Interest Rates

1
Interest Rates

• To understand the risks owing to interest rate
  variations, how to minimize those risks, or how
  to profit from them requires an understanding of
  how interest rates and the prices of financial
  instruments are related.
• Principal is the amount of credit extended when
  one makes a loan or purchases a bond.

2
Interest Yields

• Interest is the payment by the issuer of a
  financial instrument that compensates the
  purchaser for the use of their funds.
• The interest rate is the amount of interest
  expressed as a percentage of the principal.
• Capital gain is a rise in the value of a
  financial instrument at the time it is sold
  relative to its market value at the time it was
  purchased.

3
Discounted Present Value

• Discounted present value is the value today of a
  payment to be received at a future date.
• Calculating discounted present value
• The value today of a payment to be received at a
  future date.
• Payment one year from now/(1 r).
• Discounted present value of payment to be
  received n years in the future
• Payment n years from now/(1 r)n.

4
Present Values of a Future Dollar
Compounded Annual Interest Rate Year 3 5 8 1
0 20 1 .971 .952 .926 .909 .833 2 .943 .907 .8
57 .826 .694 3 .915 .864 .794 .751 .578 4 .889 .
823 .735 .683 .482 5 .863 .784 .681 .620 .402 6
.838 .746 .630 .564 .335 7 .813 .711 .583 .513 .2
79 8 .789 .677 .540 .466 .233 9 .766 .645 .500 .
424 .194 10 .744 .614 .463 .385 .162
5
Calculating the Yield to Maturity

• Perpetuity
• A bond with an infinite term to maturity.
• Perpetuity price C/r where C is the annual
  coupon
• Simple rule
• Prices of existing bonds are inversely related to
  changing market interest rates.

6
Term to Maturity and Interest-Rate Risk

• Interest rate risk is the possibility that the
  market value of a financial instrument will
  change as interest rates vary.
• Capital loss is a decline in the market value of
  a financial instrument at the time it is sold as
  compared with its market value at the time it was
  purchased.

7
The Term Structure

• Term Structure of interest rates is the
  relationship among yields on financial
  instruments with identical risk, liquidity, and
  tax characteristics but differing terms to
  maturity.
• Yield Curve is a chart illustrating the
  relationship among yields on bonds that differ
  only in their term to maturity.

8
Yield Curves
Typically, yield curves slope upward interest
yields rise at longer terms to maturity.
9
Yield Curves

• Economists offer three fundamental explanations
  for why yield curves are typically upward
  sloping.
• Segmented Markets
• Expectations Theory
• Preferred Habitat Theory

10
Segmented Markets Theory

• Segmented markets theory is a theory of the term
  structure of interest rates that views bonds with
  differing maturities as nonsubstitutable, so
  their yields differ because they are determined
  in separate markets.
• Drawbacks to theory
• Yields tend to move together.
• Does not explain natural tendency of the yield
  curve to slope upward or downward.

11
Expectations Theory

• Expectations theory explains how expectations
  about future yields can cause yields on
  instruments with different maturities to move
  together.
• It can provide insight into why the yield curve
  may systematically slope upward or downward
• An upward-sloping yield curve indicates a general
  expectation by savers that short-term interest
  rates will rise.
• A downward-sloping yield curve indicates a
  general expectation that short-term interest
  rates will decline. ? yield curves seldom slope
  downwards!

12
The Preferred Habitat Theory

• Preferred habitat theory is a theory of the term
  structure of interest rates that views bonds as
  imperfectly substitutable, so yields on
  longer-term bonds must be greater than those on
  shorter-term bonds even if short-term interest
  rates are not expected to rise or fall appeal
  to liquidity
• An associate term is the Term premium is the
  amount by which the yield on a long-term bond
  must exceed the yield on a short-term bond to
  make individuals willing to hold either bond if
  they expect short-term bond yields to remain
  unchanged

13
The Risk Structure of Interest Rates

• Risk structure of interest rates is the
  relationship among yields on financial
  instruments that have the same maturity but
  differ because of variations in default risk,
  liquidity, and tax rates.
• Default risk is the chance that an individual or
  a firm that issues a financial instrument may be
  unable to honor its obligations to repay the
  principal and/or to make interest payments.

14
Excess Returns

• If uncovered interest parity fails to hold, a
  saver can anticipate earning excess returns.
• Peso problem is an upward bias in depreciation
  expectations resulting from a perceived small
  probability of a large currency realignment.
• The peso problem is but one reason for persistent
  excess returns in emerging economies.

15
Currency Futures

• Introduction and Example

16
Currency Futures

• A derivative instrument.
• Traded on centralized exchanges only
• Highly standardized contracts.
• Clearinghouse as counter-party.

17
Currency Futures

• Began in the International Money Market of
  Chicago Mercantile Exchange in 1972.
• Others are COMEX in NY and Chicago Board of Trade
  and London International Financial Futures
  Exchange (LIFFE). 

18

• Contracts mature on the third Wednesday of March,
  June, Sept, Dec.
• Futures contracts are specified contract amounts.
• All orders to buy and sell futures traded on the
  CME must be
• (a) executed by an individual member of the
  Exchange
• (b) made in the name of a clearing member firm
  of the Exchange
• (c) carried in an account held by a clearing
  member firm
• (d) "cleared" through the CME's clearing member
  firms.

19
Currency Futures

• Initial Margin The customer must put up funds to
  guarantee the fulfillment of the contract - cash,
  letter of credit, Treasuries.
• Maintenance Margin The minimum amount the margin
  account can fall to.
• Mark-to-the-market A daily settlement procedure
  that marks profits or losses incurred on the
  futures to the customers margin account.

20
Sample Bond Performance Requirements(maintenance
margin)From the CME, 15 March 2000
21
Long and Short Exposures

• Long a company has pound denominated assets that
  exceed in value its pound denominated
  liabilities.
• Short a person having pound denominated
  liabilities that exceed in value his/her pound
  denominated assets.

22
Hedging With a Currency Future

• To hedge a foreign exchange exposure, the
  customer assumes a position in the opposite
  direction of the exposure.
• For example, if the customer is long the pound
  (has future assets in pounds), they would short
  the futures market (or contract to SELL pounds
  forward)

23
How an Order is Executed (Figure from the CME)
24
Hedging With a Currency Future

• If a short position is taken, an appreciation of
  the future will lead to losses, a depreciation
  will lead to gains.
• If a long position is taken, an appreciation of
  the future will lead to gains, a depreciation
  will lead to losses.

25
Example

• A US manufacturing company has a division that
  operates in Mexico. At the end of June the
  parent company anticipates that the foreign
  division will have profits of 4 million Mexican
  pesos (MP) to repatriate.
• The parent company has a foreign exchange
  exposure, as the dollar value of the profits will
  rise and fall with changes in the exchange value
  between the MP and the dollar.

26
Example, continued

• The firm is long the peso, so to hedge the
  exposure they will go short in the futures
  market.
• The face amount of each peso future contract is
  MP500,000, so the firm will go short 8
  contracts.
• If the peso depreciates, the dollar value of the
  divisions profits falls, but the futures account
  generates profits, at least partially offsetting
  the loss. The opposite holds for an appreciation
  of the peso.

27
Gain
Underlying Long Position
Change spot value
Change in futures price
Futures Position
Loss
28
Example, continued

• The previous diagram illustrates the effect of a
  change in the value of the peso.
• An increase in the value of the peso increases
  the dollar value of the underlying long position
  and decreases the value of the futures position.
• A decrease in the value of the peso decreases the
  value of the underlying position and increases
  the value of the futures position.

29
Example, continued

• On the 25th, the spot rate opens at 0.10660
  (/MP) while the price on a MP future opens at
  0.10310.
• The spot rate closes at 0.10635 and MP at
  0.10258.
• The loss on the underlying position is
• (0.10635-0.10660)?MP4 mil. -1,000
  (depreciation of the peso)
• The gain on the futures position is
• (0.10310-0.10258)?8?MP500,0002,080
• ( depreciation of the futures with a short
  position)

30
Gain and Loss on Underlying and Futures
Position Day 1
Underlying Long Position MP4 million
Gain
2,080
Change spot value
-0.00025
Change in futures price
-0.00052
1,000
Futures Position MP500,000 x 8
Loss
31
Example, continued

• On the 28th, the spot rate moves to 0.10670
  (/MP) and the price on a MP future to 0.10285.
• The gain on the underlying position is
• (0.10670-0.10635)?MP4 mil. 1,400
• The loss on the futures position is
• (0.10258-0.10285)?8?MP500,000-1,080

32
Gain and Loss on Underlying and Futures
Position Day 2
Underlying Long Position MP4 million
Gain
1,400
0.00032
Change spot value
0.00035
Change in futures price
1,080
Futures Position MP500,000 x 8
Loss
33
Example, continued

• On the 29th, the spot rate moves to 0.10680
  (/MP) and the price on a MP future to 0.10290.
• The gain on the underlying position is
• (0.10680-0.10670)?MP4 mil. 400
• The loss on the futures position is
• (0.10285-0.10290)?8?MP500,000-200

34
Gain and Loss on Underlying and Futures
Position Day 3
Underlying Long Position MP4 million
Gain
400
0.0001
Change spot value
0.00005
Change in futures price
200
Futures Position MP500,000 x 8
Loss
35
Example, continued

• For the three days considered, the underlying
  position gained 800 in value and the futures
  contracts yielded 800.
• Suppose you wanted to close the futures position
  (without making delivery of the currency).
• The position is simply reversed. That is, you
  would go long 8 MP futures, reversing your
  current position and closing out your account.
• As long as the maintenance amount does not fall
  below a minimum set by CME, only the initial
• margin is kept in the account. This is retrieved
  by position reversal.

36
The initial margin for a hedger/member is
2000 And the maintenance is 2000 per MP
contract. We assumed 16,000 was put in the
account for the 8 contracts
37
The contract specifies that you will get back
428, 400 when the delivery date occurs. Your
gain is shown as follows if on Sep. 29 you close
out the contract by longing the Peso at the same
time buying from yourself at the current rate,
you pay 411,600 and receive 428,400 making a
profit of 800.
38
Summary
Long Position If future rate?, money is added to
the margin balance If future rate?, money is
taken from the margin balance Short Position If
future rate?, money is taken from the margin
balance If future rate?, money is added to the
margin balance
39
Additional Information

• For additional information on currency futures,
  visit the following sites
• The Chicago Mercantile exchange at www.cme.com.
• The Futures Industry Institute at www.fiafii.orb.

40
Currency Options
41
Currency Options

• A currency option is a contract that gives the
  owner the right, but not the obligation, to buy
  or sell a currency at a specified price at or
  during a given time.
• Call Option An option that gives the owner the
  right to buy a currency.
• Put Option An option that gives the owner the
  right to sell a currency.

42
Currency Options

• American Option An option that can be exercised
  any time before or on the expiration date.
• European Option An option that can only be
  exercised on the expiration date.

43
Currency Options

• Exercise or Strike Price The price at which the
  option may be exercised.
• Option Premium The amount that must be paid to
  purchase the option contract.
• Break-Even The point at which profits from
  exercising the option exactly matches the premium
  paid.

44
Currency Options

• out of the money unprofitable if exercised
• Call option strike price gtspot rate
• Put option strike price lt spot rate
• If the spot rate equals the exercise price, the
  option is said to be at the money.
• in the money profitable to exercise
• Call option strike priceltspot rate
• Put option strike price gt spot rate

45
Call Option

• The holder of a call option expects the
  underlying currency to appreciate in value.
• Consider 4 call options on the euro, with a
  strike of 92 (/) and a premium of 0.94 (both
  cents per unit).
• The face amount of a euro option is 62,500.
• The total premium is
• 0.0094462,5002,350.

46
Call Option Hypothetical Pay-Off
Profit
Payoff Profile
1,400
Break-Even
92
92.94
92.5
0
Spot Rate
88.15
93.5
-1,100
-2,350
Out-of- the-money
Loss
At
In-the-money
47
Put Option

• The holder of a put option expects the underlying
  currency to depreciate in value.
• Consider 8 put options on the euro with a strike
  of 90 (/) and a premium of 1.95 (both cents per
  unit).
• The face amount of a euro option is 62,500.
• The total premium is
• 0.0195862,5009,750.

48
Put Option Hypothetical payoff at a spot rate
of 88.15
Profit
Payoff Profile
Break-Even
88.05
90
0
Spot Rate
88.15
-500
-9,750
Loss
In-the-money
At
Out-of-the-money
49
Currency Swaps
50
Introduction

• A currency swap is an agreement between two
  parties to exchange a given amount of one
  currency for another, or a stream of payments or
  receipts in one currency for a stream of payments
  or receipts in another currency.
• Currency swaps, in contrast to interest rate
  swaps, typically involve an exchange of
  principle.
• A cross-currency swap involves the additional
  exchange of a floating interest rate for a fixed
  rate.

51
Purpose

• A currency swap allows a firm to lock in the
  domestic currency value of a debt issue or future
  receipt.
• It can allow a firm access to more favorable loan
  conditions.

52
Difference with Forward

• A forward contract could be used to accomplish
  the same thing as a swap.
• As opposed to forwards, swaps usually involve the
  immediate matching of two counter parties with
  opposite needs, or a double coincidence of wants.
• Long-dated forwards, therefore, tend to be much
  more costly to the firm.

53
Example

• Consider the following example A US firm wants
  to borrow euros to finance a project in Europe.
  The firm is not well know in the foreign markets.
  Higher information costs translate into higher
  financing costs. Hence, the firm finds it
  cheaper to borrow dollars in the domestic market.

54
Example

• At the same time, a European firm is in need of
  dollar financing.
• An intermediary (or swap dealer) can arrange a
  swap between the two firms.
• Each firm borrows in their own home
  marketpresenting the respective home market with
  a well-know identity versus and unknown
  identitythereby reducing the cost of funds to
  each firm.

55
Solution

• The US firm issues dollar-denominated debt in the
  US market, while the European firm issues
  euro-denominated debt in the European market.
• Using the proceeds from the debt issues, the two
  firms swap the dollar principal for an equivalent
  euro principal.

56
Solution

• The US firm makes periodic euro payments to the
  dealer in exchange for an agreed amount of
  dollars. The dollars are used to pay interest to
  US bondholders.
• The European firm makes periodic dollar payments
  to the dealer in exchange for an agreed amount of
  euros. The euros are used to pay interest to the
  European bondholders.

57
Solution The US Firm

• At the end of the maturity period, the US firm
  pays euro-denominated principal to the dealer in
  exchange for the dollar equivalent.
• The dollar funds received from the dealer are
  used to repay the principal to the bondholders.
• The initial inflow and subsequent outflows of the
  firm replicate euro denominated debt, but at a
  lower cost.

58
Illustration US Firm

• Note that the swap has two branches One between
  the US firm and the dealer and another between
  the European firm and the dealer.
• The swap, from the perspective of the US firm is
  illustrated in the next slide.

59
Dealer
Dealer
Dealer
Dealer
principal
principal
payment
payment
equivalent
payment
equivalent
payment
Firm
Firm
Firm
Firm
principal
principal
interest
interest
Bondholders
Bondholders
Bondholders
Bondholders