International Finance

1
International Finance

• Lecture 6

2
World Financial Markets and Institutions

• International Banking and Money Market
• International Bond Market
• International Equity Markets
• Futures and Options on Foreign Exchange
• Currency and Interest Rate Swaps
• International Portfolio Investment

3
Futures Contracts

• A futures contract specifies that a certain
  currency will be __________ for another at a
  specified time in the future at prices specified
  today.
• A futures contract is different from a forward
  contract
• Futures are standardized contracts trading on
  organized exchanges with daily resettlement
  through a clearinghouse.
• Standardizing Features
• __________ Size
• __________ Month
• Daily __________
• ________ requirements (initial, maintenance
  margins)

4
Currency Futures Markets

• The Chicago Mercantile Exchange (CME) is by far
  the largest.
• Others include
• The Philadelphia Board of Trade (PBOT)
• The MidAmerica Commodities Exchange
• The Tokyo Financial Exchange
• The London International Financial Futures
  Exchange (LIFFE)

5
After Hours Trading

• __________ -hours trading on CME GLOBEX runs from
  230 p.m. to 400 p.m dinner break and then back
  at it from 600 p.m. to 600 a.m. CST.
• Singapore Exchange (SGX) offers contracts.
• There are other markets, but none are close to
  CME and SGX trading volume.

6
Daily Resettlement An Example

• Suppose you want to speculate on a rise in the
  / exchange rate (specifically you think that
  the dollar will appreciate).

Currently __________. The 3-month forward price
is __________.
7
Daily Resettlement

• Currently 1 140 and it appears that the
  dollar is strengthening.
• If you enter into a 3-month futures contract to
  sell at the rate of 1 150 you will make
  money if the yen depreciates. The contract size
  is 12,500,000
• You do not have to have now, either way you
  have committed yourself to sell 12,500,000 and
  receive in exchange 12,500,000 1/150 /
  _________
• Your initial margin is 4 of the contract value

8
Daily Resettlement

• On Thursday the futures rate closes at 1 149,
  then your positions value drops. Heres why.
• Your have a short position in . The
  mark-to-market profit/loss for short position
  is_______.
• That is, you have lost ________overnight
• The 559.28 comes out of your 3,333.33 margin
  account, leaving 2,774.05

9
Reading a Futures Quote
Highest and lowest prices over the lifetime of
the contract.
Daily Change
Closing price
Lowest price that day
Highest price that day
Opening price
Number of open contracts
Expiry month
10
Currency Futures Trading Example

• CAN futures contract expiring on June 14 trades
  on CME at US0.7761 on January 9. On the last
  trading day of the contract in June the spot rate
  is US0.7570. The contract size is CAN100,000.
• What is the profit/loss for a trader who took a
  long position in the contract on January 9?
• What is the profit/loss for a trader who took a
  short position in the contract on January 9?

11
Currency Futures Trading Example
12
Eurodollar Interest Rate Futures

• Widely used futures contract for hedging
  short-term U.S. dollar interest rate risk.
• The underlying asset is a 1,000,000 90-day
  Eurodollar depositthe contract is __________.
• Traded on the CME and the Singapore International
  Monetary Exchange.
• Eurodollar futures prices are stated as an index
  number of three-month LIBOR calculated as F
  100 LIBOR.
• For example, if the closing price F is 98.23, the
  implied yield is 5.77 percent __________
• Hedging/speculation just like with forwards,
  except standardized amounts and daily resettlement

13
Example

• The size of a yen futures contract at CME is 12.5
  million yen. The initial margin is 2,025 per
  contract and the maintenance margin is 1,500.
  You decide to buy ten contracts with maturity on
  June 17, at the current futures price of
  0.01056. Today is April 1 and the spot rate is
  0.01041. Indicate cash flows on your position if
  the following prices are subsequently observed.

April 1 April 2 April 3 April 4 June 16 June 17
Spot, /Y 0.01041 0.01039 0.01000 0.01150 0.01150 0.01100
Futures, /Y 0.01056 0.01054 0.01013 0.01160 0.01151 0.01100
14
Example solved
April 1 April 2 April 3 April 4 June 16 June 17
Spot, /Y 0.01041 0.01039 0.01000 0.01150 0.01150 0.01100
Futures, /Y 0.01056 0.01054 0.01013 0.01160 0.01151 0.01100
Gain/Loss
Margin before CF
CF from investor
Margin after CF
15
Example

• It is 1 April now and current 3-month LIBOR is
  6.25. Eurodollar futures contracts are traded on
  CME with size of 1 million at 93.280 with June
  delivery. The initial margin is 540 and the
  maintenance margin is 400. You are a corporate
  treasurer and you know your company will have to
  pay 10 million in cash for goods that will be
  delivered on June 17. You will sell the goods for
  profit, but you will not receive payment until
  September 17. Thus, you know you will have to
  borrow 10 million for 3 months in June.
• What is the forward rate implicit in the
  Eurodollar futures price?
• How to lock in 3-month borrowing rate for June 17
  using Eurodollar futures?
• On June 17, the Eurodollar futures is quoted at
  91, and the current Eurodollar rate is 9. You
  close your position at that time. What are your
  cash flows?

16
Example solved

• Implicit rate __________ __________ Note that
  forward rate 6.72 gt spot 6.25, term structure
  __________ sloping
• You will have to borrow 10 million for 3 months
  as you know. Borrow __________ instruments.
  Borrow in the future and lock in the rate
  __________. You __________ Eurodollar contracts.
• Interest rates ____________________
• Your profit from the short position in the
  futures contracts is _____________________________
  _.
• Your borrowing cost is ____________________
  ___
• Your total borrowing CF _______ _______
  168,000. For 3 months borrowing
  you pay ________ __________ 1.68 Convert this
  into per annum __________________

17
Options Contracts

• An option gives the holder __________, but not
  the obligation, to buy or sell a given quantity
  of an asset in the future, at prices agreed upon
  today.
• Call vs. Put options. Call/Put options gives the
  holder the right, to buy/sell a given quantity of
  some asset at some time in the future, at prices
  agreed upon today.
• European vs. American options.
• European options can only be exercised __________
  expiration date. American options can be
  exercised at any time up to and including the
  expiration date.
• Since this option to exercise early generally has
  value, American options are usually __________
  than European options, other things equal.

18
Options Contracts

• In-the-money options
• Profitable to exercised __________
• At the money options
• Profit 0 if exercised __________
• Out of the money options
• __________ if exercised under the options terms
• Intrinsic Value
• In the money The difference between the exercise
  price of the option and the spot price of the
  __________ asset.
• Out of the money __________

19
Currency Options Markets

• Currency
• 20-hour trading day.
• __________ is much bigger than exchange volume.
• Trading is in six major currencies against the
  U.S. dollar.
• View standard specifications from PHLX
• Options on currency futures
• Options on a currency futures contract. Exercise
  of a currency futures option results in a long
  futures position for the ________of a call or the
  __________of a put.
• Exercise of a currency futures option results in
  a short futures position for the __________ of a
  call or the __________ of a put.

20
Basic Relationships at Expiry

• At expiry, an American call option is worth the
  same as a European option with the same
  characteristics.
• If the call is in-the-money, it is worth
  __________
• If the call is out-of-the-money, it is
  __________.
• CaT CeT MaxST - E, 0

• At expiry, an American put option is worth the
  same as a European option with the same
  characteristics.
• If the put is in-the-money, it is worth _______
• If the put is out-of-the-money, it is _______.
• PaT PeT MaxE - ST, 0

21
Basic Option Profit Profiles
Call. Long position (_____). If the call is
in-the-money, it is worth ST E. If the call is
out-of-the-money, it is worthless and the buyer
of the call loses his entire investment of
c0. Call. Short position (_____). If the call is
in-the-money, the writer loses ST E. If the
call is out-of-the-money, the writer keeps the
option premium.

• Put. Long position (______). If the put is
  in-the-money, it is worth E ST. If the put is
  out-of-the-money, it is worthless and the buyer
  of the put loses his entire investment of p0.
• Put. Short position (______). If the put is
  in-the-money, it is worth E ST. If the put is
  out-of-the-money, it is worthless and the seller
  of the put keeps the option premium of p0.

22
American Option Pricing

• With an American option, you can do everything
  that you can do with a European optionthis
  option to exercise early has value.
• CaT gt CeT MaxST - E, 0
• PaT gt PeT MaxE - ST, 0

23
Market Value, Time Value and Intrinsic Value for
an American Call
The black line shows the _________ at maturity
(not profit) of a call option. Note that even an
out-of-the-money option has value________________
__.
24
Example

• Calculate the payoff at expiration for a call
  option on the euro in which the underlying is
  0.90 at expiration, the option is on EUR 62,500,
  and the exercise price is
• 0.75
• 0.95

25
Example

• Calculate the payoff at expiration for a put
  option on the euro in which the underlying is
  0.90 at expiration, the option is on EUR 62,500,
  and the exercise price is
• 0.75
• 0.95

26
Example

• Calculate the payoff at expiration for a call
  option on a currency futures contract in which
  the underlying is at 1.13676 at expiration, the
  futures contract is for CAN1,000,000 and the
  exercise price is
• 1.13000
• 1.14000

27
Example

• Calculate the payoff at expiration for a put
  option on a currency futures contract in which
  the underlying is at 1.13676 at expiration, the
  futures contract is for CAN1,000,000 and the
  exercise price is
• 1.13000
• 1.14000

28
Pricing currency options

• Bounds on option prices are imposed by arbitrage
  conditions (ignore in this course)
• Exact pricing formulas (theoretical)
• Lattice models, for example binomial model
  (ignore for now)
• Pricing based on continuous time modeling and
  stochastic calculus (mathematics used in modeling
  heat transfers, flight dynamics, and
  semiconductors). No derivations here. More
  _________ than binomial.
• Idea model evolution of the underlying assets
  price in ____________ time (i.e. not
  week-by-week) and calculate expected value of the
  option payoff.

29
Currency Option Pricing
r the interest rate (foreign or domestic), T
time to expiration, years S current exchange
rate, E exercise exchange rate, DC/FC
30
Example

• Consider a 4-month European call option on GBP in
  the US. The current exchange rate is 1.6000, the
  exercise price is 1.6000, the riskless rate in
  the US is 8 and in the UK is 11. The volatility
  is 20. What is the call price?

31
Example

• Consider a 2-month European put option on GBP in
  the US. The current exchange rate is 1.5800, the
  exercise price is 1.6000, the riskless rate in
  the US is 8 and in the UK is 11. The volatility
  is 15. What is the put price?

32
Put-call parity for currency options
33
Option Value Determinants
Call Put 1. Exchange rate
2. Exercise price
3. Interest rate at home
4. Interest rate in other country 5. Variability
in exchange rate 6. Expiration date The
value of a call option C0 must fall within max
(S0 E, 0) lt C0 lt S0. The precise position
will depend on the above factors.
34
Empirical Tests

• The European option pricing model works fairly
  well in pricing American currency options.
• It works best for ______________ and
  _______________ options.
• When options are in-the-money, the European
  option pricing model tends to _____________
  American options.

35
World Financial Markets and Institutions

• International Banking and Money Market
• International Bond Market
• International Equity Markets
• Futures and Options on Foreign Exchange
• Currency and Interest Rate Swaps
• International Portfolio Investment

36
Preliminaries

• In Corp Fi we learn how to package debt and/or
  equity financing (_____________).
• Now assume that we have done so, i.e., the
  optimal capital structure is in place. For a MNC
  this is a _________________________ securities
  denominated in different currencies with some
  being ________________.
• Question How a non-financial corporation can
  manage this complex exposure?

37
Risk exposures

• MNEs are exposed to a variety of risks
• Interest rate
• Currency
• Business Cycle
• Inflation
• Commodity
• Industry
• We have so far focused only on currency risk.
• Now extend to _____________________
• Both asset and liability sides of a MNC is
  exposed to it (think of ____________ and _____
  that MNEs hold on the _____________).

38
Risk exposures

• Corporate floating-rate loans are the dominant
  financing instrument
• Two types of risks with loans
• Credit risk
• Re-pricing risk
• Task is to measure the impact of the risks on the
  cost of debt and come up with suitable hedging
  strategy

39
Motivation for Swaps

• A UK firm wants to convert ______________ into
  ________________ to offset its revenues from US
  sales
• The UK firms alternatives include
• A ___________ in US dollars
• A ____________ that trades floating-rate debt
  for the fixed-rate debt of a U.S. company

40
Parallel Loan
British Petroleum
Ford
Citigroup
HSBC
BPUS
FordUK
41
Parallel loans provided accessto new capital
markets

• Parallel loan Borrow in ________________ and
  then trade for the debt of a foreign counterparty
  
• Provided access to new capital markets
• Legally _________________ on cross-border
  currency transactions
• Provided ___________________ for foreign
  subsidiaries
• May lower the firms _________________

42
Problems with parallel loans

• The foreign counterparty may have _______________
  
• Parallel loans ___________________ on the balance
  sheet
• Search costs can be _______

43
The swap contract

• Solution Package the parallel loans into a
  single legal agreement called the ______________
• Reduced the default risk of parallel loans via
  the _______________ (if one party defaults, the
  other is automatically freed from its obligation)
• Swaps _____________________ on the balance sheet
• High swap volume led to ___________

44
Development of the swaps market

• 1981
• ______________ engineers the first currency swap
  between the _____________ and _____
• Early 1980s
• Customized, low-volume, high-margin deals
• Late 1980s and 1990s
• Commercial and investment banks begin to serve as
  swaps dealers
• Swaps turn into a ___________, ____________,
  _____________ business
• Volume and liquidity grow

45
Swap Market

• In 2001 the notional principal of
• Interest rate swaps was 58,897,000,000,000.
• Currency swaps was 3,942,000,000,000
• The most __________ currencies are
• US, JPY, Euro, SFr, GBP

• A ___________ is a generic term to describe a
  financial institution that facilitates swaps
  between counterparties. It can serve as either a
  broker or a dealer.
• A broker ___________ counterparties but does not
  assume any of the risks of the swap.
• A dealer ____________ to accept either side of a
  currency swap, and thus may assume exchange rate
  risk.

46
Size of the Swap Market
47
Swaps

• A swap is an agreement to exchange cash flows at
  ___________________ according to certain
  specified rules (traded on OTC)
• Notional Principal
• Counterparties _________ and ________________
  (market makers)

48
Swaps

• Interest Rate Swaps
• Currency Swaps
• Basket Swaps swap a currency for a weighted
  basket of other currencies. The basket is chosen
  to _________________ of a MNC.

49
Interest rate swaps

• Interest rate swap
• Similar to a currency swap, but cash flows in a
  _____________ are exchanged
• A _________________ is paid during the life of
  the swap
• The __________________ is not usually swapped

50
An Example of a Plain Vanilla Interest Rate Swap

• An agreement by Microsoft to _________
  ___________ pay a _______________ every 6
  months for 3 years on a notional principal of
  100 million
• Next slide illustrates cash flows
• Note that in practice Fixed Rates are on
  __________ or __________ basis whereas Floating
  Rates are on _________ basis.

51
Cash Flows to Microsoft
---------Millions of Dollars---------
LIBOR
FLOATING
FIXED
Net
Date
Rate
Cash Flow
Cash Flow
Cash Flow
Mar.5, 2008
4.2
Sept. 5, 2008
4.8
2.10
2.50
0.40
Mar.5, 2009
5.3
2.40
2.50
0.10
Sept. 5, 2009
5.5
2.65
2.50
0.15
Mar.5, 2010
5.6
2.75
2.50
0.25
Sept. 5, 2010
5.9
2.80
2.50
0.30
Mar.5, 2011
6.4
2.95
2.50
0.45
52
Typical Uses of anInterest Rate Swap

• Converting a liability from
• _______________________
• _______________________
• Converting an investment from
• _____________________
• _____________________

53
Banc One Swaps

• Backus, Telmer and Clapper (94) describe Banc
  Ones use of interest rate swaps.
• According to Bankers Magazine 1991, Banc One
  viewed itself as McDonalds of retail banking
• 80s and 90s saw its rapid growth through
  acquisitions of banks all over US
• Franchises were decentralized which led to
  ___________________________________ gt
  _______________________________.

54
Banc One Swaps

• Backus, Telmer and Clapper (94) computed the
  exposure
• 1 drop in interest rates in early 90s would
  lead to ______________________
• Solution by Banc One
• ___________________________, mostly ______, with
  notional principal 40 bil.

55
How does it work?

• Example
• If assets are ________ to R gt financing with
  fixed-rate debt __________________
• This is because firms bottom line is
• _____________________ (long in a riskless
  security and short in a risky)
• What happens _______ gt _______ gt ___________.
• Hedge by a swap _____________ ________________.

56
Back to Intel and Microsoft (MS) Transform a
Liability
5.2
Intel
MS
LIBOR0.1
57
A Dealer is Involved

5.2
Intel
MS
LIBOR0.1
58
The Comparative Advantage Argument

• AAACorp wants to borrow __________
• BBBCorp wants to borrow __________
• Swap Dealer will charge 4 basis points.

59
The AAA-BBB Swap when a Financial Institution is
Involved
10
AAA
F.I.
BBB
LIBOR1
60
The Comparative Advantage Argument

• We are not comparing ____________, rather
  _________________ from a single companys point
  of view
• AAA Corp has a comparative advantage in
  _________________ markets
• BBB Corp has a comparative advantage in
  ______________ markets

61
Criticism of the Comparative Advantage Argument

• The 10.0 and 11.2 rates available to AAA Corp
  and BBB Corp in fixed rate markets are
  _________________
• The LIBOR0.3 and LIBOR1 rates available in
  the floating rate market are _______________
• Floating Spread smaller than Fixed Spread may
  just reflect that _________________ of the BBB
  company ______________ than those of AAA
• BBB Corps fixed rate depends on the
  ___________________ it borrows at in the future

62
Another Example of an Interest Rate Swap

• Consider this example of a plain vanilla
  interest rate swap.
• Bank A is a AAA-rated international bank located
  in _______. and wishes to raise 10,000,000 to
  finance floating-rate Eurodollar loans. Two
  alternatives
• 5-year fixed-rate Eurodollar bonds at 10 percent.
• It would make more sense for the bank to issue
  floating-rate notes at LIBOR to finance
  floating-rate Eurodollar loans.

63
Example of an Interest Rate Swap

• Firm B is a BBB-rated __________. It needs
  10,000,000 to finance an investment with a
  five-year economic life. Two alternatives
• Issuing 5-year fixed-rate Eurodollar bonds at
  11.75 percent.
• Alternatively, firm B can raise the money by
  issuing 5-year floating-rate notes at LIBOR ½
  percent.
• Firm B would prefer to borrow at a fixed rate.

64
Example of an Interest Rate Swap

• The borrowing opportunities of the two firms are

65
Example of an Interest Rate Swap
Swap Bank
Company B
Bank A
LIBOR 1/8 LIBOR ¼ 1/8 10 ½ - 10 3/8
1/8 ¼
66
Example of an Interest Rate Swap
Swap Bank
Bank A
10
67
Example of an Interest Rate Swap
Heres whats in it for B
Swap Bank
Company B
LIBOR ½
68
The Quality Spread Differential

• The Quality Spread Differential represents the
  potential gains from the swap that can be shared
  between the counterparties and the swap bank.
• QSD Fixed Differential Floating Differential
  
• There is no reason to presume that the gains will
  be shared ____________.
• In the above example, company B is less
  credit-worthy than bank A, so they probably would
  have gotten less of the QSD, in order to
  compensate the swap bank for the default risk.

69
Example

• Determine the upcoming payment in a plain vanilla
  interest rate swap in which the notional
  principal is 70 million Euro. The end user makes
  semi-annual fixed 7 payments, and the dealer
  makes semi-annual floating payments at Euribor,
  which was 6.25 on the last settlement period.
  The floating payments are made on the basis of
  180 days in the settlement period and 360 days in
  a year. The fixed payments are made on the basis
  180 days in the settlement period and 365 days in
  a year. Payments are netted, determine which
  party pays and what amount.

70
Example

• A US company enters into an interest rate swap
  with a dealer. In this swap, the notional
  principal is 50 million and the company will pay
  a floating rate of LIBOR and receive a fixed rate
  of 5.75. Interest is paid semiannually and the
  current LIBOR is 5.15. The floating rate are
  made on the basis of 180/360 and the fixed rate
  payments are made on the basis of 180/365.
  Calculate the first payment and indicate which
  party pays.

71
Interest rate swap valuation

• You can represent a swap as a bond portfolio or a
  series of FRAs. We use bond portfolio
  representation.
• From the point of view of floating-rate payer,
  this is a long position in the fixed rate bond
  and short position in the floating rate bond.
• ______________________
• From the point of view of fixed-rate payer, this
  is a long position in the floating rate bond and
  short position in the fixed rate bond.
• ______________________
• Immediately after the interest payment, the
  floating rate bond is worth exactly the notional
  amount

72
Example

• Consider a financial institution that pays LIBOR
  0.25 and receives 10.50 p.a. (annual
  compounding) from a swap end user on a notional
  principal of 10 million. The swap has remaining
  life of 4 years. The fixed rates have fallen from
  10.5 to 9 and the swap end user wants to get
  out of the deal. How much should the financial
  institution charge for the right to cancel the
  agreement?

73
An Example of a Currency Swap

• An agreement to pay 11 on a sterling
  principal of 10,000,000 receive 8 on a US
  principal of 15,000,000 every year for 5 years

74
Exchange of Principal

• In an interest rate swap the principal is
  _____________
• In a currency swap the principal is __________ at
  the __________ and the ______ of the swap.

75
The Cash Flows IBM pays fixed 11 in sterling and
receives 8 in USD
76
Typical Uses of a Currency Swap

• Conversion from a liability in one currency to a
  liability in another currency
• Conversion from an investment in one currency to
  an investment in another currency

77
Comparative Advantage Arguments for Currency Swaps

• General Motors wants to ____________
• Qantas wants to ______________
• Dealer charges 10 basis points.

USD
AUD
General Motors
5.0
12.6
Qantas
7.0
13.0
78
The Swap when a Dealer is Involved
USD 5
GM
Qantas
AUD 13
79
Swap Market Quotations

• Swap banks will tailor the terms of interest rate
  and currency swaps to customers needs
• They also make a market in plain vanilla swaps
  and provide quotes for these. Since the swap
  banks are dealers for these swaps, there is a
  ___________________.

80
Variations of Basic Currency and Interest Rate
Swaps

• Currency Swaps
• fixed for _______
• fixed for _______
• floating for __________
• Interest Rate Swaps
• __________for floating
• _________ for floating

81
Risks of Interest Rate and Currency Swaps

• Interest Rate Risk
• Interest rates might move against the
  ____________ after it has only gotten half of a
  swap on the books, or if it has an unhedged
  position.
• Basis Risk
• If the floating rates of the two counterparties
  are not pegged to the same ___________ (i.e.
  LIBOR)
• Exchange rate Risk

82
Swap Market Efficiency

• Swaps offer ______________________ and that has
  accounted for their existence and growth.
• Swaps assist in tailoring financing to the type
  desired by a particular borrower.
• Since not all types of debt instruments are
  available to all types of borrowers, both
  counterparties can benefit (as well as the swap
  dealer) through financing that is more
  _____________ for their asset maturity structures.

83
Example

• A US company can issue a US-denominated bond but
  needs to borrow in GBP. Consider a currency swap
  in which the US company pays a fixed rate in the
  foreign currency, GBP, and the counterparty pays
  a fixed rate in US. The notional principals are
  50 million and GBP 30 million, and the fixed
  rates are 5.6 in US and 6.25 in GBP. Both sets
  of payments are made on the basis of 30 days per
  month, 365 days per year, and the payments are
  made semi-annually.
• What are the following cash flows (i) initial,
  (ii) semi-annual, (iii) final

84
Valuation of currency swaps

• Currency swaps can be represented as bond
  portfolios or a series of forwards. We use bond
  representation.
• From the point of view of foreign currency payer
  (domestic currency receiver), this is a long
  position in the domestic bond and short position
  in the foreign bond.
• ________________________________________________
• From the point of view of domestic currency payer
  (foreign currency receiver), this is a long
  position in the foreign bond and short position
  in the domestic bond.
• ________________________________________________

85
Example

• In Japan term structure of interest rates is flat
  at 4 and in the US it is 9. A financial
  institution has entered into a currency swap in
  which it receives 5 p.a. in JPY and pays 8 p.a.
  in USD once a year. The principals are 10
  million and JPY 1,200 million. The swap will last
  for another 3 years, and the current JPY/USD
  exchange rate is JPY 110. What is the value of
  this swap for the financial institution?

86
Swaptions

• An option to enter into swap
• Types
• Payer swaption
• Gives the right to enter into a swap as a
  _________ rate payer and __________ rate receiver
• Equivalent to ___________ option
• Receiver swaption
• Gives the right to enter into a swap as a
  __________ rate payer and ___________ rate
  receiver
• Equivalent to ___________ option