imported>Doug Williamson |
imported>Doug Williamson |
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| | (Rf). |
| 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.
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| | The theoretical rate of investment returns which can be earned on hypothetical investments which are considered to be risk-free for modelling purposes. |
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| <span style="color:#4B0082">'''Example 1'''</span>
| | The Capital asset pricing model (CAPM) incorporates this type of risk free rate. |
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| GBP 1 million is borrowed or invested.
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| GBP 1.03 million is repayable at the end of the period.
| | Historically, the rates of return on certain types of domestic central government debt were considered to be a close enough proxy for such hypothetical risk-free investments. |
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| | In the modern era, domestic central government debt is no longer considered to be risk-free for this purpose, nor for a number of other purposes for which it was historically considered to be risk-free. |
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| The periodic yield (r) is:
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| r = (End amount / Start amount) - 1
| | ====Interest rate benchmarks==== |
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| Which can also be expressed as:
| | The term 'risk-free rates' (RFRs) is also used in the context of interest rate benchmark rates. |
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| r = (End / Start) - 1
| | For example, risk-free rates that might be used as alternatives to LIBOR. |
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| ''or''
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| r = <math>\frac{End}{Start}</math> - 1
| | == See also == |
| | | * [[Benchmark]] |
| | | * [[Capital asset pricing model]] |
| = <math>\frac{1.03}{1}</math> - 1
| | * [[Credit spread ]] |
| | | * [[Gilts]] |
| = 0.03
| | * [[Interest rate risk]] |
| | | * [[LIBOR]] |
| = '''3%'''
| | * [[Risk-free rates]] |
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| <span style="color:#4B0082">'''Example 2'''</span>
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| GBP 0.97 million is borrowed or invested.
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| GBP 1.00 million is repayable at the end of the period.
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| The periodic yield (r) is:
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| r = <math>\frac{End}{Start}</math> - 1
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| = <math>\frac{1.00}{0.97}</math> - 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 = 1.00, as expected.
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| <span style="color:#4B0082">'''Example 3'''</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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| The periodic yield (r) is defined as:
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| r = <math>\frac{End}{Start}</math> - 1
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| ''Rearranging this relationship:''
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| 1 + r = <math>\frac{End}{Start}</math>
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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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| <span style="color:#4B0082">'''Example 4'''</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 defined as:
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| r = <math>\frac{End}{Start}</math> - 1
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| ''Rearranging this relationship:''
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| 1 + r = <math>\frac{End}{Start}</math>
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| Start = <math>\frac{End}{(1 + r)}</math>
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| ''Substitute the given data into this relationship:''
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| Start = <math>\frac{1.00}{(1 + 0.030928)}</math>
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| = '''GBP 0.97m'''
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| ''Check:''
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| Amount at start = 0.97 x 1.030928 = 1.00, as expected.
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| ====Effective annual rate====
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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====
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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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| *[[Effective annual rate]] | |
| *[[Discount rate]] | |
| *[[Nominal annual rate]] | |
| *[[Nominal annual yield]] | |
| *[[Periodic discount rate]] | |
| *[[Yield]] | |
| *[[Forward yield]]
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| *[[Zero coupon yield]] | |
| *[[Par yield]]
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| ===Other resources===
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| [[Media:2013_09_Sept_-_Simple_solutions.pdf| The Treasurer students, Simple solutions]]
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(Rf).
The theoretical rate of investment returns which can be earned on hypothetical investments which are considered to be risk-free for modelling purposes.
The Capital asset pricing model (CAPM) incorporates this type of risk free rate.
Historically, the rates of return on certain types of domestic central government debt were considered to be a close enough proxy for such hypothetical risk-free investments.
In the modern era, domestic central government debt is no longer considered to be risk-free for this purpose, nor for a number of other purposes for which it was historically considered to be risk-free.
Interest rate benchmarks
The term 'risk-free rates' (RFRs) is also used in the context of interest rate benchmark rates.
For example, risk-free rates that might be used as alternatives to LIBOR.
See also
