copyright anbirts1 definition of risk variability of possible returns or the chance that the outcome...

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Definition of Risk

Variability of Possible Returns

Or

The Chance That The Outcome

Will Not Be As Expected

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Interest Rate RiskThe risk of loss of interest revenue that occurs when interest rates change, through the mismatch of re-pricing of assets and liabilities.

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Lend 6 Months at 5.5Fund Three months at 4.25

Time: Months

Inte

res

t R

ate

s P

A

Yield curve

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Interest Rate Risk

• Measuring Impact• Gap analysis• Duration (later)

Example4 year loan, USD 9,000,000Current interest rate 8% Amortised by 8 equal semi annual payments of

principal

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Interest Rate Risk - Gap Analysis

(1) At 12% interest and 80% forecast op profit (2) at 10% interest and 80% forecast op profit

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

(2) Op Profit

Short Fall (302) (246) (188) (132) (74) (18) 39 97

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Interest Rate Risk

Instruments

• Forward Forward Money

• Financial Futures

• Forward Rate Agreement

• Interest Rate Swap

• Interest Rate Options

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Forward Forward MoneySituation: Need to borrow GBP 1,000,000 from 30 days time for 30 days

Current Interest Rate1 month 3-3½2 month 3¾-4Borrowing 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 month997,540.31 x .03 x 30/365 = 2,459.69 = 1,000,000 in total at T30Cost of Borrowing: 997,540.31 x .0425 x 60/365 = 6969.12Total to Repay at 60 days = 1,004,509.43Effective Cost of Borrowing = 4,509.43 x 365/30 = 5.4865 from T30-T60

1,000,000

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Financial FuturesDefinition

• 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 FuturesAn 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

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Financial FuturesExample

• Date: 21st October 2009• Situation: USD 1,000,000 due November 21st 2009• 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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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



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)



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



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



• Will this always be so?

• No

Cash market

Futures market

TodayExpiry

Basis



• 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%


Forward Rate Agreements (FRA’s)

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.


FRA ExampleNeed to borrow GBP 1,000,000 in 30 days time for 30 days. Worried rates will rise.

Rate Agreed 51/8 (5.125)Actual Rate On Day T30 51/4

Compensation amount paid by Bank to Company1,000,000 x .05125 x 30/365 = 4,212.331,000,000 x .0525 x 30/365 = 4,315.07

= 102.74

= 102.74 = 102.30 1 + (.0525 x 30/365)

Quote Period Rate

1-2 5-51/8

1-4 51/8-51/4

3-12 51/4-53/8


Test

1,000,000, - 102.30 = 999,897.70

999,897.70 x .0525 x30/365 = 4,314.63

Less Compensation Amount = 102.30

Total Net Interest Paid 4,212.33


Interest Rate SwapComparative Advantage

Fixed Floating

AAA 8 Libor + 1/4

BBB 10 Libor + 1/2

Difference 2 1/4

Benefit 13/4


81/2

L

-(L + ½)

+(L)

-81/2

Net –9.0

AAA

-(8)

+ 8.1/2

-L

Net – (L –1/2)Benefit

¾ + 1

13/4

BBB81/2

L

-(L + ½)

+(L)

-81/2

Net –9.0


Interest Rate Swap

AAA

-(8)

+ 8.51/2

-L

Net – (L –1/2) 1/4

¾ ¾

13/4 Benefit

Bank81/2

L

-(L + ½)

+(L)

-83/4

–91/4

BBB

L

83/4

+ 1/4


Interest Rate Cap or Ceiling Agreement

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.


Interest Rate Cap

Unhedged Rate

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Hedged Rate

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Cap: 5 Years, 6 Mo Rollover, Strike Price 7%, Premium 225 per million


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.


Interest Rate Collar

Unhedged Rate

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Unhedged Rate

Hedged Rate

Collar: 5 year, 6 Mo Rollover, Zero Premium, Strike Prices 7% and 3%


Duration

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


DurationDuration 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


Duration

Duration = 4,312.13 = 4.31 years

1,000

Known as Macauley Duration


Uses of Duration

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.


Uses of Duration

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%.

copyright anbirts1 definition of risk variability of possible returns or the chance that the outcome...

Documents

rate options slide

current rate

cash market slide

futures price

rate swap

actual rate

todays rate

expected slide