imported>Doug Williamson |
imported>Doug Williamson |
| Line 1: |
Line 1: |
| __NOTOC__
| | ''European Union (EU).'' |
| 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.
| |
|
| |
|
| | | Supervisory Review and Evaluation Process. |
| <span style="color:#4B0082">'''Example 1'''</span>
| |
| | |
| 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%'''
| |
| | |
| | |
| <span style="color:#4B0082">'''Example 2'''</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.
| |
| | |
| | |
| <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== | | ==See also== |
| | | * [[European Banking Authority]] |
| *[[Effective annual rate]] | | * [[ICAAP]] |
| *[[Discount rate]] | | * [[ILAAP |
| *[[Nominal annual rate]] | | * [[Liquidity risk]] |
| *[[Nominal annual yield]] | | * [[Pillar 2]] |
| *[[Periodic discount rate]] | | * [[TSCR]] |
| *[[Yield]] | |
| *[[Forward yield]]
| |
| *[[Zero coupon yield]]
| |
| *[[Par yield]]
| |
| | |
| | |
| ===Other resources===
| |
| [[Media:2013_09_Sept_-_Simple_solutions.pdf| The Treasurer students, Simple solutions]]
| |
