MAFINRISK 2010
Market Risk
ALM and Internal Transfer
Rates
Session 3
Andrea Sironi
Agenda






Objectives of a ITR system
An example
Gross and net ITR
How to determine ITRs?
Transactions with implicit options
The ideal features of a ITR system
2
The Internal Transfer Rate
System
 With the ITR System a bank pursues 4
different goals:
Transfer the interest rate risk generated by different
entities to a central treasury division where it can
be properly managed
Eliminate the funding problem from the branches
Evaluate the marginal contribution to the bank
profitability of different branches
Centralize the risk management activity and
evaluate its economic performance
3
An example
 A branch raises 1
m€ with a 1Y Fixed
rate Note (3%)
and places a 3Y
fixed rate loan
(6%)
Curva dei tassi zero-coupon
Zero Coupon Curve
6,00%
5,50%
5,00%
4,50%
4,00%
3,50%
1
2
3
4
5
6
7
8
9
10
Scadenza (anni)
Maturity
Market interest rates for 1Y and 3Y are 4% and 5%
4
follows
 To eliminate the interest rate risk the branch makes a
virtual 1Y loan to the treasury division and, at the same
time, sells a virtual 3Y Note to the same division.
Branch
Treasury
Real 1Y Note
(int rate = - 3%)
Virtual 1Y Loan
(1Y ITR = + 4%)
Virtual 1Y Loan
(1Y ITR = - 4%)
Real 3Y Loan
(int rate = + 6%)
Virtual 3Y Note
(3Y ITR = - 5%)
Virtual 3Y Note
(3Y ITR = + 5%)
Interest margin = +2%
Interest Margin = +1%
5
follows
Figure 2 – Example of how an ITR system works
Branch
loans
Treasury Department
deposits
loans
1 mln €
1 year
3%
1 mln €
3 years
6%
1 mln €
1 year
4%
1 mln €
3 years
5%
+30,000
1 mln €
1 year
4%
deposits
+10,000
1 mln €
3 years
5%
-10,000
Legend:
=20,000
real deals
fictitious deals
profits/losses
6
follows
 The treasury receives an ex-ante interest margin of 1%
(5% - 4%)
 The treasury, in order to hedge the interest rate risk,
should issue a 3Y note at the 5% market rate and make a
1Y loan at the 4% market rate. In this way the interest
risk is hedged but the profit has gone.
 Even if the treasury does not hedge the interest rate risk
the interest margin of the operative branch is fixed. The
risk has been transferred to the treasury division.
7
An example (continues)



If the yield curve were negatively sloped, the treasury
margin would be negative  treasury could realize
hedging transactions aimed at eliminating risk and cancel
the negative margin
The negative slope would reflect the interest rates
decrease expectations  if treasury does not hedge it
would benefit from future interest rate changes
The branch would have a guaranteed 2% margin, which
could in turn be divided into two components:


A positive margin given by the liability side (1% = 4%-3%),
guaranteed for a one year time period
A positive margin given by the asset side (1% = 6%-5%),
guaranteed for a three years time period
8
Gross and net internal transfer
rates

Internal transfer of gross cash flows  every single cash
inflow is virtually sent to the treasury division and every
single cash outflow is virtually generated by the treasury
division. The financial statement of the branches is
perfectly hedged, only the treasury division bears some
interest rate risk.

Internal transfer of net cash flows  only the net cash
flow of every operative branch is transferred to the
treasury division. Part of the ALM is performed by the
branches.
9
follows

A system based on the internal transfer of gross
cash flows is usually preferred because:

A system based on the internal transfer of net cash
flows uses a single transfer rate for cash flows at
different maturities

A system based on the transfer of net cash flows
leaves part of the interest rate risk to the branches

The interest rate risk of the bank is different form the
sum of the exposures of the various branches.
10
An example of a net cash flows
system
Branch A
Amount
Maturity
Rate
- Liability
50,000
1Y
3%
- Asset
150,000
3Y
6%
- Liability
150,000
1Y
3%
- Asset
50,000
3Y
6%
Branch B
Bank
- Liability
200,000
- Asset
200,000
- Interest Margin
6,000
3%
Branch A receives a virtual liability of 100,000 from the treasury division,
Branch B receive a virtual asset for the same amount.
11
follows
ITR= 1Y rate (4%)
ITR= 2Y rate (4,5%)
ITR= 3Y rate (5%)
Branch A
Amount
Maturity
Rate
Amount
Maturity
Rate
Amount
Maturity
Rate
- Virtual liability
100,000
1Y
4.00%
100,000
2Y
4.50%
100,000
3Y
5.00%
3Y
5.00%
- Interest Margin
3,500
3,000
2,500
Branch B
- Virtual Asset
- Interest Margin
100,000
1Y
4.00%
2,500
100,000
2Y
4.50%
3,000
100,000
3,500
Treasury
- Virtual liability to A
100,000
1Y
4.00%
100,000
2Y
4.50%
100,000
3Y
5.00%
- Virtual Asset from B
100,000
1Y
4.00%
100,000
2Y
4.50%
100,000
3Y
5.00%
0.00%
0
0.00%
0
- Interest Margin
 interest margins
0
6,000
6,000
0.00%
6.000
12
Net ITR
•We obtain different margins for the different branches
depending on the ITR (1, 2 or 3 year maturity) we choose
•If 1 year ITR  branch A, having funded a 3 year asset
(150,000 euro) with a 1 year liability, is exposed to an
increase in interest rates
•Branch B, having used part of its 1 year liabilities to fund
a 3 year loan (50,000 euro), is exposed to a reduction of
interest rates
•The interest rate risk is still within the branches
13
An example of a gross ITR
system
Branch A
Amount
Maturity
Rate
- Virtual Asset
50,000
1Y
4.00%
- Virtual Liability
150,000
3Y
5.00%
- Margin of interest
2,000
1.00%
Branch B
- Virtual Asset
150,000
1Y
4.00%
- Virtual Liability
50,000
3Y
5.00%
- Margin of interest
2,000
1.00%
Treasury
- Virtual Liability A
150,000
3Y
5.00%
- Virtual Liability B
50,000
3Y
5.00%
- Virtual Asset A
50,000
1Y
4.00%
- Virtual Asset B
150,000
1Y
4.00%
- Margin of interest
2,000
Total Interest Margin
6,000
1.00%
14
Gross ITR
• In this case all cash flows are transferred to the treasury
at the conditions corresponding to their maturities
•  Multiple ITR
• The two branches economic results are equivalent (2,000
euro) and immunized from interest rate changes
• Interest rate risk is entirely transfered to the treasury
• If treasury wants to keep this interest rate risk, it would
receive a 2,000 euro remuneration
15
The choice of the Internal
Transfer Rates

The choice of the ITR should:

Be grounded on market rates (the rates should be representative
of real investment/financing opportunities)

Distinguish between bid and ask rates. For a virtual liability we
should use an ask rate, for a virtual asset a bid rate is the correct
choice.

Consider every single cash flow as a separate operation.
16
The choice for a fixed rate
operation

For a fixed rate operation the ITR is chosen only once at
the very beginning of the operation.
Figure 3 – ITR for a fixed-rate transaction
Branch
Mortgage
Internal debt
100,000
100,000
10 years
5%
10 years
4%
Treasury Dept.
Branch profit:
Internal loan
5,000 – 4,000 = 1,000
100,000
10 years
5%
17
The choice for a floating rate
operation

The ITR changes after every renegotiation of the floating
rate operation
Figure 4 – ITR for a floating-rate transaction
Branch
Mortgage
Internal Debt
100,000
100,000
floating rate
Euribor + 1.5%
floating rate
Euribor
Treasury Dept.
Internal loan
Branch profit:
1,5% x 100,000 = 1,500
100,000
floating rate
Euribor
18
The choice of ITR: some
problems


ITR for operations indexed to “administrative” rates (e.g.
official rates, Prime rate, etc.)
2 problems:
 (i) no financial instrument is available in the market to
hedge the related interest rate risk
 (ii) it’s difficult to measure (and therefore transfer to
treasury) the basis risk
19
The choice of ITR: some
problems




Ex.: mortgage indexed to Prime Rate
2 alternative ways of setting the ITR
 Libor  does not allow to transfer the entire interest
rate risk to the treasury; however, it gives the branch
an incentive to lend at prime
 (Prime – spread)  grants a complete transfer of
interest rate risk to treasury (basis risk). The branch
only deals with credit risk. However, no incentive to
lend at Prime
The aim of an ITR system is to centralize interest rate
risk management and transfer all sources of this risk to a
single unit (treasury)  second alternative should be
preferred
Problem of incentives  work on spread  e.g. (i)
expected difference (Prime Rate – Libor) + (ii) premium
20
The choice of ITR: some
problems
Example 1



A branch grants a mortgage indexed to Prime Rate +
0.25%
Based on historical data, the bank estimates that:
 Prime Rate = Libor + 2%
ITR is not set as “Prime Rate - 2%”, but rather as:
 Prime Rate - (2%+k)

Branch result  2.25%+k

k is included in order to give the branch an incentive to
lend at a favourable rate  Prime rate tends to decrease
at a slower pace when market rates decrease and
viceversa
21
The choice of ITR: some
problems
Example 2


A branch has granted a mortgage indexed at
official ECB rate +2%
Hp. ECB rate =2.5%; Libor 6 m = 3.15%
Libor = 3.15% = ECB rate + k = 2.5% + 0.65%



ITR = ECB rate+0.65%
Branch income  1.35%
Interest rate risk is taken by the treasury

22
ITR for operations with implicit
options

Examples:
 Option to convert from fixed to floating  the bank is
selling to the debtor an option to convert a liability
from fixed to floating
 Maximum rate  option for the debtor not to pay
more than X% in case of an increase in market rates

A proper ITR system must take into account the value of
these options
23
ITR for operations with implicit
options

Mortgage with the option to convert from fixed to
floating (or viceversa) is equivalent to a loan + sale of
a swaption  the buyer gets the right but not the
obligation to buy at a future date and at predefined
conditions (fixed rate and maturity) an Interest Rate
Swap
Table 6 – Example of a loan converted from a fixed to a floating rate
Date
Interest on the
Interest Rate Swap flows
Final net flows
loan
(from when the swaption is
exercised)
+ 1 year
-7%
(not available)
-7%
+ 2 years
-7%
+7%
-(Libor+s)
-(Libor+s)
+ 3 years
-7%
+7%
-(Libor+s)
-(Libor+s)
24
ITR for operations with implicit
options
Figure 7 – ITR for a fixed rate loan convertible to floating rate
Treasury
Income
Expenses
Interest payable
Int. receivable
5%
5%
[Value of the
swaption
1000 euro]
on the
market
Value of the
swaption
1000 euro
internal deal
Branch A
Expenses
Interest payable
5%
Value of the
swaption
Income
Interest
receivable
7%
1000 euro
from
customer
The option is sold
by the treasury to
the branch 
treasury can hedge
by buying a
swaption in the
market, paying a
premium equal to
the one paid by the
branch  the
spread to the client
must take into
account the cost of
the swaption
25
ITR for operations with implicit
options


Maximum rate  the bank has sold to the client an
interest rate cap  the implicit option must be paid by
the customer
Minimum rate  the bank has bought an interest rate
floor from the client  the branch sells the floor to
the treasury
26
ITR for operations with implicit
options
Figure 8 – ITR for a floating-rate loan with a floor
Treasury Dept.
Expenses
Interest payable
Income
Int. receivable
Libor
Libor
Value of the floor Value of the floor
x%
x%
Branch
on the market
Expenses
Interest payable
Libor
Income
Int. receivable
Libor + s%
Value of the floor Value of thefloor
x%
x%
with the customer
27
ITR for operations with implicit
options
Max and Min rates for a loan
 When the bank funds a client at floating interest rate
fixing:




A maximum rate (the client company will never pay more then a
predefined threshold);
A minimum rate (the client company will never pay less then a
predefined threshold);
…the bank is implicitly selling the client an Interest Rate
Cap and, at the same time, buying from the client an
Interest Rate Floor  selling an Interest Rate Collar
 the client company must pay a premium for the
acquisition of the cap and at the same time receive a
premium for the sale of the floor
28
ITR for operations with implicit
options



Example: a client gets a loan at “Libor+s” and buys a
collar (max rate 7%, min rate 4%) paying a premium
(cap value > floor value)  treasury sells the collar to
the branch; the branch in turn sells the collar to the
client
If Libor becomes equal to 3.5%, the client must pay
the difference between floor rate and market rate to
the branch (0.5%); the same must be done by the
branch to the treasury
If Libor goes to 7.5%, the branch must pay to the client
the difference between market rate and cap rate; the
same must be done by the treasury to the branch
29
ITR for operations with implicit
options
Prepayment option
 The borrower has bought an option to buy back the
loan before maturity
 This option must be paid by the borrower to the
branch
 The branch in turn is selling this option to the
treasury
 If interest rates decrease and the borrower exercises
the option, then the branch would in turn exercise the
option with the treasury
30
ITR for operations with implicit
options
Figure 9 – ITR for a loan with an early repayment option
Treasury Dept.
Expenses
Interest payable
6%
Income
Int. receivable
ITR: 6%
Value of the
call
500 euro
on the
market
internal deal
Branch
Expenses
Interest payable
IRT: 6%
Value of the
call
Income
Interest
receivable
ITR + s:
6% + 2% = 8%
500 euro
from
customer
31
ITR for operations with implicit
options
Figure 10 – Effects of exercising the early repayment option
Treasury Dept.
Assets
Internal loan
Liabilities
Market funding
6%
6%
Internal loan
5%
on the
market
internal deals
Branch
Assets
Loan to customer
6%+2%
Loan to customer
5%+2%
Liabilities
Internal funding
6%
Internal funding
5%
from
customer
32
The ideal characteristics of an
ITR system
1.
2.
3.
4.
5.
An ITR system should be such that the resulting profits
of the different operating units is equal to the global
profitability of the entire bank
The ITR system should be based on a gross cash flow
system
The ITR system should be based on rates differentiated
by maturity (multiple ITR)
The ITR system should be based on market rates, that
can be actually negotiated by the treasury
The ITR system should be based on different rates for
assets and liabilities (bid and offer rates)
33
The ideal characteristics of an
ITR system (continues)
6.
The ITR system should be such to protect operating
units from changes in the interest rates (directional risk)
7. The ITR system should be such that branches
profitability changes only come from credit risk (other
than operating revenues and costs)  not from interest
rate risk
8. Operating units should not be hedged from basis risk
unless this risk can in turn be hedged by the treasury in
the market
9. The ITR system must be such to protect the operating
units from the risks related to implicit options
10. The ITR system must be arbitrage-free  the operating
units must not be able to realize arbitrages against the
treasury
34
Questions & Exercises
1.
Branch A of a bank only has fixed-rate deposits, with a maturity of
one year, for 100 million euros; branch B has only fixed-rate loans,
for the same amount, with a maturity of 3 years. Market rates, on
the 1 and 3 year maturity respectively, currently are 5% and 4%.
Consider the following statements:
I.
One cannot use market rates as ITRs, as they would lead to a
negative margin for the Treasury Unit;
II. 3- and 4-years ITRs must be set exactly at 5% and 4%;
III. The Treasury Unit can both hedge interest rate risk and meanwhile
have a positive net income;
IV. The Treasury Unit can hedge interest rate risk, but doing so would
bring its net income down to zero.
Which one(s) is (are) correct?
A. All four.
B. II and IV.
C. I and III
D. II and III.
35
Questions & Exercises
2. Consider the following statements: “internal transfer rate systems
based on flat rates (uniform rates for all maturities)…:
i) …are wrong because internal trades take place at non-market rates”;
ii) …are correct because internal trades involve no credit risk, so there is
no need for maturity-dependent risk-premiums”;
iii) …are wrong because they are equivalent to a system where only net
balances are transferred between the branches and the Treasury
department”;
iv) …are wrong because part of the interest rate risk remains with the
branches”.
Which of them would you agree with?
A) Only ii);
B) Both i) and iv);
C) All but ii);
D) Both iii) and iv).
36
Questions & Exercises
3.
(a)
(b)
(c)
A bank has two branches, A and B. Branch A has 100 million euros of oneyear term deposits, at a fixed rate of 1.5%, and 40 million euros of 3 year
fixed-rate loans at 5%. Branch B has 100 million euros of 3 year fixed rate
loans at 5%, and 6-month deposits for 80 million euros, at 1%. Market
yields for 6-month, 1 year and 3 years funds are 2%, 3%, 4% respectively.
The o/night market rate is 1%.
Compute the (maturity adjusted) one-year repricing gap and the expected
annual profits of both branches (assuming that short term items can be
rolled over at the same rate), under the following hypotheses:
each branch funds (or invests) its net balance (between assets and liabilities
with customers) on the market for overnight funds;
each branch funds (or invests) its net balance (between assets and
labilities) through virtual one-year deals with the Treasury;
the bank has a system of ITRs based on gross cash flows and market rates.
Finally, suppose you are the manager of branch B and that your salary
depends on the profits and losses experienced by your branch. Which
solution, among a), b) and c) would you like best if you were expecting
rates to stay stable? How could your choice be criticised?
37
Questions & Exercises
4.
A branch issues a 10-year floating-rate loan at Libor +
1%. The borrower may convert it to a fixed rate loan
after 5 years; also, he may payback the whole debt after
8 years. If the bank is using an appropriate system of
internal transfer rates the branch should…
A) buy from the Treasury a 5-year swaption and an 8-year
call on the residual debt;
B) buy from the Treasury a 5-year swaption and sell the
Treasury an 8-year call on the residual debt;
C) sell the Treasury a 5-year swaption and an 8-year put on
the residual debt;
D) buy from the Treasury a 5-year swaption and an 8-year
put on the residual debt.
38
Questions & Exercises
5.
A)
B)
C)
D)
A bank is issuing a floating-rate loan, with a collar
limiting rates between 5% and 12%. Suppose s is the
spread on the loan and p is the spread on a comparable
loan (same borrower, same collateral, same maturity,
etc.) with no collar. Which of the following statements is
correct?
s > p, because the borrower is actually buying an option
from the bank;
s < p, because the borrower is actually selling the bank
an option;
s = p, because the bank is both selling and buying an
option;
the relationship between s and p depends on… (specify).
39