Managing Interest Rate Risk
Managing Interest Rate Risk
Managing Interest Rate Risk
=
n
Y
Par n
dY
dP
( )
n
Y
Par
P
+
=
1
( ) ( )
n
Y
Par
Y
n
+
+
=
1 1
( )
P
Y
n
dY
dP
+
=
1 Y
n
Duration
+
=
1
10
$0m
$2m
$4m
$6m
$8m
$10m
$12m
$14m
$16m
$18m
$20m
0.0% 5.0% 10.0% 15.0%
Yield
P
0
10-year government zero coupon bond, par value $10,000, YTM 7%, matures in 10-
years. Current market price $5,084. Value of portfolio holding $10m.
Change in bonds value against change in yields
Bond valuations revisited
Slope or tangent of chart at
point
Value of bond portfolio
FFAS 2008
(Y)
(P)
For a given bond duration
increases as yield falls
Estimated value from
change in yields using
duration is a first order
approximation* always
gives a lower value than
actual value
* Does not take into account curvature of price/yield chart - convexity
11
Duration of zero coupon bond
35 . 9
07 . 1
10
=
) Y ( V
y 1
n
) V ( A
+
= A
632 , 4 $
10 )^ 08 . 1 ( 000 , 10 $ =
Example: Zero coupon bond e.g T-bill
10-year government zero coupon bond, par value $10,000, YTM 7%. Current market
price $5,084 [=$10,000/(1.07)^10] .
Duration
Absolute change in Value
at given yield
V D
Y
V
=
A
A
) (
) (
) ( ) ( Y V D V A = A
Change in value for
100 bpt change in yield
475 $
01 . 0 084 , 5 $ 35 . 9 =
Value at 6% yield
559 , 5 $
475 $ 084 , 5 $ = +
609 , 4 $
475 $ 084 , 5 $ =
Value at 8% yield
( ) Y 1
n
D
ZCB
+
=
583 , 5 $
10 )^ 06 . 1 ( 000 , 10 $ =
Demonstrates that estimated value using duration gives a lower value than actual value
Calculated exactly
12
Duration of coupon bond
PV of each cashflow (coupons and principal) values V
1
, V
2
, V
3
, duration D
1
, D
2
,
D
3
Treat each payment as a ZCB
Duration of coupon bond = PV-weighted duration average
FFAS 2012
For 100 bpt change coupon bond value changes by $10,535 x 2.63 x 0.01 = $277
( ) ) ... ( / ...
2
1
1
1
2 2 1 1 N
N
n
N
n
N N p
V V V D V D V D V D + + + + + + =
= =
Years
1 2 3
Coupon 800 800 800
Principal 10,000
Total 800 800 10,800
Discount factor 1.06x 1.12x 1.19x PV
Discounted cashflows 755 712 9,068 10,535
Duration of cashflows 0.94 1.89 2.83
Duration x PV 712 1,343 25,664 27,719
Bond duration 2.63 (=27,719 10,535)
Example: 3-year annual coupon bond, 8% coupon rate, 6% YTM,
13
Examples of modified duration of bonds
Coupon rate
All other things (term, YTM) being equal the lower the coupon rate the longer duration
Yield-to-maturity
All other things being equal (term, coupon rate) the lower the YTM the longer duration
Term
All other things being equal (coupon rate, YTM) the longer the term the longer the
duration
Instrument YTM Duration Duration
90-day T-Bill 4% 0.24 =0.25/(1.04)
5 -year ZCB 6% 4.72 =5/(1.06)
5-year 5% coupon bond 6% 4.23
5-year 10% coupon bond 6% 3.92
5-year 10% corporate loan 8% 3.87
Modified Duration
Gives the % change in price for a 100 bpt change in yield and this is key
14
Portfolio duration
Individual bond holdings values V
1
, V
2
, V
3
, duration D
1
, D
2
, D
3
Portfolio of different bonds
Present-value weighted duration average
FFAS 2012
Value($m) Duration
T-Bills 100 0.24
Treasurybond 200 4.25
TreasuryZCB 25 9.35
Corporatebonds 50 2.50
Assets 375
Valuex
duration
24
850
234
125
3.29 1,233
Portfolio
duration
Issuedbonds 300 2.50
750 2.50
Equity 75
Impactof100bptfall
($m)
0.240
8.500
2.338
1.250
12.337
(7.50)
+4.838
( ) ) ... ( / ...
2
1
1
1
2 2 1 1 N
N
n
N
n
N N p
V V V D V D V D V D + + + + + + =
= =
L L A A E E
D V D V D V =
483
( )
E L L A A E
V D V D V D =
6.45
Equity itself has no duration but has been invested in portfolio of bonds with duration of 6.45
Change in value of equity for 100 bpt change = $75m x 6.45 x 0.01 = $4.838m
Liabilities
= 1,233 375
= 1,233 750 = 483 75
15
Using derivatives to change portfolio interest rate exposure
FFAS 2012
An asset manager has a $200m holding of 6-year illiquid corporate bonds with
duration 4 years.
Portfolio loss if rates rise 100 bpt = 4 $200m 0.01 = $8m
Asset manager wants to reduce her $ exposure to a 100 bpt rate hike to $2m
over the next 6 months. Given the illiquid nature of the bonds difficult to achieve
quickly by selling them.
Instructs trader to create derivative positions which will produce offsetting
gains of $6m (=$8m - $2m) in the event of rates rising by 100 bpts to achieve
this objective.
There are many ways to achieve this using derivatives.
For purposes of this example we will assume trader is constrained to using
forward rate agreements (FRAs)
Derivatives will be accounted for at fair-value. On day 1 these derivatives
fair-value will be zero as done at market rates.
16
Forward rate agreement (FRA)
180-day fixed-floating FRA, single netted payment
OTC (Over-the counter, not traded on an exchange)
Fixed rate payer at 6%
Floating leg payer LIBOR + 200 bpts
Notional principal $1,200m, Libor 4% at inception
Libor 5% at settlement
Fixed rate
payer/receive
floating
Floating rate
payer/receive
fixed
$1,200m x 7% x 0.5 = $42m
$1,200m x 6% x 0.5 = $36m
FFAS 2012
$6m
Shortens
duration
Lengthens
duration
Entering into forward rate agreements with notional principal of $1,200m would
produce offsetting gains of $6m if rates rise 100 bpts (i.e. 12 standardised
contracts each with nominal value of $100m)
Would also reduce gains on the position to $2m if LIBOR falls 100 pts
17
Portfolio immunization
$$$ Portfolio value = $75m, portfolio duration = 6.45 years
m m 968 $ 75 $
5 . 0
45 . 6
=
a) FRAs, duration 0.5, notional value of pay-fixed FRAs to immunize portfolio =
Yield change impact on
neutralized provided
H H
V D
P P
V D
$968m x 0.5 x 0.01 = $4.838m
A bank has achieved its annual earnings target and management is more concerned with
protecting bonuses and avoiding losses than increasing profits further.
Interest rates are volatile due to current economics conditions. At the November ALCO meeting
executive management tells Treasury to take action necessary to protect the bank from losses
through to the end of the year irrespective of whether rates rise or fall. Treasury acts to immunize
the bank from changes in rates using derivatives.
H
V
P
H
P
V
D
D
m m 6 . 201 $ 75 $
4 . 2
45 . 6
=
b) Interest rate swaps (equivalent to multiple period FRAs), duration 2.4, notional value
of pay-fixed swaps =
$201.6m x 2.4 x 0.01 = $4.838m
E
V
18
More on derivatives used
Floating-floating
Master netting agreements (ISDA)
Basis e.g. LIBOR versus T-bond
rates
Term e.g. Short Term versus Long
Term rates
Credit e.g. BAA bond yields
versus risk-free
Credit risk when net recipient
On balance sheet at fair value
(replacement cost)
FFAS 2012
Interest rate swaps - multiple-period
FRAs
Swaptions
Interest rate swap futures
Bond indices futures
Basis spread futures
Caps and collars
Fixed-floating
T-bill futures
Much faster/ cheaper than
adjusting balance sheet directly
Depth and liquidity of
derivatives markets crucial
Portfolio has to be constantly
rebalanced
ISDA International Swaps and Derivatives Association
19
Effective duration
Callable (negative convexity) and putable bonds
Many bank assets and liabilities have embedded options
Banks calculate an Effective duration that takes these into
account based on behavioral modelling
-$4,000
-$2,000
$0
$2,000
$4,000
$6,000
$8,000
$10,000
$12,000
$14,000
$16,000
2.0% 4.0% 6.0% 8.0% 10.0% 12.0%
Yield-to-maturity
Vanilla bond price
-$4,000
-$2,000
2.0% 4.0% 6.0% 8.0% 10.0% 12.0%
Price
Callable
bond price
FFAS 2012
$0
$2,000
$4,000
$6,000
$8,000
$10,000
$12,000
$14,000
$16,000
2.0% 4.0% 6.0% 8.0% 10.0% 12.0%
Putable
Price
Vanilla bond
Putable
bond price
Yield-to-maturity
Fixed rate mortgages Time deposits
20
Duration recap
Duration = % change in the value of a bond for a 100 bpt change in yields. Measured in years.
Duration of a ZCB (single payment) given by
( ) Y
n
D
ZCB
+
=
1
At low yields and short durations, duration of ZCB ~ term
Duration for a portfolio of assets and liabilities is given by the NPV- weighted sum of the
durations of the individual holdings
First order approximation, change in value (V) of a bond with yield (Y) and duration (D) for a
given change in yield is given by
) ( ) ( Y V D V A = A
Duration of an FRA is given by the duration of the underlying positions
Risk managers who want to shorten (asset) duration take the pay-fixed side of FRAs or
interest rate SWAPs
The value of a portfolio of assets and liabilities of total value V
T
with duration D
T
can be
protected from either rising or falling rates by adding hedging derivative positions such that:
H H
V D P P
V D
L L A A E E
D V D V D V =
Many bank assets and liabilities contain embedded options banks use effective duration
rather than (modified) duration to take these into account
21
Practical issues
Large shifts
- Duration first order
approximation
Non-parallel shifts
- Not all YTMs change by same
amount across yield curve
Portfolio re-balancing continuous
and incremental
- Time to maturity keeps changing
Calculation and modeling
complexity (convexity and embedded
options)
FFAS 2012
Reported earnings versus economic value
Awkward earnings mix of Mark-To-Market (MTM) and accrued
income
Banks (and many other corporations) like to minimise volatility in
reported earnings
Have to balance this with maximising economic value
22
Sensitivity analysis
Number of interest rate scenarios test impact of
standard recommended regulatory 200 bpt shocks
Parallel shifts
Steepeners short end down, long end up
Flatteners short end up, long end down
FFAS 2012
Complements duration matching e.g. Annual Earnings At
Risk
Inverted yield curves
23
Examples of interest rate scenarios
Yields
Time
Parallel shift upwards
Inversion with short term
rates rising long-term
rates falling
Parallel shift downwards
Short term rates falling
long-term rates rising
Steepener
Flattener
24
Key Performance Ratios
Asset yields = Interest income Average interest earning assets
Funding costs = Interest expense Average interest bearing deposits
Net interest spread = Asset yields Funding costs
Net interest margin = Net interest income Average interest earning
assets
Analysts focus on net interest spread
US Bank disclosures on net interest spreads
Asset yields reported on tax equivalent basis
Reported average interest bearing liabilities exclude demand deposits
Demand deposits should be treated as interest bearing liabilities with a
rate of 0% and added to reported interest bearing liabilities in
calculating funding costs
25
Interpreting ratios
Asset yields
Higher yields for loans than securities and deposits with other banks
SME, personal loans and credit cards have higher yields than corporate loans and
residential mortgages
Higher yields usually reflect higher risk taking and at expense of higher credit losses
Funding costs
Low funding costs usually associated with high level of retail deposits compared with
other wholesale funding
Credit ratings
Tradeoffs
Large retail banks have large branch networks and generally lower funding costs than
wholesale banks
More stable funding from (retail) deposits compared with wholesale funding
Higher operating costs from bricks and mortar banking
Net interest spread
If a bank has higher net interest spreads relative to other banks operating in same
market
Have to look at whether due to higher yields or lower funding costs or a combination
of the two
26
Hedge accounting versus economic hedging
Hedge accounting (IFRS)
Hedge accounting based on designated
single hedged item/hedged instrument
(pool)
Cumbersome and costly to implement
(requirements for documentation and
testing)
Inflexible and restrictive
Banks would like to be able to use hedge
accounting for credit default swaps but find
it difficult to demonstrate effectiveness
for good reason
Banks would like to use fair value hedge
accounting for demand deposits but these
cant be designated as held at fair value
Bank economic hedging
Banks are in the business of pricing and
trading risk not eliminating it
Do seek to keep level of risk within
acceptable limits
Manage balance sheet on a portfolio
basis
Use derivatives to adjust total
asset/liability durations
Continually adjusting as portfolios
change and management risk tolerance
alters
Even when banks do apply fair-value
hedges to trading/FV/AFS assets and
liabilities there is little incentive for them
to account as hedged instruments
Banks complained that cash-flow hedging would create unwanted volatility in equity
. but Tier 1 capital calculated after reversal of gains/(losses) of cash-flow hedge reserves
Banks make limited use of hedge accounting in any case
27
Specific instances when banks do use hedge accounting
Some banks have more fixed rate liabilities (e.g demand deposits) than
fixed rate assets
Use swaps and cash-flow hedge accounting of floating rate large corporate
loans in order to hedge part of their demand deposits
Some banks have substantial quantities of fixed rate long-term debt
Use swaps and fair-value hedges to convert some of their fixed rate long-term
debt issues into floating rate. Debt held at fair value.
Hedges of net investments in foreign operations using foreign currency
borrowings or FX forwards (accounted for similarly to cash flow hedges).
Gains/losses held in cash-flow reserves until disposal of operation.
28
Structural Foreign Exchange Risk
Only very large banks actively involved in FX trading zero sum
game
Most banks aim to avoid having net FX positions
Some hedge translation exposures from foreign subsidiaries others
content to accept the variability in equity
There can however be risks with hedged foreign currency lending
Changes to exchange rate systems may have significant negative
impact on banks
29
Hedged foreign currency lending
Examples: Thailand, Indonesia, South Korea 1997, Argentina 2001, Eastern
Europe (e.g. Latvia, Ukraine, Hungary, Poland) 2008
Foreign currency (e.g. Swiss Franc, US$) loans sold to domestic borrowers to fund
purchase of domestic assets (e.g. residential property, factories)
Incentive for borrower is lower interest rate on foreign currency loan
Foreign currency loans funded with by foreign currency borrowings
Bank is fully hedged
FX risks being taken by borrowers
FX risks transformed into credit risks
Use of short-term foreign funding also exposes bank to higher liquidity risks and
risk of inflated funding costs
Devaluation of domestic currency will inflate value of assets denominated in
foreign currency and reduce leverage ratio
Combination of high proportion of foreign currency loans and steep devaluation
likely to make it difficult for banks to meet regulatory capital requirements may
force capital raising
30
100
900
1,000
1,000
1,000
FCY
borrowings
Domestic
deposits
and other
liabilities
FCY loans
Domestic
assets
100
900
2,000
1,000
2,000
FCY
borrowings
Domestic
deposits
and other
liabilities
FCY loans
Domestic
assets
Equity
Equity
Exchange rate 1 FCY unit = 1 Domestic unit
Leverage ratio = 5%
Gearing = 20x
Exchange rate 1 FCY unit = 2 Domestic unit
Leverage ratio = 3.3%
Gearing = 30x
Impact of 50% devaluation of local
currency versus foreign currency on
bank balance sheet structure
31
100
1,700
200
2,000
Borrowings
from other
Eurozone
countries
Domestic
deposits
and other
liabilities
Domestic
assets
DCY50
DCY1,700
DCY2,000
Domestic
deposits
and other
liabilities
Domestic
assets
Equity
Equity
Leverage ratio = 5%
Gearing = 20x
10% of funding from other Eurozone institutions
At time of exit 1 = 1 Domestic Unit of Currency
Exchange rate 1 = 1.25 Domestic unit
Loss of DCY50 on foreign Euro borrowing
Leverage ratio = 2.5%, Gearing = 40x
Impact on bank BS of country exiting Eurozone effective 25% devaluation
Borrowings
from other
Eurozone
countries
DCY250
(200)
BS In Euros
BS In Domestic Currency
Country exits Euro
Conversion rate of
domestic assets and
liabilities 1:1 from
Euro to domestic
currency
Followed by
devaluation of
domestic currency
against Euro
After Devaluation
32
Session objectives
Owl 2004
Explain the nature of bank interest
rate risks and methods used to
measure and control interest rate
risk.
Calculate the change in value of a
bond for a given change in yields.
Explain the concept of duration and
its usefulness
Calculate the duration for a
portfolio of bonds.
Calculate the notional value of FRAs
or interest rate swaps necessary to
immunize value of bond portfolio
from interest rate changes
On completion of this session students should be able to
Explain the difference between
modified duration and effective
duration
Give examples of other methods
banks use to manage interest rate
risk disclosures
Calculate key performance ratios
(asset yields, funding costs and net
interest spread)
Explain how economic hedges differ
from accounting hedges.
Explain the risks to banks providing
hedged foreign currency loans to
domestic borrowers and banks
operating in the Eurozone in event of
country exiting