Bond and Periodic yield: Difference between pages

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1.  
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.  


A marketable longer-term debt instrument usually administered by a trustee.  
It is often denoted by a lower case (r).


Bonds typically require the issuer to repay the amount borrowed plus interest over a designated period of time.


The current market yield on the bond is both the market rate of return to the debt investor and the pre-tax market cost to the issuer of debt capital.
==Calculating periodic yield from start and end cash==
Given the cash amounts at the start and end of an investment or borrowing period, we can calculate the periodic yield.


Issuers of bonds include a wide range of corporate and public sector entities, including central governments.


<span style="color:#4B0082">'''Example 1: Periodic yield (r) of 3%'''</span>


2.  
GBP 1 million is borrowed or invested.  


In trade finance, an instrument issued by a bank or an insurance company, in favour of a buyer, on behalf of a supplier, as additional assurance to the buyer that the supplier will perform its obligations under the supply contract.
GBP 1.03 million is repayable at the end of the period.  


Such a bank bond or insurance company bond will be supported by an indemnity issued by the supplier in favour of the bank or insurance company.


The periodic yield (r) is:


3.
r = (End amount / Start amount) - 1


A guarantee provided by one party to another.
Which can also be expressed as:


r = (End / Start) - 1


4.
''or''


An amount of money provided as security for a guarantee.
r = <math>\frac{End}{Start}</math> - 1




== See also ==
= <math>\frac{1.03}{1}</math> - 1
* [[Agent bank]]
* [[An introduction to debt securities]]
* [[Bearer bond ]]
* [[Bond futures]]
* [[Bond issue]]
* [[Bond mandate]]
* [[Bonding]]
* [[Bulldog bond]]
* [[Callable bond]]
* [[Catastrophe bond]]
* [[Clean price]]
* [[CMO]]
* [[Convertible bonds]]
* [[Corporate bond]]
* [[Counter-indemnity]]
* [[Coupon bond]]
* [[Covered bond]]
* [[Depositary]]
* [[Dirty price]]
* [[Drop-lock bond]]
* [[Eurobond]]
* [[Exchangeable bond]]
* [[Floating rate note]]
* [[Foreign bond]]
* [[Gilts]]
* [[Government paper]]
* [[Guarantee]]
* [[Indemnity]]
* [[Investment-grade bond]]
* [[Jumbo]]
* [[My word is my bond]]
* [[Obligation]]
* [[On-demand bond]]
* [[Par bond]]
* [[Par yield]]
* [[Paying agent]]
* [[Performance bond]]
* [[Redeemable bond]]
* [[Retained bonds]]
* [[Security]]
* [[Shallow discount bond]]
* [[Short term]]
* [[Straight bond]]
* [[Yield to maturity]]


[[Category:Long_term_funding]]
= 0.03
[[Category:Compliance_and_audit]]
 
[[Category:Manage_risks]]
= '''3%'''
[[Category:Risk_frameworks]]
 
[[Category:Treasury_operations_infrastructure]]
 
<span style="color:#4B0082">'''Example 2: Periodic yield of 3.09%'''</span>
 
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.
 
 
==Calculating end cash from periodic yield==
We can also work this relationship in the other direction.
 
Given the cash amount at the start of an investment or borrowing period, together with the periodic yield, we can calculate the end amount.
 
 
<span style="color:#4B0082">'''Example 3: End amount from periodic yield'''</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'''
 
 
==Calculating start cash from periodic yield==
We can also work the same relationship reversing the direction of time travel.
 
Given the cash amount at the end of an investment or borrowing period, again together with the periodic yield, we can calculate the start amount.
 
 
<span style="color:#4B0082">'''Example 4: Start amount from periodic yield'''</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 (EAR)==
 
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 (d)==
 
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 11:34, 2 December 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.

It is often denoted by a lower case (r).


Calculating periodic yield from start and end cash

Given the cash amounts at the start and end of an investment or borrowing period, we can calculate the periodic yield.


Example 1: Periodic yield (r) of 3%

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: Periodic yield of 3.09%

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.


Calculating end cash from periodic yield

We can also work this relationship in the other direction.

Given the cash amount at the start of an investment or borrowing period, together with the periodic yield, we can calculate the end amount.


Example 3: End amount from periodic yield

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


Calculating start cash from periodic yield

We can also work the same relationship reversing the direction of time travel.

Given the cash amount at the end of an investment or borrowing period, again together with the periodic yield, we can calculate the start amount.


Example 4: Start amount from periodic yield

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 (EAR)

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 (d)

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