totaling £950 million and
one 5 year Japanese yen tranche of ¥ 90
billion.

8. Sako Mwakalobo
PARTICIPANTS IN EUROBOND MARKET
• Private enterprises, for example in France, one
of them is Renault
• Public enterprises
• Financial institutions
• Governments and Central Banks
• International organizations, such as World
Bank, European Bank of investment
The industrialized countries seems to have
greater recourse to the market; Western Europe
is on the top, followed by Japan and USA

9. Sako Mwakalobo
Investors and financial institutions
• The investors in the Euromarkets are
mostly institutional investors, such as
insurance companies, mutual funds,
pension funds.
• The principal financial institituions and
banks that participate in these issues
are of international reputation, namely
Dutsche Bank, Paribas, Merril Lynch,
Goldman Sachs, Credit Lyonnais.

10. Sako Mwakalobo
ORGANISATION OF EUROBOND MARKET
• The market can be bifurcated into two
segments, namely, Primary market in
which securities are issued and the
Secondary market in which securities
are traded.
• The figure below indicates the steps
involved in a primary issue.

11. Sako Mwakalobo
Issuer
Selection of the lead manager
Selection of co-lead managers by the lead manager
Guarantee syndicate:
•Lead manager
•Co-lead managers
•Major Guarantor
•Minor Guarantor
•Sub-major and sub
Minor guarantors
Placement syndicate:
•Banks
•Placements
•Establishment
Different phases of Euro-issue

12. Sako Mwakalobo
Types of instruments ( characteristics of
Eurobonds
• The international bond market has been much
more innovative than the domestic bond market
in the types of instruments offered to investors.
• Straight fixed rate issue- these are the most
current and represent about three-for the of
total volume. The issues have been designated
maturity date at which the principal of the
bond issue is promised to be repaid. During the
life of the bond , fixed coupon payments, which
are percentage of face value are paid as
interest to the bondholders. In contrast to
many domestic bonds, which make semiannual
coupon payments, coupon interest on
Eurobonds is typically paid annually.

13. Sako Mwakalobo
Types of Instruments
• Floating rate bonds( FRN)- the interest rate of the
bonds is revised every three or six months.
Common reference rates are either three or six
months US dollar LIBOR.
• Equity related bonds- there are two types of
bonds.
• Convertible bonds – issue allows the investor to
exchange the bond for a predetermined number
of equity shares of the issuer. The floor value of
convertible bond is its straight rate bond
values.
• Bonds with warrants – these are straight fixed-
rate bonds with the addition of a call option ( or
warrant) feature. The warrant entitles the
bondholder to purchase a certain number of
equity shares in the issuer at the pre-stated
price over a predetermined period of time

14. Sako Mwakalobo
Types of instruments
• Zero-coupon bonds – are sold at a
discount from face value and do not pay
any coupon interest over their life. At
maturity the investor receives the full
face value.
• Stripped bond – is a zero coupon bond
that results from stripping the coupons
and principal from a coupon bond. The
results is the series of zero-coupon
bonds represented by the individual
coupon and principal payments.

15. Sako Mwakalobo
Types of instruments
• Reverse floating rate bonds- the bonds
pay a higher interest rate when the rate
of reference decreases. The coupon is
fixed at a rate minus- LIBOR so that
when LIBOR decreases, the interest rate
increases. e.g. suppose Euro-bank offers
a rate of 16- LIBOR %; therefore, a LIBOR
of 7.5 per cent, the effective rate is 16 –
8.2%, i.e 7.8%.

16. Sako Mwakalobo
See handout 6 for continuation of
stock markets, stock exchange
procedures and assessment of
shares performance

17. Sako Mwakalobo
The Nature of Derivatives
A derivative is an instrument whose
value depends on the values of other
more basic underlying variables

18. Sako Mwakalobo
Examples of Derivatives
•Futures Contracts
•Forward Contracts
•Swaps
•Options

19. Sako Mwakalobo
Derivatives Markets
• Exchange traded
• Traditionally exchanges have used the
open-outcry system, but increasingly
they are switching to electronic trading
• Contracts are standard there is virtually
no credit risk
• Over-the-counter (OTC)
• A computer- and telephone-linked
network of dealers at financial
institutions, corporations, and fund
managers
• Contracts can be non-standard and there
is some small amount of credit risk

20. Sako Mwakalobo
Size of OTC and Exchange Markets
Source: Bank for International Settlements. Chart shows total principal amounts
for OTC market and value of underlying assets for exchange market
0
20
40
60
80
100
120
140
160
180
200
220
240
Jun-98 Jun-99 Jun-00 Jun-01 Jun-02 Jun-03 Jun-04
Size of Market ($
trillion)
OTC
Exchange

21. Sako Mwakalobo
Ways Derivatives are Used
• To hedge risks
• To speculate (take a view on the
future direction of the market)
• To lock in an arbitrage profit
• To change the nature of a liability
• To change the nature of an
investment without incurring the
costs of selling one portfolio and
buying another

22. Sako Mwakalobo
Forward Contracts
• Forward contracts are similar to futures
except that they trade in the over-the-
counter market
• Forward contracts are particularly
popular on currencies and interest rates

23. Sako Mwakalobo
Foreign Exchange Quotes for JPY
Jan 22, 2007 (16:23 EST)
Bid Offer
Spot 121.62 121.63
1-month
forward
121.08 121.09
3-month
forward
120.17 120.18
6-month
forward
118.75 118.77

24. Sako Mwakalobo
Forward Price
• The forward price for a contract is
the delivery price that would be
applicable to the contract if were
negotiated today (i.e., it is the
delivery price that would make the
contract worth exactly zero)
• The forward price may be different
for contracts of different maturities

25. Sako Mwakalobo
Terminology
• The party that has agreed to buy
has what is termed a long position
• The party that has agreed to sell
has what is termed a short position

26. Sako Mwakalobo
Example
• On June 3, 2003 the treasurer of a
corporation enters into a long forward
contract to buy £1 million in six months
at an exchange rate of 1.6100
• This obligates the corporation to pay
$1,610,000 for £1 million on December 3,
2003
• What are the possible outcomes?

27. Sako Mwakalobo
Profit from a
Long Forward Position
Profit
Price of Underlying
at Maturity, ST
K

28. Sako Mwakalobo
Profit from a
Short Forward Position
Profit
Price of Underlying
at Maturity, ST
K

29. Sako Mwakalobo
Futures Contracts
• Agreement to buy or sell an asset for a
certain price at a certain time
• Similar to forward contract
• Whereas a forward contract is traded
OTC, a futures contract is traded on an
exchange

30. Sako Mwakalobo
Exchanges Trading Futures
• Chicago Board of Trade
• Chicago Mercantile Exchange
• LIFFE (London)
• Eurex (Europe)
• BM&F (Sao Paulo, Brazil)
• TIFFE (Tokyo)
• and many more (see list at end of book)

31. Sako Mwakalobo
Examples of Futures Contracts
Agreement to:
• buy 100 oz. of gold @ US$400/oz.
in December (NYMEX)
• sell £62,500 @ 1.5000 US$/£ in
March (CME)
• sell 1,000 bbl. of oil @
US$20/bbl. in April (NYMEX)

32. Sako Mwakalobo
1. Gold: An Arbitrage
Opportunity?
Suppose that:
The spot price of gold is
US$300
The 1-year forward price of
gold is US$340
The 1-year US$ interest rate
is 5% per annum
Is there an arbitrage opportunity?

33. Sako Mwakalobo
2. Gold: Another Arbitrage
Opportunity?
Suppose that:
-The spot price of gold is
US$300
-The 1-year forward price
of gold is US$300
-The 1-year US$ interest
rate is 5% per annum
Is there an arbitrage opportunity?

34. Sako Mwakalobo
The Forward Price of Gold
If the spot price of gold is S and the forward
price for a contract deliverable in T years is
F, then
F = S (1+r )T
where r is the 1-year (domestic currency)
risk-free rate of interest.
In our examples, S = 300, T = 1, and r =0.05 so
that
F = 300(1+0.05) = 315

35. Sako Mwakalobo
1. Oil: An Arbitrage Opportunity?
Suppose that:
- The spot price of oil is US$19
- The quoted 1-year futures
price of oil is US$25
- The 1-year US$ interest rate
is 5% per annum
- The storage costs of oil are
2% per annum
Is there an arbitrage opportunity?

36. Sako Mwakalobo
2. Oil: Another Arbitrage
Opportunity?
Suppose that:
- The spot price of oil is US$19
- The quoted 1-year futures
price of oil is US$16
- The 1-year US$ interest rate
is 5% per annum
- The storage costs of oil are
2% per annum
Is there an arbitrage opportunity?

37. Sako Mwakalobo
Options
• A call option is an option to buy a
certain asset by a certain date for a
certain price (the strike price)
• A put option is an option to sell a
certain asset by a certain date for a
certain price (the strike price)

38. Sako Mwakalobo
American vs European Options
• An American option can be exercised at
any time during its life
• A European option can be exercised only
at maturity

39. Sako Mwakalobo
Intel Option Prices (Jan 22, 2007;
Stock Price=86.79)
Strike
Price
Feb
Call
Mar
Call
Apr
Call
Feb
Put
Mar
Put
Apr
Put
85.00 4.10 5.70 7.70 2.05 3.30 4.90
90.00 1.85 3.30 5.30 4.70 5.90 7.50

40. Sako Mwakalobo
Exchanges Trading Options
• Chicago Board Options Exchange
• American Stock Exchange
• Philadelphia Stock Exchange
• Pacific Exchange
• LIFFE (London)
• Eurex (Europe)
• and many more

41. Sako Mwakalobo
Options vs Futures/Forwards
• A futures/forward contract gives the
holder the obligation to buy or sell at a
certain price
• An option gives the holder the right to
buy or sell at a certain price

42. Sako Mwakalobo
Types of Traders
• Hedgers
• Speculators
• Arbitrageurs
Some of the largest trading losses in derivatives have
occurred because individuals who had a mandate to be
hedgers or arbitrageurs switched to being speculators

43. Sako Mwakalobo
Hedging Examples
• A US company will pay £10 million
for imports from Britain in 3 months
and decides to hedge using a long
position in a forward contract
• An investor owns 1,000 Microsoft
shares currently worth $28 per
share. A two-month put with a strike
price of $27.50 costs $1. The
investor decides to hedge by buying
10 contracts

44. Sako Mwakalobo
Value of Microsoft Shares with
and without Hedging
20,000
25,000
30,000
35,000
40,000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging

45. Sako Mwakalobo
Speculation Example
• An investor with $4,000 to invest feels
that Amazon.com’s stock price will
increase over the next 2 months. The
current stock price is $40 and the
price of a 2-month call option with a
strike of 45 is $2
• What are the alternative strategies?

46. Sako Mwakalobo
Arbitrage Example
• A stock price is quoted as £100 in
London and $172 in New York
• The current exchange rate is 1.7500
• What is the arbitrage opportunity?

47. Sako Mwakalobo
Hedge Funds
• Hedge funds are not subject to the same rules as mutual
funds and cannot offer their securities publicly.
• Mutual funds must
• disclose investment policies,
• makes shares redeemable at any time,
• limit use of leverage
• take no short positions.
• Hedge funds are not subject to these constraints.
• Hedge funds use complex trading strategies are big
users of derivatives for hedging, speculation and
arbitrage

48. Sako Mwakalobo
Real World Situation - Cash
• Japanese Bank: Borrow USD in Interbank
Euromarket for 3 month term, T
• Could perform the same transaction as a
Synthetic in the FX and domestic yen mkt
• Borrow yen in local mkt for term T, at
L(t0,Y)
• Sell yen and buy USD in spot FX mkt at
e(t0,Y)
• Finally, the bank buys yen in the
forward FX mkt for delivery at t0+T

49. Sako Mwakalobo
Real World Situation - Cash
• Cash Flows are Additive
+
+
=
t0 t0+T
Y
Yx(1+L(t0,Y)xT)
USD
Y
Yx(1+L(t0,Y)xT)
USD
USDx(1+L(t0,$)xT)
Borrow Y for T at L(t0,Y)
Pay back:
Yx(1+L(to,Y)xT)
Buy USD sell Y at e(t0,Y)
Y=e(t0,Y)xUSD
Buy Y forward, t0+T
delivery in amount so
Yx(1+L(t0,Y)xT)
= f(t0,T;Y)xUSD1
USD1=USDx(1+L(t0,$)xT)
USDx(1+L(t0,$)xT)

50. Sako Mwakalobo
Real World Situation – Cash
• At t0
•Borrowing rates in USD & Yen are
known
•Exchange rate USD & Yen are known
• Forward market for Yen must preclude
riskless arbitrage so,
e(t0,Y)xUSD x (1+L(t0,Y)xT) = f(t0,T;Y) x USDx(1+L(t0,$)xT)
or,
f(t0,T;Y) = e(t0,Y) x [(1+L(t0,Y)xT) / (1+L(t0,$)xT)]

51. Sako Mwakalobo
Money Rates – Close Friday,
1/26/07
/ YEN /
1WK .345
1MO .35
2MO .435
3MO .47
4MO .505
5MO .515
6MO .545
9MO .585
1YR .655
/ US DOLLAR /
1WK 5.265
1MO 5.275
2MO 5.285
3MO 5.295
4MO 5.295
5MO 5.355
6MO 5.365
9MO 5.385
1YR 5.39

52. Sako Mwakalobo
Spot/Forwards – USD-JPY
U S D -J P Y S P O T / F O R W A R D S Source CMPN Composite (NY)
Close Time of Bid Ask Bid Rate Ask Rate Time of PRD
Fri 1/26 Offset Offset Offset Rate 2
Spot 16:59 121.54 121.54 121.54 121.54 16:59
1 Week 16:59 -11.59 -11.59 121.42 121.42 16:59
1 Month 16:59 -47.80 -47.80 121.06 121.06 16:59
2 Month 16:59 -96.20 -96.20 120.58 120.58 16:59
3 Month 16:59 -140.80 -140.80 120.13 120.13 16:59
4 Month 16:59 -192.90 -192.90 119.61 119.61 16:59
5 Month 16:59 -239.41 -239.41 119.15 119.15 16:59
6 Month 16:59 -287.14 -287.14 118.67 118.67 16:59
9 Month 16:59 -424.05 -424.05 117.30 117.30 16:59
1 Year 16:59 -554.20 -554.20 116.00 116.00 16:59
2 Year 16:59 -1022.37 -1022.37 111.32 111.32 16:59
3 Year 16:59 -1422.50 -1422.50 107.32 107.32 16:59
4 Year 16:59 -1789.00 -1789.00 103.65 103.65 16:59
5 Year 16:59 -2146.00 -2146.00 100.08 100.08 16:59
* All forward offset rates on this screen are direct quotes from banks; see
FRD for rates calculated through USD

53. Sako Mwakalobo
1. Gold: An Arbitrage
Opportunity?
Suppose that:
The spot price of gold is
US$300
The 1-year forward price of
gold is US$340
The 1-year US$ interest rate
is 5% per annum
Is there an arbitrage opportunity?

54. Sako Mwakalobo
2. Gold: Another Arbitrage
Opportunity?
Suppose that:
-The spot price of gold is
US$300
-The 1-year forward price
of gold is US$300
-The 1-year US$ interest
rate is 5% per annum
Is there an arbitrage opportunity?

55. Sako Mwakalobo
The Forward Price of Gold –
The Principal of Cash and
Carry
• If the spot price of gold is S(t0) and the forward price
for a contract deliverable in T years is F(t0,T), then
• Can borrow money, buy gold, and sell the commodity
forward - where there should be no arbitrage:
F(t0,T) - S(t0) x (1+r )T
= 0
where r is the 1-year money rate of interest to finance
the gold carry trade.
• In our examples, S = 300, T = 1, and r =0.05 so that
F(t0,T) = 300(1+0.05) = 315
• The no arbitrage 1 year forward price of gold is $315

56. Sako Mwakalobo
The Forward Price of Gold – The
Principal of Cash and Carry
• How does this come about?
S(t0)
t0
receive
pay S(t0)x(1+r)
Gold
S(t0)
F(t0)
Gold
Own
Deliver
Gold
Gold
Borrow S(t0)
Buy Gold at S(t0)
Sell Gold Forward at F(t0)
No Arbitrage condition says:
F(t0) – S(t0)x(1+r) = 0
+
+
=

57. Sako Mwakalobo
Gold Arbitrage?
• The no arbitrage gold, 1-year forward condition is
F(t0,T) - S(t0) x (1+r )T
= 0
• If 1-year forward is $340, then
F(t0,T) - S(t0) x (1+r )T
> 0
so our strategy is to borrow money, buy gold, sell it forward,
deliver gold, and pay off loan for a riskless profit of $25
• If 1-year forward is $300, then
F(t0,T) - S(t0) x (1+r )T
< 0
and if I own gold, I can sell it, deposit proceeds, buy forward,
pay with the proceeds of the deposit and collect a riskless
profit of $15 over the 1-year period

58. Sako Mwakalobo
Hedging Example
• A US company will pay £10 million for imports from
Britain in 3 months and decides to hedge using a
long position in a forward contract
• Possible strategies:
• Buy £ now, deposit in bank, withdraw £10
million in 3 months, pay for imports
• Buy £10 million forward in 3 months, deposit
USD, use deposit proceeds to settle and pay
for imports
• Do nothing now and buy £10 million in the
spot FX market in 3 months
• First 2 are riskless, third has currency risk.
• Which makes most sense?

59. Sako Mwakalobo
Futures Contracts
• Available on a wide range of underlyings
• Exchange traded
• Specifications need to be defined:
• What can be delivered,
• Where it can be delivered, &
• When it can be delivered
• Settled daily

60. Sako Mwakalobo
Forward Contracts vs Futures
Contracts
Private contract between 2 parties Exchange traded
Non-standard contract Standard contract
Usually 1 specified delivery date Range of delivery dates
Settled at end of contract Settled daily
Delivery or final cash
settlement usually occurs
Contract usually closed out
prior to maturity
FORWARDS FUTURES
Some credit risk Virtually no credit risk

61. Sako Mwakalobo
Margins
• A margin is cash or marketable
securities deposited by an investor with
his or her broker
• The balance in the margin account is
adjusted to reflect daily settlement
• Margins minimize the possibility of a loss
through a default on a contract

62. Sako Mwakalobo
Example of a Futures Trade
• An investor takes a long position in
2 December gold futures contracts
on June 5
• contract size is 100 oz.
• futures price is US$400
• margin requirement is
US$2,000/contract (US$4,000 in total)
• maintenance margin is
US$1,500/contract (US$3,000 in total)

63. Sako Mwakalobo
A Possible Outcome
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
400.00 4,000
5-Jun 397.00 (600) (600) 3,400 0
. . . . . .
. . . . . .
. . . . . .
13-Jun 393.30 (420) (1,340) 2,660 1,340
. . . . . .
. . . . .
. . . . . .
19-Jun 387.00 (1,140) (2,600) 2,740 1,260
. . . . . .
. . . . . .
. . . . . .
26-Jun 392.30 260 (1,540) 5,060 0
+
= 4,000
3,000
+
= 4,000
<

64. Sako Mwakalobo
Other Key Points About Futures
• They are settled daily
• Closing out a futures position
involves entering into an offsetting
trade
• Most contracts are closed out
before maturity

65. Sako Mwakalobo
Collateralization in OTC Markets
• It is becoming increasingly common for
contracts to be collateralized in OTC
markets
• They are then similar to futures
contracts in that they are settled
regularly (e.g. every day or every week)

66. Sako Mwakalobo
Another Detail for Cash and Carry
Arbitrage
• Contract price changes with longer term
•Higher or Lower
• To this point we have neglected storage cost
• Lets re-visit no-arbitrage equation
F(t0,T) - S(t0) x [(1+r )T
] = - Storage (T)
• Storage costs ignored in earlier gold example
• No storage costs for FX
• Lets look at consequence of storage

67. Sako Mwakalobo
Futures Prices for Gold on Feb 4, 2004: Prices
Increase with Maturity
Storage Costs < Financing
(a) Gold
398
399
400
401
402
403
404
405
406
407
408
Feb-04 Apr-04 Jun-04 Aug-04 Oct-04 Dec-04
Contract Maturity Month
FuturesPrice($peroz)

68. Sako Mwakalobo
Futures Prices for Oil on February 4, 2004:
Prices Decrease with Maturity
Storage Cost > Financing
(b) Brent Crude Oil
24
25
26
27
28
29
30
Mar-04 May-04 Jul-04 Sep-04 Nov-04 Jan-05
Contract Maturity Month
FuturesPrice($perbarrel)

69. Sako Mwakalobo
Delivery
• If a futures contract is not closed out before
maturity, it is usually settled by delivering the
assets underlying the contract. When there
are alternatives about what is delivered,
where it is delivered, and when it is delivered,
the party with the short position chooses.
• A few contracts (for example, those on stock
indices and Eurodollars) are settled in cash

70. Sako Mwakalobo
Some Terminology
• Open interest: the total number of contracts
outstanding
• equal to number of long positions or
number of short positions
• Settlement price: the price just before the
final bell each day
• used for the daily settlement process
• Volume of trading: the number of trades in 1
day

71. Sako Mwakalobo
Convergence of Futures to Spot
Time Time
(a) (b)
Futures
Price
Futures
Price
Spot Price
Spot Price

72. Sako Mwakalobo
Questions
• When a new trade is completed
what are the possible effects on
the open interest?
• Can the volume of trading in a day
be greater than the open interest?

73. Sako Mwakalobo
Regulation of Futures
• Regulation is designed to
protect the public interest
• Regulators try to prevent
questionable trading practices
by either individuals on the
floor of the exchange or
outside groups

74. Sako Mwakalobo
Accounting & Tax
• Ideally hedging profits (losses) should be
recognized at the same time as the losses
(profits) on the item being hedged
• Ideally profits and losses from speculation
should be recognized on a mark-to-market
basis
• Roughly speaking, this is what the
accounting and tax treatment of futures in
the U.S.and many other countries
attempts to achieve

75. Sako Mwakalobo
Forward Contracts vs Futures
Contracts
Private contract between 2 parties Exchange traded
Non-standard contract Standard contract
Usually 1 specified delivery date Range of delivery dates
Settled at end of contract Settled daily
Delivery or final cash
settlement usually occurs
Contract usually closed out
prior to maturity
FORWARDS FUTURES
Some credit risk Virtually no credit risk

76. Sako Mwakalobo
Foreign Exchange Quotes
• Futures exchange rates are quoted as the
number of Tshs per unit of the foreign
currency
• Forward exchange rates are quoted in the
same way as spot exchange rates. This
means that GBP, EUR, AUD, and NZD are
quoted as Tshs per unit of foreign currency.
Other currencies (e.g., CAD and JPY) are
quoted as units of the foreign currency per
Tshs.

77. Sako Mwakalobo
Long & Short Hedges
• A long futures hedge is appropriate
when you know you will purchase an
asset in the future and want to lock in
the price
• A short futures hedge is appropriate
when you know you will sell an asset in
the future & want to lock in the price

78. Sako Mwakalobo
Arguments in Favor of Hedging
Companies should focus on the main
business they are in and take steps
to minimize risks arising from
interest rates, exchange rates, and
other market variables

79. Sako Mwakalobo
Arguments against Hedging
• Shareholders are usually well diversified
and can make their own hedging
decisions
• It may increase risk to hedge when
competitors do not
• Explaining a situation where there is a
loss on the hedge and a gain on the
underlying can be difficult

80. Sako Mwakalobo
Convergence of Futures to Spot
(Hedge initiated at time t1 and closed out at time t2)
Time
Spot
Price
Futures
Price
t1 t2

81. Sako Mwakalobo
Basis Risk
• Basis is the difference
between spot & futures
• Basis risk arises because of
the uncertainty about the
basis when the hedge is
closed out

82. Sako Mwakalobo
Short Hedge
• Suppose that
F1 : Initial Futures Price
F2 : Final Futures Price
S1 : Initial Asset Price
S2 : Final Asset Price
• You hedge the future sale of an asset (one which you
might be long) by entering into a short futures contract
P/L = (S1– F1) – (S2– F2) = S1– [S2+ (F1 – F2)]
= S1– [F1+ (S2 – F2)]
• Price Realized = S2+ (F1– F2) = F1+ Basis

83. Sako Mwakalobo
Long Hedge
• Suppose that
F1 : Initial Futures Price
F2 : Final Futures Price
S1 : Initial Asset Price
S2 : Final Asset Price
• You hedge the future purchase of an asset (one you
might be short) by entering into a long futures
contract
P/L = – (S1– F1) + (S2– F2) = – S1+ [S2 – (F2 – F1)]
= – S1+ [F1+ (S2 – F2)]
• Cost of Asset = S2– (F2– F1) = F1+ Basis

84. Sako Mwakalobo
Choice of Contract
• Choose a delivery month that is as close
as possible to, but later than, the end of
the life of the hedge
• When there is no futures contract on the
asset being hedged, choose the contract
whose futures price is most highly
correlated with the asset price. This is
known as cross hedging.

85. Sako Mwakalobo
Optimal Hedge Ratio
Proportion of the exposure that should optimally be
hedged is
where
σS is the standard deviation of ∆S, the change in the
spot price during the hedging period,
σF is the standard deviation of ∆F, the change in the
futures price during the hedging period
ρ is the coefficient of correlation between ∆S and
∆F.
F
S
σ
σ
ρ

86. Sako Mwakalobo
Optimal Hedge Ratio – Minimum
Variance Result
• The number of futures, NF, in ratio h (the hedge ratio),
required to hedge NA units of an asset follows from P/L
P/L = (NAS1 – NFF1) – (NAS2 – NFF2)
= NF ∆F - NA ∆S = NA x (∆Fh – ∆S) where NF = h x NA
min [∆Fh – ∆S] when the variance of the linear combination
of ∆F & ∆S ,
v = Var [∆Fh – ∆S] = σS
2
– h2
σF
2
– 2 h ρ σSσF
minimize v when h is such that dv/dh = 0 if d2
h/dh2
> 0
or 2 h σF
2
– 2 ρ σSσF = 0 implies
h =
F
S
σ
σ
ρ

87. Sako Mwakalobo
Hedging Using Index Futures
To hedge the risk in a portfolio the
number of contracts that should be
shorted is
where P is the value of the portfolio,
β is its beta, and A is the value of
the assets underlying one futures
contract
β
P
A

88. Sako Mwakalobo
Reasons for Hedging an Equity
Portfolio
• Desire to be out of the market for a short
period of time. (Hedging may be cheaper
than selling the portfolio and buying it
back.)
• Desire to hedge systematic risk
(Appropriate when you feel that you have
picked stocks that will outpeform the
market.)

89. Sako Mwakalobo
Example
Value of S&P 500 is 1,000
Value of Portfolio is $5 million
Beta of portfolio is 1.5
What position in futures contracts on the
S&P 500 is necessary to hedge the
portfolio?

90. Sako Mwakalobo
Changing Beta
• What position is necessary to reduce the
beta of the portfolio to 0.75?
• What position is necessary to increase
the beta of the portfolio to 2.0?

91. Sako Mwakalobo
Hedging Price of an Individual
Stock
• Similar to hedging a portfolio
• Does not work as well because only the
systematic risk is hedged
• The unsystematic risk that is unique to
the stock is not hedged

92. Sako Mwakalobo
Why Hedge Equity Returns
• May want to be out of the market for a while.
Hedging avoids the costs of selling and
repurchasing the portfolio
• Suppose stocks in your portfolio have an
average beta of 1.0, but you feel they have been
chosen well and will outperform the market in
both good and bad times. Hedging ensures that
the return you earn is the risk-free return plus
the excess return of your portfolio over the
market.

93. Sako Mwakalobo
Rolling The Hedge Forward
• We can use a series of futures
contracts to increase the life of a
hedge
• Each time we switch from 1 futures
contract to another we incur a type
of basis risk