Title: Swaps
1Swaps
2Introduction
- An agreement between two parties to exchange cash
flows in the future. - The agreement specifies the dates that the cash
flows are to be paid and the way that they are to
be calculated. - A forward contract is an example of a simple
swap. With a forward contract, the result is an
exchange of cash flows at a single given date in
the future. - In the case of a swap the cash flows occur at
several dates in the future. In other words, you
can think of a swap as a portfolio of forward
contracts.
3Mechanics of Swaps
- The most commonly used swap agreement is an
exchange of cash flows based upon a fixed and
floating rate. - Often referred to a plain vanilla swap, the
agreement consists of one party paying a fixed
interest rate on a notional principal amount in
exchange for the other party paying a floating
rate on the same notional principal amount for a
set period of time. - In this case the currency of the agreement is the
same for both parties.
4Notional Principal
- The term notional principal implies that the
principal itself is not exchanged. If it was
exchanged at the end of the swap, the exact same
cash flows would result.
5An Example
- Company B agrees to pay A 5 per annum on a
notional principal of 100 million - Company A Agrees to pay B the 6 month LIBOR rate
prevailing 6 months prior to each payment date,
on 100 million. (generally the floating rate is
set at the beginning of the period for which it
is to be paid)
6The Fixed Side
- We assume that the exchange of cash flows should
occur each six months (using a fixed rate of 5
compounded semi annually). - Company B will pay
- (100M)(.025) 2.5 Million
- to Firm A each 6 months.
7Summary of Cash Flows for Firm B
- Cash Flow Cash Flow Net
- Date LIBOR Received Paid Cash
Flow - 3-1-98 4.2
- 9-1-98 4.8 2.10 2.5 -0.4
- 3-1-99 5.3 2.40 2.5 -0.1
- 9-1-99 5.5 2.65 2.5 0.15
- 3-1-00 5.6 2.75 2.5 0.25
- 9-1-00 5.9 2.80 2.5 0.30
- 3-1-01 6.4 2.95 2.5 0.45
8Swap Diagram
- LIBOR
- Company A Company B
- 5
9Offsetting Spot Position
Assume that A has a commitment to borrow at a
fixed rate of 5.2 and that B has a commitment
to borrow at a rate of LIBOR .8
- Company A
- Borrows (pays) 5.2
- Pays LIBOR
- Receives 5
- Net LIBOR.2
- Company B
- Borrows (pays) LIBOR.8
- Receives LIBOR
- Pays 5
- Net 5.8
10Swap Diagram
-
- Company A Company B
-
- The swap in effect transforms a fixed rate
liability or asset to a floating rate liability
or asset (and vice versa) for the firms
respectively.
LIBOR
LIBOR.8
5.2
5
5.8
LIBOR .2
11Role of Intermediary
- Usually a financial intermediary works to
establish the swap by bring the two parties
together. - The intermediary then earns .03 to .04 per annum
in exchange for arranging the swap. - The financial institution is actually entering
into two offsetting swap transactions, one with
each company.
12Swap Diagram
-
- Co A FI Co B
- A pays LIBOR.215
- B pays 5.815
- The FI makes .03
LIBOR
LIBOR
5.2
LIBOR.8
5.015
4.985
13Day Count Conventions
- The above example ignored the day count
conventions on the short term rates. - For example the first floating payment was listed
as 2.10. However since it is a money market rate
the six month LIBOR should be quoted on an actual
/360 basis. - Assuming 184 days between payments the actual
payment should be - 100(0.042)(184/360) 2.1467
14Day Count Conventions II
- The fixed side must also be adjusted and as a
result the payment may not actually be equal on
each payment date. - The fixed rate is often based off of a longer
maturity instrument and may therefore uses a
different day count convention than the LIBOR.
If the fixed rate is based off of a treasury note
for example, the note is based on a different day
convention.
15Role of the Intermediary
- It is unlikely that a financial intermediary will
be contacted by parties on both side of a swap at
the same time. - The intermediary must enter into the swap without
the counter party. The intermediary then hedges
the interest rate risk using interest rate
instruments while waiting for a counter party to
emerge. - This practice is referred to as warehousing swaps.
16Why enter into a swap?
- The Comparative Advantage Argument
- Fixed Floating
- A 10 6 mo LIBOR.3
- B 11.2 6 mo LIBOR 1.0
- Difference between fixed rates 1.2
- Difference between floating rates 0.7
- B Has an advantage in the floating rate.
17Swap Diagram
-
- Co A FI Co B
- A pays LIBOR.065 instead of LIBOR.3
- B pays 10.965 instead of 11.2
- The FI makes .03
LIBOR
LIBOR
10
LIBOR1
9.965
9.935
18Spread Differentials
- Why do spread differentials exist?
- Differences in business lines, credit history,
asset and liabilities, etc
19Valuation of Interest Rate Swaps
- After the swap is entered into it can be valued
as either - A long position in one bond combined with a short
position in another bond or - A portfolio of forward rate agreements.
20Relationship of Swaps to Bonds
- In the examples above the same relationship could
have been written as - Company B lent company A 100 million at the six
month LIBOR rate - Company A lent company B 100 million at a fixed
5 per annum
21Bond Valuation
- Given the same floating rates as before the cash
flow would be the same as in the swap example. - The value of the swap would then be the
difference between the value of the fixed rate
bond and the floating rate bond.
22Fixed portion
- The value of either bond can be found by
discounting the cash flows from the bond (as
always). The fixed rate value is straight
forward it is given as - where Q is the notional principal and k is the
fixed interest payment
23Floating rate valuation
- The floating rate is based on the fact that it is
a series of short term six months loans. - Immediately after a payment date Bfl is equal to
the notional principal Q. Allowing the time
until the next payment to equal t1 - where k is the known next payment
24Swap Value
- If the financial institution is paying fixed and
receiving floating the value of the swap is - Vswap Bfl-Bfix
- The other party will have a value of
- Vswap Bfix-Bfl
25Example
- Pay 6 mo LIBOR receive 8
- 3 mo 10
- 9 mo 10.5
- 15 mo 11
- Bfix 4e .-1(.25)4e -.105(.75)104e
-.11(1.25)98.24M - Bfloat 100e -.1(.25) 5.1e -.1(.25) -102.5M
- -4.27 M
26A better valuation
- Relationship of Swap value to Forward Rte
Agreements - Since the swap could be valued as a forward rate
agreement (FRA) it is also possible to value the
swap under the assumption that the forward rates
are realized.
27To do this you would need to
- Calculate the forward rates for each of the LIBOR
rates that will determine swap cash flows - Calculate swap cash flows using the forward rates
for the floating portion on the assumption that
the LIBOR rates will equal the forward rates - Set the swap value equal to the present value of
these cash flows.
28Swap Rate
- This works after you know the fixed rate.
- When entering into the swap the value of the swap
should be 0. - This implies that the PV of each of the two
series of cash flows is equal. Each party is
then willing to exchange the cash flows since
they have the same value. - The rate that makes the PV equal when used for
the fixed payments is the swap rate.
29Example
- Assume that you are considering a swap where the
party with the floating rate will pay the three
month LIBOR on the 50 Million in principal. - The parties will swap quarterly payments each
quarter for the next year. - Both the fixed and floating rates are to be paid
on an actual/360 day basis.
30First floating payment
- Assume that the current 3 month LIBOR rate is
3.80 and that there are 93 days in the first
period. - The first floating payment would then be
31Second floating payment
- Assume that the three month futures price on the
Eurodollar futures is 96.05 implying a forward
rate of 100-96.05 3.95 - Given that there are 91 days in the period.
- The second floating payment would then be
32Example Floating side
Period Day Count Futures Price Fwd Rate Floating Cash flow
91 3.80
1 93 96.05 3.95 490,833.3333
2 91 95.55 4.45 499,236.1111
3 90 95.28 4.72 556,250.0000
4 91 596,555.5555
33PV of Floating cash flows
- The PV of the floating cash flows is then
calculated using the same forward rates. - The first cash flow will have a PV of
34PV of Floating cash flows
- The PV of the floating cash flows is then
calculated using the same forward rates. - The second cash flow will have a PV of
35Example Floating side
Period Day Count Fwd Rate Floating Cash flow PV of Floating CF
91 3.80
1 93 3.95 490,833.3333 486,061.8263
2 91 4.45 499,236.1111 489,495.4412
3 90 4.72 556,250.0000 539,396.1423
4 91 596,555.5555 525,668.5915
36PV of floating
- The total PV of the floating cash flows is then
the sum of the four PVs - 2,040,622.0013
37Swap rate
- The fixed rate is then the rate that using the
same procedure will cause the PV of the fixed
cash flows to have a PV equal to the same amount. - The fixed cash flows are discounted by the same
rates as the floating rates. - Note the fixed cash flows are not the same each
time due to the changes in the number of days in
each period. - The resulting rate is 4.1294686
38Example Swap Cash Flows
Period Day Count Fwd Rate Floating Cash flow Fixed CF
91 3.80
1 93 3.95 490,833.3333 533,389.7003
2 91 4.45 499,236.1111 521,918.9541
3 90 4.72 556,250.0000 516,183.5810
4 91 596,555.5555 521,918.9541
39Swap Spread
- The swap spread would then be the difference
between the swap rate and the on the run treasury
of the same maturity.
40Swap valuation revisited
- The value of the swap will change over time.
- After the first payments are made, the futures
prices and corresponding interest rates have
likely changed. - The actual second payment will be based upon the
3 month LIBOR at the end of the first period. - Therefore the value of the swap is recalculated.
41Currency Swaps
- The primary purpose of a currency swap is to
transform a loan denominated in one currency into
a loan denominated in another currency. - In a currency swap, a principal must be specified
in each currency and the principal amounts are
exchanged at the beginning and end of the life of
the swap. - The principal amounts are approximately equal
given the exchange rate at the beginning of the
swap.
42A simple example
- Assume that company A pays a fixed rate of 11 in
sterling and receives a fixed interest rate of 8
in dollars. - Let interest payments be made once a year and the
principal amounts be 15 million and L10 Million - Company A
- Dollar Cash Sterling Cash
- Flow (millions) Flow (millions)
- 2/1/1999 -15.00 10.00
- 2/1/2000 1.20 -1.10
- 2/1/2001 1.20 -1.10
- 2/1/2002 1.20 -1.10
- 2/1/2003 1.20 -1.10
- 2/1/2004 16.20 -11.10
43Intuition
- Suppose A could issue bonds in the US for 8
interest, the swap allows it to use the 15
million to actually borrow 10million sterling at
11 (A can invest L 10M _at_ 11 but is afraid that
will strength it wants US denominated
investment)
44Comparative Advantage Again
- The argument for this is very similar to the
comparative advantage argument presented earlier
for interest rate swaps. - It is likely that the domestic firm has an
advantage in borrowing in its home country.
45Example using comparative advantage
- Dollars AUD (Australian )
- Company A 5 12.6
- Company B 7 13.0
- 2 difference in US .4 difference in AUD
46The strategy
- Company A borrows dollars at 5 per annum
- Company B borrows AUD at 13 per annum
- They enter into a swap
- Result
- Since the spread between the two companies is
different for each firm there is the ability of
each firm to benefit from the swap. We would
expect the gain to both parties to be 2 - 0.4
1.6 (the differences in the spreads).
47Swap Diagram
-
- Co A FI Co B
- A pays 11.9 AUD instead of 12.6 AUD
- B pays 6.3 US instead of 7 US
- The FI makes .2
AUD 11.9
AUD 13
5
AUD 13
6.3
5
48Valuation of Currency Swaps
- Using Bond Techniques
- Assuming there is no default risk the currency
swap can be decomposed into a position in two
bonds, just like an interest rate swap. - In the example above the company is long a
sterling bond and short a dollar bond. The value
of the swap would then be the value of the two
bonds adjusted for the spot exchange rate.
49Swap valuation
- Let S the spot exchange rate at the beginning
of the swap, BF is the present value of the
foreign denominated bond and BD is the present
value of the domestic bond. Then the value is
given as - Vswap SBF BD
- The correct discount rate would then depend upon
the term structure of interest rates in each
country
50Other swaps
- Swaps can be constructed from a large number of
underlying assets. - Instead of the above examples swaps for floating
rates on both sides of the transaction. - The principal can vary through out the life of
the swap. - They can also include options such as the ability
to extend the swap or put (cancel the swap). - The cash flows could even extend from another
asset such as exchanging the dividends and
capital gains realized on an equity index for a
fixed or floating rate.
51Beyond Plain Vanilla Swaps
- Amortizing Swap -- The notional principal is
reduced over time. This decreases the fixed
payment. Useful for managing mortgage portfolios
and mortgage backed securities. - Accreting Swap The notional principal increases
over the life of the swap. Useful in
construction finances. For example is the
builder draws down an amount of financing each
period for a number of periods.
52Beyond Plain Vanilla
- You can combine amortizing and accreting swaps to
allow the notional principal to both increase and
decrease. - Seasonal Swap -- Increase and decrease of
notional principal based of f of designated plan - Roller Coaster Swap -- notional principal first
increases the amortizes to zero.
53Off Market Swap
- The interest rate is set at a rate above market
value. - For example the fixed rate may pay 9 when the
yield curve implies it should pay 8. - The PV of the extra payments is transferred as a
one time fee at the beginning of the swap (thus
keeping the initial value equal to zero)
54Forward and Extension Swaps
- Forward swap the payments are agreed to begin
at some point in time in the future - If the rates are based on the current forward
rate there should not be any exchange of
principal when the payments begin. Other wise it
is an off market swap and some form of
compensation is needed - Extension Swap an agreement to extend the
current swap (a form of forward swap)
55Basis Swaps
- Both parties pay floating rates based upon
different indexes. - For example one party may pay the three month
LIBOR while the other pays the three month T-
Bill. - The impact is that while the rates generally move
together the spread actually widens and narrows,
Therefore the return on the swap is based upon
the spread.
56Yield Curve Swaps
- Both parties pay floating but based off of
different maturities. Is similar to a basis swap
since the effective result is based on the spread
between the two rates. A steepening curve thus
benefits the payer of the shorter maturity rate.
- This is utilized by firms with a mismatch of
maturities in assets and liabilities (banks for
example). It can hedge against changes in the
yield curve via the swap.
57Rate differential (diff) swap
- Payments tied to rate indexes in different
currencies, but payments are made in only one
currency.
58Corridor Swap
- Payments obligation only occur in a given range
of rates. For example if the LIBOR rate is
between 5 and 7. - The swap is basically a tool based on the
uncertainty of rates.
59Flavored Currency Swaps
- The basic currency swap can be modified similar
to many of the modifications just discussed. - Swaps may also be combined to produce desired
outcomes. - CIRCUS Swap (Combined interest rate and currency
swap). Combines two basic swaps
60Circus Swap Diagram
- LIBOR
- Company A Company B
- 5 US
- 6 German Marks
- Company A Company C
- LIBOR
61Circus Swap Diagram
- Company B
- Company A 5 US
- 6 German Marks
- Company C
-
62Swapation
- An option on a swap that specifies the tenor,
notional principal fixed rate and floating rate - Price is usually set a a of notional principal
- Receiver Swapation
- The holder has the right to enter into a swap as
the fixed rate receiver - Payer Swapation
- The holder has the right to enter into a
particular swap as the fixed rate payer.
63Swapation as call (or put) Options
- Receiver swapation similar to a call option on
a bond. The owner receives a fixed payment (like
a coupon payment) and pays a floating rate (the
exercise price) - Payer swapation if exercised the owner is
paying a stream similar to the issue of a bond.
64In-the-Money Swapations
- A receiver swapation is in the money if interest
rates fall. The owner is paying a lower fixed
rate in exchange for the fixed rate specified in
the contract. - Similarly a payer swapation is generally in the
money if interest rates increase since the owner
will receive a higher floating rate.
65When to Exercise
- The owner of the receiver swapation should
exercise if the fixed rate on the swap underlying
the swapation is greater than the market fixed
rate on a similar swap. In this case the swap is
paying a higher rate than that which is available
in the market.
66A fixed income swapation example
- Consider a firm that has issued a corporate bond
with a call option at a given date in the future.
- The firm has paid for the call option by being
forced to pay a higher coupon on the bond than on
a similar noncallable bond. - Assume that the firm has determined that it does
not want to call the bond at its first call date
at some point in the future. - The call option is worthless to the firm, but it
should theoretically have value.
67Capturing the value of the call
- The firm can sell a receiver swapation with terms
that match the call feature of the bond. - The firm would receive for this a premium that is
equal to the value of the call option.
68Example
- Assume the firm has previously issued a 9 coupon
bond that makes semiannual payments and matures
in 7 years with a face value of 150 Million. - The bond has a call option for one year from
today.
69Example continued
- The firm can sell a European Receiver Swapation
with an expiration in one year. The Swapation
terms are for semiannual payments at a fixed rate
of 9 in exchange for floating payments at LIBOR. - The firm receives a premium for the swapation
equal to a fixed percentage of the 150 Million
notional value (equal to the value of the call
option). - The firm can keep the premium but has a potential
obligation in one year if the counter party
exercises the swap.
70Example Continued
- In one year the fixed rate for this swap is 11
- The option will expire worthless since the owner
can earn a fixed 11 on a similar swap. - The firm gets to keep the premium.
71Example Continued
- If in one year the fixed rate of interest on a
similar swap is 7 the owner will exercise the
swap since it calls for a 9 fixed rate. - The firm can call the bond since rates have
decreased. It can finance the call by issuing a
floating rate note at LIBOR for the term of the
swap. - The floating rate side of the swap pays for the
note and the firm is still paying the original 9
fixed, but it has also received the premium on
the swapation
72Extendible and Cancelable swaps
- Similar to extension swaps except extension swaps
represent a firm commitment to extend the swap.
An extendible swap has the option to extend the
agreement. - Arranged via a plain vanilla swap an a swapation.
73Extendible and Cancelable
- Extendible pay fixed swap
- plain vanilla pay fixed plus payer swapation
- Extendible Receive-Fixed Swap
- plain vanilla receive fixed swap receiver
swapation - Cancelable Pay Fixed Swap
- plain vanilla pay fixed swap receiver
swapation - Cancelable Receive Fixed Swap
- plain vanilla receive fixed swap payable
swapation
74Creating synthetic securities using swaps
- The origins of the swap market are based in the
debt market. - Previously there had been restrictions on the
flow of currency. - A parallel loan market developed to get around
restrictions on the flow of currency from one
country to another, Especially restrictions
imposed by the Bank of England.
75The Parallel Loan Market
- Consider two firms, one British and one American,
each with subsidiaries in both countries. - Assume that the free-market value of the pound is
L11.60 and the officially required exchange
rate is L11.44. - Assume the British Firm wants to undertake a
project in the US requiring an outlay of
100,000,000.
76Parallel Loan Market
- The cost of the project at the official exchange
rate is 100,000,0000/1.44 L69,444,000 - The cost of the project at the free market
exchange rate is 100,000,0000/1.60 L62,500,000 - The firm is paying an extra L7,000,000
77Parallel Loan Market
- The British firm lends L62,500,000 pounds to the
US subsidiary operating in England at a floating
rate based on LIBOR and The US firm lends
100,000,000 to the British firm at a fixed rate
of 7 in the US the official exchange rate is
avoided. - The result is a basic fixed for floating currency
swap. (In this case each loan is separate
default on one loan does not constitute default
on the other).
78Synthetic Fixed Rate Debt
- A firm with an existing floating rate debt can
easily transform it into a fixed rate debt via an
interest rate swap. - By receiving floating and paying fixed, the firm
nets just a spread on the floating transaction
creating a fixed rate debt (the rate paid on the
swap plus the spread)
79Synthetic Floating Rate Debt
- Combining a fixed rate debt with a pay floating /
receive fixed rate swap easily transforms the
fixed rate. Again the fixed rates cancel out (or
result in a spread) leaving just a floating rate.
80Synthetic Callable Debt
- Consider a firm with an outstanding fixed rate
debt without any call option. - It can create a call option. If it had a call
option in place it would retire the debt if
called. Look at this as creating a new financing
need (you need to finance the retirement of the
debt.) - You want the ability to call the bond but not the
obligation to do so.
81Synthetic Callable Debt
- Buying a receiver swapation allows the firm to
receive a fixed rate, canceling out its current
fixed rate obligation. - It will pay a new floating rate as part of the
swap (similar to financing the call with new
floating rate debt).
82Synthetic non callable Debt
- Basically the earlier example swapations.
83Synthetic Dual Currency Debt
- Dual Currency bond principal payments are
denominated in one currency and coupon payments
denominated in another currency. - Assume you own a bond that makes its payments in
US dollars, but you would prefer the coupon
payments to be in another currency with the
principal repayment in dollars. - A fixed for fixed currency swap would allow this
to happen
84Synthetic Dual Currency Debt
- Combine a receive fixed German marks and pay US
dollars swap with the bond. - The dollars received from the bond are used to
pay the dollar commitment on the swap. You then
just receive the German Marks.
85All in Cost
- The IRR for a given financing alternative, it
includes all costs including administration,
flotation , and actual cash flows. - The cost is simply the rate that makes the PV of
the cash flows equal to the current value of the
borrowing.
86Compare two alternative proposals
- A 10 year semiannual 7 coupon bond with a
principal of 40 million priced at par - A loan of 40 million for 10 years at a floating
rate of LIBOR 30 Bps reset every six months
with the current LIBOR rate of 6.5. Plus a swap
transforming the loan to a fixed rate commitment.
The swap will require the firm to pay 6.5 fixed
and receive floating.
87All in cost
- The bond has a all in cost equal to its yield to
maturity, 7 - Assuming the firm must pay 400,000 to enter into
the swap so it only nest 39,600,000. Today.
The net interest rate it pays is 6.8 implying
semiannual payments of (.068/2)(40,000,000)
1,360,000 plus a final payment of 40,000,000.
This implies a rate of .034703 every six months
or .069406 every year.
88BF Goodrich and RabobankAn early swap example
- In the early 1980s BF Goodrich needed to raise
new funds, but its credit rating had been
downgraded to BBB-. The firm needed 50,000,000
to fund continuing operations. - They wanted long term debt in the range of 8 to
10 years and a fixed rate. Treasury rates were
at 10.1 and BF Goodrich anticipated paying
approximately 12 to 12.5 - taken from Kolb - Futures Options and Swaps
89Rabobank
- Rabobank was a large Dutch banking organization
consisting of more than 1,000 small agricultural
banks. The bank was interested in securing
floating rate financing on approximately
50,000,000 in the Eurobond market. - With a AAA rating Rabobank could issue fixed rate
in the Eurobond market for approximately 11 and
for a floating rate of LIBOR plus .25
90The Intermediary
- Salomon Brothers suggested a swap agreement to
each party. - This would require BF Goodrich to issue the first
public debt tied to LIBOR in the United States.
Salomon Brothers felt that there would be a
market for the debt because of the increase in
deposits paying a floating rate due to
deregulation.
91Problems
- Rabobank was interested in the deal,but fearful
of credit risk. A direct swap would expose it to
credit risk. Without an active swap market it
was common for swaps to be arranged between the
two counter parties. - The two finally reached an agreement to use
Morgan Guaranty as an intermediary.
92The agreement
- BF Goodrich issued a noncallable 8 year floating
rate note with a principal value of 50,000,000
paying the 3 month LIBOR rate plus .5
semiannually. The bond was underwritten by
Salomon. - Rabobank issued a 50,000,000 non callable 8 year
Eurobond with annual payments of 11 - Both entered into a swap with Morgan Guaranty
93The swaps
- BF Goodrich promised to pay Morgan Guaranty
5,500,000 each year for eight years (matching the
coupon on the Rabobanks debt). Morgan agreed to
pay BF Goodrich a semi annual rate tied to the 3
month LIBOR equal to .5(50,000,000)(3 mo
LIBOR-x) - x represents an undisclosed discount
- Rabobank received 5,500,000 each year for 8
years and paid semi annul payments of LIBOR-x
94The intermediary role
- The two swap agreements were independent of each
other eliminating the credit risk concerns of
Rabobank. - Morgan received a one time fee of 125,000 paid
by BF Goodrich plus an annual fee of 8 to 37 Bp
(40,000 to 185,000) also paid by BF Goodrich.
95BF Goodrich
- Assuming that the discount from LIBOR was 50 Bp
and that the service fee was 22.5 BP (the
midpoint of the range). BF Goodrich paid an all
in cost of 11.9488 annually compared to 12 to
12.5 if they had issued the debt on their own.
96Rabobanks Position
- At the time of financing it would have paid LIBOR
plus 25 to 50 Bp. Given that it paid no fees and
the fixed rate canceled out it ended up paying
LIBOR - x.
97Securing financing
- BF Goodrich was able to secure financing via its
use of the swaps market, this is a common use of
the market. - The example provides a good illustration of the
idea of the comparative advantage arguments we
discussed earlier.
98A Second Example of securing financing
- It is possible for swaps to increases
accessibility two the debt market - Mexcobre (Mexicana de Corbre) is the copper
exporting subsidiary of Grupo Mexico. In the
late 1980s it would have had a difficult time
borrowing in international credit markets due to
concerns or default risk - However it was able to borrow 210 million for 38
months from a group of banks led by Paribas - from Managing Financial Risk by Smithson, Smith
and Wilford
99The original loan
- The banks lent the firm 210 Million at a fixed
rate of 11.48. The debt replaced borrowing from
the Mexican government which had cost the firm
23. - A Belgian company Sogem agreed to buy 4,000 tons
of copper per month at the prevailing spot rate
from Mexcobre making payments into an escrow
account in New York that was used to service the
debt with any extra funds returned to Mexcobre.
100Quarterly payments of 11.48 interest plus
principal
Banks
Escrow
Excess cash if it builds up
210 million loan
Cash based on Spot Price
4,000 tons of copper per month
Mexcobre
SOGEM
101Swaps
- Swaps were added between Paribas and the escrow
account to hedge the price risk of copper and
between Paribas and the banks to change the banks
position to a floating rate
102Paribas
Spot Price per ton
Floating
Fixed
2,000 per ton
Quarterly payments of 11.48 interest plus
principal
Banks
Escrow
Excess cash if it builds up
Cash per ton based on Spot Price
210 million loan
4,000 tons of copper per month
Mexcobre
SOGEM
103Duration of Interest Rate Swaps
- A plain vanilla swap can be valued as a portfolio
of two bonds, therefore the duration of the swap
should equal the duration of the bond portfolio. - The duration can be either positive or negative
depending on the side of the swap - Kolb, Futures Options and Swaps
104Duration of Swaps
- Duration of Receive Fixed Swap
- Duration of Underlying coupon bond
- - Duration of underlying floating Rate Bond
- gt0
- Duration of Pay Fixed Swap
- Duration of underlying floating Rate Bond
- - Duration of Underlying coupon bond
- lt0
105Example
- Consider a swap with a semiannual fixed rate of
7 and a floating rate that resets each six
months. - The duration of the fixed rate side (assuming a
100 notional principal) is 5.65139 years - Duration of Receive Fixed Swap
- 5.65139-0.55.15369
- Duration of Pay Fixed Swap
- 0.5-5.65139-5.15369
106Calculating Duration
- Duration of floating rate security is equal to
the time between resetting of the rate. - Therefore the duration of the swap actually
depends upon the duration of the fixed rate side. - Receive Fixed rate swaps will then usually
lengthen the duration of an existing position
while pay fixed swaps will shorten the duration
of an existing position.
107Immunization with Swaps
- Swaps can be used to hedge interest rate risk by
impacting the duration of the assets and
liabilities on the balance sheet. - Going to look at a fictional financial services
firm FSF
108Balance Sheet for FSF
- Liabilities
- 6mo money mkt 75,000,000
- (avg yield 6)
- Floating Rate Notes 40,000,000
- (5 yr mat7.3 yld semi)
- Coupon Bond 24,111,725
- (10 yr semi 6.5 coup
- 25,000,000 par, 7 YTM
- Net worth 16,355,408
- Total Liab NW 155,467,133
- Assets
- Cash 7,000,000
- Marketable Sec 18,000,000
- (6 mo mat Yield 7)
- Amortizing loans 130,467,133
- (10 yr avg mat
- semiannual
- 8 avg yield)
- Total Assets 1555,467,133
109Basic Duration
110Duration
- Assets
- Duration
- Cash 0.00
- Marketable Sec 0.500
- Amortizing loans 4.604562
- Total Duration
- (7,000,000/155,467,133)0.000
- (18,000,000/155,467,133)0.500
- (130,467,133/155,467,133)4.605
- 3.922013
- Liabilities
- Duration
- 6mo money mkt 0.5000
- Floating Rate Notes 0.5000
- Coupon Bond 7.453369
- Total Duration
- (75,000,000/155,467,133)0.500
- (40,000,000/155,467,133)0.500
- (24,111,725/155,467,133)7.45337
- 1.705202
111Hedging the portfolios separately
- It is easy to use duration to hedge the interest
rate risk of the portfolio. - The idea is to construct a portfolio with a
duration of zero. - Let MVi be the market value and Di be the
Duration of the assets (A), liabilities (L) or
hedge vehicle (H) then - MVA(DA)MVH(DH) 0
- and
- MVL(DL)MVH(DH) 0
112Swap notional value
- Given the duration of the hedge (a swap) it is
then possible to solve for a notional value (or
market value) of the swap that would make the
portfolio duration zero. - Previously we found the duration of a swap
- Duration of Receive Fixed Swap
- 5.65139-0.55.15369
- Duration of Pay Fixed Swap
- 0.5-5.65139-5.15369
113Asset Hedge
- The asset can then be hedged by solving for the
notional value (MVH) of the pay fixed swap - MVA(DA)MVH(DH) 0
- 155,467,133(3.922)(-5.15369)(MVH) 0
- MVH118,365,451
114Liability Hedge
- The liabilities can then be hedged by solving for
the notional value (MVH) of the receive fixed
swap - MVL(DL)MVH(DH) 0
- (-139,111,725)(1.705202)(5.15369)(MVH) 0
- MVH46,048,651
115Hedging Assets and Liabilities together
- The entire balance sheet can be hedged with one
interest rate swap by using GAP analysis.
116Static GAP Analysis(The repricing model)
- Repricing GAP
- The difference between the value of interest
sensitive assets and interest sensitive
liabilities of a given maturity. - Measures the amount of rate sensitive (asset or
liability will be repriced to reflect changes in
interest rates) assets and liabilities for a
given time frame.
117GAP Analysis
- Static GAP-- Goal is to manage interest rate
income in the short run (over a given period of
time) - Measuring Interest rate risk calculating GAP
over a broad range of time intervals provides a
better measure of long term interest rate risk.
118Interest Sensitive GAP
- Given the Gap it is easy to investigate the
change in the net interest income (NII) of the
financial institution.
119Example
- Over next 6 Months
- Rate Sensitive Liabilities 120 million
- Rate Sensitive Assets 100 Million
- GAP 100M 120M - 20 Million
- If rate are expected to decline by 1
- Change in net interest income
- (-20M)(-.01) 200,000
120GAP Analysis
- Asset sensitive GAP (Positive GAP)
- RSA RSL gt 0
- If interest rates h NII will h
- If interest rates i NII will i
- Liability sensitive GAP (Negative GAP)
- RSA RSL lt 0
- If interest rates h NII will i
- If interest rates i NII will h
- Would you expect a commercial bank to be asset or
liability sensitive for 6 mos? 5 years?
121Important things to note
- Assuming book value accounting is used -- only
the income statement is impacted, the book value
on the balance sheet remains the same. - The GAP varies based on the bucket or time frame
calculated. - It assumes that all rates move together.
122Steps in Calculating GAP
- Select time Interval
- Develop Interest Rate Forecast
- Group Assets and Liabilities by the time interval
(according to first repricing) - Forecast the change in net interest income.
123Alternative measures of GAP
- Cumulative GAP
- Totals the GAP over a range of of possible
maturities (all maturities less than one year for
example). - Total GAP including all maturities
124Other useful measures using GAP
- Relative Interest sensitivity GAP (GAP ratio)
- GAP / Bank Size
- The higher the number the higher the risk that is
present - Interest Sensitivity Ratio
125What is Rate Sensitive
- Any Asset or Liability that matures during the
time frame - Any principal payment on a loan is rate sensitive
if it is to be recorded during the time period - Assets or liabilities linked to an index
- Interest rates applied to outstanding principal
changes during the interval
126Unequal changes in interest rates
- So far we have assumed that the change the level
of interest rates will be the same for both
assets and liabilities. - If it isnt you need to calculate GAP using the
respective change. - Spread effect The spread between assets and
liabilities may change as rates rise or decrease
127Strengths of GAP
- Easy to understand and calculate
- Allows you to identify specific balance sheet
items that are responsible for risk - Provides analysis based on different time frames.
128Weaknesses of Static GAP
- Market Value Effects
- Basic repricing model the changes in market
value. The PV of the future cash flows should
change as the level of interest rates change.
(ignores TVM) - Over aggregation
- Repricing may occur at different times within the
bucket (assets may be early and liabilities late
within the time frame) - Many large banks look at daily buckets.
129Weaknesses of Static GAP
- Runoffs
- Periodic payment of principal and interest that
can be reinvested and is itself rate sensitive. - You can include runoff in your measure of rate
sensitive assets and rate sensitive liabilities. - Note the amount of runoffs may be sensitive to
rate changes also (prepayments on mortgages for
example)
130Weaknesses of GAP
- Off Balance Sheet Activities
- Basic GAP ignores changes in off balance sheet
activities that may also be sensitive to changes
in the level of interest rates. - Ignores changes in the level of demand deposits
131Basic Duration Gap
132Basic DGAP
- If the Basic DGAP is
- If Rates h
- i in the value of assets gt i in value of liab
- Owners equity will decrease
- If Rate i
- h in the value of assets gt h in value of liab
- Owners equity will increase
133Basic DGAP
- If the Basic DGAP is (-)
- If Rates h
- i in the value of assets lt i in value of liab
- Owners equity will increase
- If Rate i
- h in the value of assets lt h in value of liab
- Owners equity will decrease
134Basic DGAP
- Does that imply that if DA DL the financial
institution has hedged its interest rate risk? - No, because the amount of assets gt amount of
liabilities otherwise the institution would be
insolvent.
135DGAP
- Let MVL market value of liabilities and MVA
market value of assets - Then to immunize the balance sheet we can use the
following identity
136DGAP calculation
137Hedging with DGAP
- The net cash flows represented on the balance
sheet have the same properties as a long position
in a bond with a duration of 2.396201. - We can hedge using our equation from before and
the duration of the interest rate swap. -
138Hedging with DGAP
- Since the duration of our position is positive we
want the duration of the hedge to be negative.
This requires the pay fixed swap from before with
a notional value equal to MVH below. - MVi(Di)MVH(DH) 0
- 155,467,725(2.396201)(-5.151369)MVH0
- MVH72,316,800
139DGAP and owners equity
- Let DMVE DMVA DMVL
- We can find DMVA DMVL using duration
- From our definition of duration
140 141DGAP Analysis
- If DGAP is ()
- An h in rates will cause MVE to i
- An i in rates will cause MVE to h
- If DGAP is (-)
- An h in rates will cause MVE to h
- An i in rates will cause MVE to i
- The closer DGAP is to zero the smaller the
potential change in the market value of equity.
142Weaknesses of DGAP
- It is difficult to calculate duration accurately
(especially accounting for options) - Each CF needs to be discounted at a distinct rate
can use the forward rates from treasury spot
curve - Must continually monitor and adjust duration
- It is difficult to measure duration for non
interest earning assets.
143More General Problems
- Interest rate forecasts are often wrong
- To be effective management must beat the ability
of the market to forecast rates - Varying GAP and DGAP can come at the expense of
yield - Offer a range of products, customers may not
prefer the ones that help GAP or DGAP Need to
offer more attractive yields to entice this
decreases profitability.
144Changing Duration
- You can also manipulate the duration of your cash
flows. This allows you to lower your interest
rate sensitivity instead of eliminating it. - Let DG be the desired duration gap, DG be the
current duration gap, DS be the duration of the
Swap, and MVH be the notional value of required
for the swap.
145Decreasing Duration GAP to One year
- The negative sign just indicate that we need a
pay fixed swap (the duration would then be
negative making the MV positive)