imported>Doug Williamson |
imported>Doug Williamson |
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| 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.
| | ''Eurozone.'' |
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| It is often denoted by a lower case (r).
| | In relation to the Eurozone, the 'periphery' is a collective name for the five countries in the Eurozone with relatively weaker economies: |
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| | Portugal, Ireland, Italy, Greece and Spain. |
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| ==Calculating periodic yield from start and end cash==
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| Given the cash amounts at the start and end of an investment or borrowing period, we can calculate the periodic yield.
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| | These five countries are sometimes known as 'PIIGS', from the initial letters of their names, or 'SWEAP' (South and West Euro Area Periphery). |
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| <span style="color:#4B0082">'''Example 1: Periodic yield (r) of 3%'''</span>
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| GBP 1 million is borrowed or invested.
| | :<span style="color:#4B0082">'''''Core and periphery diverge'''''</span> |
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| GBP 1.03 million is repayable at the end of the period.
| | :"The eurozone periphery, except for Ireland, remains depressed relative to the core countries. Spain and Portugal are recovering at a glacial pace, but Italy remains mired in a decade-long recession. In Greece, domestic demand is cripplingly low... |
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| | :Meanwhile, Germany and the Netherlands have ballooning trade surpluses. |
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| The periodic yield (r) is: | | :The imbalances that caused the eurozone crisis have not gone away." |
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| r = (End amount / Start amount) - 1
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| ''Which can also be expressed as:'' | | :''The Treasurer magazine, Cash Management Edition April 2019 p21, Frances Coppola, economics and finance commentator and speaker.'' |
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| r = (End / Start) - 1
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| = (1.03 / 1.00) - 1
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| = 0.03
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| = '''3%'''
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| <span style="color:#4B0082">'''Example 2: Periodic yield of 3.09%'''</span>
| | == See also == |
| | | * [[Core countries]] |
| GBP 0.97 million is borrowed or invested.
| | * [[European Monetary Union]] |
| | | * [[Eurozone]] |
| GBP 1.00 million is repayable at the end of the period.
| | * [[Eurozone crisis]] |
| | | * [[Grexit]] |
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| As before, the periodic yield (r) is:
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| r = (End / Start) - 1
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| = (1.00 / 0.97) - 1
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| = 0.030928
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| = '''3.0928%'''
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| ''Check:''
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| Amount at end = 0.97 x 1.030928 = GBP 1.00m, as expected.
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| ==Calculating end cash from periodic yield==
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| We can also work this relationship in the other direction.
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| Given the cash amount at the start of an investment or borrowing period, together with the periodic yield, we can calculate the end amount.
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| <span style="color:#4B0082">'''Example 3: End amount from periodic yield'''</span>
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| GBP 0.97 million is invested.
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| The periodic yield is 3.0928%.
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| Calculate the amount repayable at the end of the period.
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| '''''Solution'''''
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| As before, the periodic yield (r) is:
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| r = (End / Start) - 1
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| ''Rearranging this relationship:''
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| 1 + r = (End / Start)
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| End = Start x (1 + r)
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| ''Substituting the given information into this relationship:''
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| End = GBP 0.97m x (1 + 0.030928)
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| = '''GBP 1.00m'''
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| ==Calculating start cash from periodic yield==
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| We can also work the same relationship reversing the direction of time travel.
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| 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.
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| <span style="color:#4B0082">'''Example 4: Start amount from periodic yield'''</span>
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| An investment will pay out a single amount of GBP 1.00m at its final maturity after one period.
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| The periodic yield is 3.0928%.
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| Calculate the amount invested at the start of the period.
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| '''''Solution'''''
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| As before, the periodic yield (r) is:
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| r = (End / Start) - 1
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| ''Rearranging this relationship:''
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| 1 + r = (End / Start)
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| Start = End / (1 + r)
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| ''Substitute the given data into this relationship:''
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| Start = End / (1 + 0.030928)
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| = '''GBP 0.97m'''
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| ''Check:''
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| Amount at end = 0.97 x 1.030928 = GBP 1.00m, as expected.
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| ==Effective annual rate (EAR)==
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| The periodic yield (r) is related to the [[effective annual rate]] (EAR), and each can be calculated from the other.
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| ====Conversion formulae (r to EAR and EAR to r)====
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| EAR = (1 + r)<sup>n</sup> - 1
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| r = (1 + EAR)<sup>(1/n)</sup> - 1
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| ''Where:''
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| EAR = effective annual rate or yield
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| r = periodic interest rate or yield, as before
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| n = number of times the period fits into a calendar year
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| ==Periodic discount rate (d)==
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| The periodic yield (r) is also related to the [[periodic discount rate]] (d), and each can be calculated from the other.
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| ====Conversion formulae (r to d and d to r)====
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| d = r / (1 + r)
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| r = d / (1 - d)
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| ''Where:''
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| d = periodic discount rate
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| r = periodic interest rate or yield
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| ==See also== | |
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| *[[Discount rate]]
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| *[[Effective annual rate]] | |
| *[[Forward yield]] | |
| *[[Nominal annual rate]] | |
| *[[Nominal annual yield]] | |
| *[[Par yield]] | |
| *[[Periodic discount rate]]
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| *[[Yield]]
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| *[[Zero coupon yield]]
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| == Other resources ==
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| [[Media:2016_02_Feb_-_Many_happy_returns.pdf| Many happy returns - calculating and applying interest rates and yields, The Treasurer]]
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| [[Media:2013_09_Sept_-_Simple_solutions.pdf| Simple solutions - converting between yields, The Treasurer]]
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| [[Category:Corporate_financial_management]]
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| [[Category:Cash_management]]
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