Internal trading and Modified duration: Difference between pages

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''Accounting''
(MD).


Sales and purchases between companies within the same accounting group.
Modified duration is an estimate of the market price sensitivity of an instrument, to small changes in yield.


It is the related proportionate price change of a market instrument or portfolio. 


Due to internal management reasons and tax transfer pricing regulations it is unlikely in practice that the sale of goods between two group companies would be at cost.


The seller would make its normal profit on the sale.
The estimate of change in market price is given by:


This would be a genuine profit in the accounts of the seller.
'''Modified duration x Starting Market price x Change in yield'''


However if the buyer has not sold the goods they have not left the group, and viewing the group as a single entity, no profit should be recognised.


A single entity cannot make a profit from selling goods to itself. The profit is said to be unrealised from the group perspective.
Often - but not always - the relevant yield is defined as the annual effective yield (EAR).


For this reason any profits or gains on internal trading are removed from the group accounts on consolidation.
For changes in EAR, modified duration is calculated from Macaulay’s duration as:




Also known as internal transfers.
MD = Duration / (1 + EAR)
 
 
For changes in simple nominal annual yields (R), modified duration is calculated as:
 
 
MD = Duration / (1 + (R / n) )
 
where n = number of compounding periods per year.
 
 
<span style="color:#4B0082">'''Example: Modified duration calculations'''</span>
 
Duration = 5.00 years.
 
Semiannual yield R = 6.00% (so n = 2)
 
and so EAR = 6.09%.
 
 
(i) With respect to the EAR:
 
MD = 5.00 / 1.0609
 
= 4.71
 
 
(ii) With respect to the Semiannual yield:
 
MD = 5.00 / 1.03
 
= 4.85
 
This shows that there would be a greater proportionate change in price for a 1% change in the Semiannual yield, than for a 1% change in the EAR.




== See also ==
== See also ==
* [[Consolidation adjustments]]
* [[Convexity]]
* [[Group]]
* [[Duration]]
* [[Transfer pricing]]
* [[Effective annual rate]]
* [[Macaulay duration]]
* [[Matching]]
* [[Modified convexity]]
* [[Price value of a basis point]]
* [[Semi-annual rate]]
* [[Volatility]]

Revision as of 14:05, 16 November 2016

(MD).

Modified duration is an estimate of the market price sensitivity of an instrument, to small changes in yield.

It is the related proportionate price change of a market instrument or portfolio.


The estimate of change in market price is given by:

Modified duration x Starting Market price x Change in yield


Often - but not always - the relevant yield is defined as the annual effective yield (EAR).

For changes in EAR, modified duration is calculated from Macaulay’s duration as:


MD = Duration / (1 + EAR)


For changes in simple nominal annual yields (R), modified duration is calculated as:


MD = Duration / (1 + (R / n) )

where n = number of compounding periods per year.


Example: Modified duration calculations

Duration = 5.00 years.

Semiannual yield R = 6.00% (so n = 2)

and so EAR = 6.09%.


(i) With respect to the EAR:

MD = 5.00 / 1.0609

= 4.71


(ii) With respect to the Semiannual yield:

MD = 5.00 / 1.03

= 4.85

This shows that there would be a greater proportionate change in price for a 1% change in the Semiannual yield, than for a 1% change in the EAR.


See also