Monetary policy and Periodic yield: Difference between pages

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imported>Doug Williamson
(Expand. Source: linked pages and Bank of England webpage http://www.bankofengland.co.uk/monetarypolicy/Pages/default.aspx)
 
imported>Doug Williamson
(Link with The Treasurer.)
 
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Monetary policy is central government or other policy to stimulate or otherwise influence economic activity by influencing money supply or interest rates.  
__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.  


Historically, mechanisms for influencing the money supply have included the use of open market operations, quantitative easing, the central bank discount rate and reserve requirements.


<span style="color:#4B0082">'''Example 1'''</span>


====UK monetary policy====
GBP 1 million is borrowed or invested.


In recent years the primary objectives of UK monetary policy have been 'stable prices' and confidence in the currency, collectively known as 'monetary stability'.
GBP 1.03 million is repayable at the end of the period.  


'Stable prices' are defined by the UK government's inflation target, currently 2% per annum as measured by the UK Retail Prices Index (RPI).


The periodic yield (r) is:


Responsibility for setting monetary policy - to achieve monetary stability - rests with the Bank of England's Monetary Policy Committee (MPC).
r = (End amount / Start amount) - 1


Which can also be expressed as:


Monetary policy in the UK has usually operated through setting the Bank of England's interest rate, the Official Bank Rate, or 'Bank Rate'.
r = (End / Start) - 1


This rate is often referred to as the 'Bank of England Base Rate'.
''or''


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


====Quantitative easing in the UK ====


In 2009 the MPC announced that in addition to setting Bank Rate, it would start to inject money directly into the economy by purchasing financial assets – often known as quantitative easing.
= <math>\frac{1.03}{1}</math> - 1


= 0.03


== See also ==
= '''3%'''
* [[Bank of England]]
 
* [[Discount rate]]
 
* [[Financial Policy Committee]]
<span style="color:#4B0082">'''Example 2'''</span>
* [[Fiscal policy]]
 
* [[Interest rate]]
GBP  0.97 million is borrowed or invested.
* [[Keynesianism]]
 
* [[Monetary Policy Committee]]
GBP 1.00 million is repayable at the end of the period.
* [[Money supply]]
 
* [[Open market operations]]
 
* [[Quantitative easing ]]
The periodic yield (r) is:
* [[Reserve requirements]]
 
* [[Retail Prices Index]]
r = <math>\frac{End}{Start}</math> - 1
* [[Supply side policy]]
 
* [[ZLB problem]]
 
= <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.
 
 
<span style="color:#4B0082">'''Example 3'''</span>
 
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'''
 
 
<span style="color:#4B0082">'''Example 4'''</span>
 
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 (r to EAR and EAR to r):'''''
 
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
 
 
====Periodic discount rate====
 
The periodic yield (r) is also related to the [[periodic discount rate]] (d), and each can be calculated from the other.
 
 
'''''Conversion formulae (r to d and d to r):'''''
 
d = r / (1 + r)
 
r = d / (1 - d)
 
 
Where:
 
d = periodic discount rate
 
r = periodic interest rate or yield
 
 
==See also==
 
*[[Effective annual rate]]
*[[Discount rate]]
*[[Nominal annual rate]]
*[[Nominal annual yield]]
*[[Periodic discount rate]]
*[[Yield]]
*[[Forward yield]]
*[[Zero coupon yield]]
*[[Par yield]]
 
 
===Other resources===
[[Media:2013_09_Sept_-_Simple_solutions.pdf| The Treasurer students, Simple solutions]]

Revision as of 22:14, 22 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 (r to EAR and EAR to r):

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


Periodic discount rate

The periodic yield (r) is also related to the periodic discount rate (d), and each can be calculated from the other.


Conversion formulae (r to d and d to r):

d = r / (1 + r)

r = d / (1 - d)


Where:

d = periodic discount rate

r = periodic interest rate or yield


See also


Other resources

The Treasurer students, Simple solutions