Or
The Chance That The Outcome
Will Not Be As Expected
1
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Interest Rate Risk
The risk of loss of interest revenue that occurs when interest rates
change, through the mismatch of re-pricing of assets and liabilities.
Interest Rates PA
8
7
6
Yield curve
5
4
3
2
1
0
1
2
3
4
Lend 6 Months at 5.5
Fund Three months at 4.25
Time: Months
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5
6
2
Interest Rate Risk
3
 Measuring Impact
 Gap analysis
 Duration (later)
Example
4 year loan, USD 9,000,000
Current interest rate 8%
Amortised by 8 equal semi annual payments of
principal
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Interest Rate Risk - Gap Analysis
Months
0-6
6-12
12-18
18-24
24-30
30-36
36-42
42-48
Principal
9000
7875
6750
5625
4500
3375
2250
1125
i @ 8%
365
319
273
228
182
137
91
46
+ Principal
1490
1444
1398
1353
1307
1262
1216
1171
Op profit
1598
1597
1598
1597
1598
1598
1597
1598
I @ 10%
456
399
342
285
228
171
114
57
+ Principal
1581
1524
1467
1410
1353
1296
1239
1182
i @ 12%
547
479
411
342
273
205
137
68
+ Principal
1672
1604
1536
1467
1398
1330
1262
1193
Op profit
1598
1597
1598
1597
1598
1597
1598
1597
Short Fall
(78)
(7)
62
130
200
267
336
404
(1) Op Profit
1279
1278
1279
1278
1279
1278
1278
1278
Short Fall
(393)
(326)
(257)
(189)
(119)
(52)
16
86
(302)
(246)
(188)
(132)
(74)
(18)
39
97
(2) Op Profit
Short Fall
(1) At 12% interest and 80% forecast
profit (2) at 10% interest and 80% forecast op profit
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4
Interest Rate Risk
5
Instruments
 Forward Forward Money
 Financial Futures
 Forward Rate Agreement
 Interest Rate Swap
 Interest Rate Options
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Forward Forward Money
6
Situation: Need to borrow GBP 1,000,000 from 30 days time for 30 days
Current Interest Rate
1 month 3-3½
2 month 3¾-4
Borrowing Spread ¼%
Action: Borrow for 2 months at 4¼%, Deposit for 1 month at 3%
Borrow today GBP 997,540.31 and Deposit for 1 month
997,540.31 x .03 x 30/365 = 2,459.69 = 1,000,000 in total at T30
Cost of Borrowing: 997,540.31 x .0425 x 60/365 = 6969.12
Total to Repay at 60 days = 1,004,509.43
Effective Cost of Borrowing = 4,509.43 x 365/30 = 5.4865 from T30-T60
1,000,000
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Financial Futures
Definition
7
 A term used to designate the standardised contracts
covering the purchase or sale of an agricultural
commodity e.g. corn, commodity e.g. oil, foreign
currency or financial instrument for future delivery
on an organised futures exchange
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Financial Futures
An Example
Three Month Eurodollar Interest Rate Future
Unit of Trading
USD 1,000,000
Delivery/Expiry Months
March, June, September, December and
four serial months, such that 24 delivery months are
available for trading, with the nearest six delivery months
being consecutive calendar months
Delivery /Expiry Day
First business day after last trading day
Last Trading Day
11.00 Two business days prior to third
Wednesday of delivery month
Quotation
100.00 minus rate of interest
Minimum Price
Movement (tick size & value)
0.01
(USD 25)
Initial Margin
(Straddle Margin)
USD 625
(USD 200)
Trading hours
08.30 – 16.00
8
Financial Futures
Example
9




Date: 21st October 2014
Situation: USD 1,000,000 due November 21st 2014
Intention: Invest three month on interbank market
Problem: Expect rates to fall from current rate of 2 %
Questions
1)
Will you buy or sell futures?
2) How many?
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Financial Futures
Example
10
Action Today
Today in the Futures Market:
Buy one December contract at 98.1
(100 -1.9%)
Note: at today’s rate of 2 % USD 1,000,000 would earn
1,000,000 x .02 x 90/360 = 5,000
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Financial Futures
Example
11
Action on 21st November
 In cash market, arrange three month deposit of USD
at current rate of 1.5 %
 1,000,000 x .015 x 90/360 = 3,750
 This equals a ‘loss’ of 1,250 over 2% rate
 Sell the future for 98.6 (100 -1.4)
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Financial Futures
Example
12






Net Result
1,000,000 x .015 x 90/360
= 3,750
Bought Future at 98.10
Sold Future at 98.60
Gain
50 basis points
At USD 25 per ‘tick’
= 1,250
= 5,000
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Financial Futures
Example
13
Question?
 Why have we managed a perfect hedge?
i.e. ended up with USD 1,005,000 at end of
deposit?
 Note: the cash price moved from 2 to 1.5
 A movement of 50 basis points
 The futures price also moved by 50 basis points
exactly offsetting the loss on the cash market
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Financial Futures
Example
14
 Will this always be so?
 No
Futures market
Basis
Cash market
Today
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Expiry
Financial Futures
Example
15
 So what if held to expiry?
 Cash market = 1.5 therefore futures price would be







98.50
But bought at 98.10
Gain 40 basis points
Therefore net result = 40 x 25 = 1,000
Plus interest earned at 1.5 = 3,750
Total
4,750
So effective interest
= 4,750/1,000,000 x 360/90 x 100 = 1.9%
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Forward Rate Agreements (FRA’s)
16
An agreement between two parties to
compensate one another, in cash, on a
certain date for the effect of any
subsequent movement in market rates
in respect of a future interest period.
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FRA Example
17
Need to borrow GBP 1,000,000 in 30 days time for 30
days. Worried rates will rise.
Quote
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Period
Rate
1-2
5 - 51/8
1-4
51/8 - 51/4
3-12
51/4 - 53/8
18
Rate Agreed 51/8 (5.125)
Actual Rate On Day T30 51/4
Compensation amount paid by Bank to Company
1,000,000 x .05125 x 30/365
= 4,212.33
1,000,000 x .0525 x 30/365
= 4,315.07
= 102.74
=
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102.74
= 102.30
1 + (.0525 x 30/365)
Test
19
1,000,000 - 102.30
= 999,897.70
999,897.70 x .0525 x30/365
=
4,314.63
Less Compensation Amount
Total Net Interest Paid
=
102.30
4,212.33
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Interest Rate Swap
Comparative Advantage
20
AAA
BBB
Difference
Benefit
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Fixed
8
10
2
Floating
Libor + 1/4
Libor + 1/2
1/4
13/4
81/2
AAA
21
BBB
L
-(8)
-(L + ½)
+ 8.1/2
+(L)
-L
-81/2
Net – (L –1/2)
Benefit
¾
+1
13/4
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Net –9.0
Interest Rate Swap
AAA
81/2
22
83/4
Bank
L
+ 1/4
BBB
L
-(8)
-(L + ½)
+ 8.51/2
+(L)
-L
Net – (L –1/2)
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-83/4
1/4
¾
¾
13/4 Benefit
–91/4
Interest Rate Cap or Ceiling Agreement
23
An interest rate cap is an agreement
between the seller or provider of the
cap and the borrower to limit the
borrower’s floating interest rate to a
specified level for an agreed period of
time. For the investor substitute floor
and investor above.
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Interest Rate Cap
24
10
9
Unhedged Rate
Effective Interest Rate
8
7
6
Hedged Rate
5
4
3
2
1
0
0
1
2
3
4
Market Interest
Rate
5
6
7
8
Cap: 5 Years, 6 Mo Rollover, Strike Price 7%, Premium 225 per million
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Interest Rate Collar Agreements
An interest rate collar is an agreement
whereby the seller or provider of the
collar agrees to limit the
borrower/investors floating interest rate
to a band limited by a specified ceiling
rate and floor rate.
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25
Interest Rate Collar
10
9
Unhedged Rate
8
7
6
5
4
Hedged
Rate
3
2
Unhedged Rate
1
0
Collar: 5 year, 6 Mo Rollover, Zero Premium, Strike Prices 7% and 3%
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26
Duration
27
You have a bond, life 5 years with annual interest
payments of 8%, face value GBP 1,000
What is your problem?
 Market Price Risk
 Re-Investment Rate Risk
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Duration
28
Duration gives an ‘average life’ of the cash flows
of an instrument by weighting the Net Present
Values of the cash flows by their timing.
Cash Flow
Year
NPV
NPV x Y
80
1
74.07
74.07
80
2
68.59
137.18
80
3
63.51
190.53
80
4
58.80
235.20
1080
5
735.03
3675.15
1,000
4,312.13
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Duration
29
Duration = 4,312.13 = 4.31 years
1,000
Known as Macauley Duration
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Uses of Duration
30
Immunisation
Wish to fix yield on a portfolio of bonds regardless of
whether interest rates go up or down.
Done by creating a portfolio of bonds with a
Duration equal to the required period.
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Uses of Duration
31
Price Sensitivity
Modified Duration which is Macauley Duration
(1 + y/n)
Where
y = yield
n = number of discounting periods
4.31 = 3.99
(1.08)
Or increase in the market interest rate of 1% will lead to a drop in the
value of the bond of approximately 3.99%.
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