Interest Rate Risk in the Banking Book and Periodic yield: Difference between pages

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imported>Doug Williamson
(Create the page. Source: IRRBB page.)
 
imported>Doug Williamson
(Expand to incorporate conversion formulae.)
 
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''Bank supervision - capital adequacy.''
__NOTOC__
Periodic yield is a rate of return - or cost of borrowing - expressed as the proportion by which the amount at the end of the period exceeds the amount at the start.  


(IRRBB).


IRRBB deals with the risks associated with a change in interest rates, and affecting a bank's banking book, as opposed to its trading book.
====Example 1====


GBP 1 million is borrowed or invested.


IRRBB includes potentially adverse effects on earnings, capital, or both.
GBP 1.03 million is repayable at the end of the period.  




Sources of IRRBB include interest rate gaps, basis risk, yield curve risk and option risk.
The periodic yield (r) is:


r = (End amount / start amount) - 1


IRRBB is treated by most regulators as a Pillar 2 risk.
Which can also be expressed as:


r = (End / Start) - 1


== See also ==
''or''
* [[Banking book]]
 
* [[Basis risk]]
r = <math>\frac{End}{Start}</math> - 1
* [[Capital adequacy]]
 
* [[EVE]]
 
* [[Interest rate risk]]
= <math>\frac{1.03}{1}</math> - 1
* [[Interest rate gap]]
 
* [[Market risk]]
= 0.03
* [[MCRMR]]
 
* [[MRBB]]
= '''3%'''
* [[NII]]
 
* [[Pillar 2]]
 
* [[Option risk]]
====Example 2====
* [[Shock]]
 
* [[Trading book]]
GBP  0.97 million is borrowed or invested.
* [[Yield curve risk]]
 
GBP 1.00 million is repayable at the end of the period.
 
 
The periodic yield (r) is:
 
r = <math>\frac{End}{Start}</math> - 1
 
 
= <math>\frac{1.00}{0.97}</math> - 1
 
= 0.030928
 
= '''3.0928%'''
 
 
''Check:''
 
Amount at end = 0.97 x 1.030928 = 1.00, as expected.
 
 
====Example 3====
 
GBP  0.97 million is invested.
 
The periodic yield is 3.0928%.
 
Calculate the amount repayable at the end of the period.
 
 
'''''Solution'''''
 
The periodic yield (r) is defined as:
 
r = <math>\frac{End}{Start}</math> - 1
 
 
''Rearranging this relationship:''
 
1 + r = <math>\frac{End}{Start}</math>
 
 
End = Start x (1 + r)
 
 
''Substituting the given information into this relationship:''
 
End = GBP 0.97m x (1 + 0.030928)
 
= '''GBP 1.00m'''
 
 
====Example 4====
 
An investment will pay out a single amount of GBP 1.00m at its final maturity after one period.
 
The periodic yield is 3.0928%.
 
Calculate the amount invested at the start of the period.
 
 
'''''Solution'''''
 
As before, the periodic yield (r) is defined as:
 
r = <math>\frac{End}{Start}</math> - 1
 
 
''Rearranging this relationship:''
 
1 + r = <math>\frac{End}{Start}</math>
 
 
Start = <math>\frac{End}{(1 + r)}</math>
 
 
''Substitute the given data into this relationship:''
 
Start = <math>\frac{1.00}{(1  +  0.030928)}</math>
 
 
= '''GBP 0.97m'''
 
 
''Check:''
 
Amount at start = 0.97 x 1.030928 = 1.00, as expected.
 
 
====Effective annual rate====
 
The periodic yield (r) is related to the [[effective annual rate]] (EAR), and each can be calculated from the other.
 
 
'''Conversion formulae'''
 
 
EAR = (1 + r)<sup>n</sup> - 1
 
 
 
r= (1 + EAR)<sup>(1/n)</sup> - 1
 
 
Where:
 
EAR = effective annual rate or yield
 
r = periodic interest rate or yield, as before
 
n = number of times the period fits into a calendar year
 
 
 
 
==See also==
 
*[[Effective annual rate]]
*[[Discount rate]]
*[[Nominal annual rate]]
*[[Periodic discount rate]]
*[[Yield]]

Revision as of 09:51, 1 November 2015

Periodic yield is a rate of return - or cost of borrowing - expressed as the proportion by which the amount at the end of the period exceeds the amount at the start.


Example 1

GBP 1 million is borrowed or invested.

GBP 1.03 million is repayable at the end of the period.


The periodic yield (r) is:

r = (End amount / start amount) - 1

Which can also be expressed as:

r = (End / Start) - 1

or

r = <math>\frac{End}{Start}</math> - 1


= <math>\frac{1.03}{1}</math> - 1

= 0.03

= 3%


Example 2

GBP 0.97 million is borrowed or invested.

GBP 1.00 million is repayable at the end of the period.


The periodic yield (r) is:

r = <math>\frac{End}{Start}</math> - 1


= <math>\frac{1.00}{0.97}</math> - 1

= 0.030928

= 3.0928%


Check:

Amount at end = 0.97 x 1.030928 = 1.00, as expected.


Example 3

GBP 0.97 million is invested.

The periodic yield is 3.0928%.

Calculate the amount repayable at the end of the period.


Solution

The periodic yield (r) is defined as:

r = <math>\frac{End}{Start}</math> - 1


Rearranging this relationship:

1 + r = <math>\frac{End}{Start}</math>


End = Start x (1 + r)


Substituting the given information into this relationship:

End = GBP 0.97m x (1 + 0.030928)

= GBP 1.00m


Example 4

An investment will pay out a single amount of GBP 1.00m at its final maturity after one period.

The periodic yield is 3.0928%.

Calculate the amount invested at the start of the period.


Solution

As before, the periodic yield (r) is defined as:

r = <math>\frac{End}{Start}</math> - 1


Rearranging this relationship:

1 + r = <math>\frac{End}{Start}</math>


Start = <math>\frac{End}{(1 + r)}</math>


Substitute the given data into this relationship:

Start = <math>\frac{1.00}{(1 + 0.030928)}</math>


= GBP 0.97m


Check:

Amount at start = 0.97 x 1.030928 = 1.00, as expected.


Effective annual rate

The periodic yield (r) is related to the effective annual rate (EAR), and each can be calculated from the other.


Conversion formulae


EAR = (1 + r)n - 1


r= (1 + EAR)(1/n) - 1


Where:

EAR = effective annual rate or yield

r = periodic interest rate or yield, as before

n = number of times the period fits into a calendar year



See also

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