imported>Doug Williamson |
imported>Doug Williamson |
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| The rate of return in the market today for a notional or actual deposit or borrowing:
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| #Starting at a fixed future date; and
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| #Ending on a later fixed future date.
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| | Copyrights, patents, trademarks and other similar and related rights. |
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| '''Example 1'''
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| The forward yield for the maturity 2-3 periods is 3% per period.
| | Intellectual property law is mainly about giving creators exclusive rights, for a limited period of time and to legally prevent others from using intellectual property, without permission. |
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| This means that a deposit of £1,000,000 at Time 2 periods would return:
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| £1,000,000 x 1.03
| | == See also == |
| | | * [[Chattel]] |
| = £1,030,000 at Time 3 periods. | | * [[Federation Against Software Theft]] |
| | | * [[Goodwill]] |
| | | * [[Intangible assets]] |
| A common application of forward yields is the pricing of forward rate agreements.
| | * [[IPR]] |
| | | * [[Know-how]] |
| | | * [[Monetisation]] |
| | | * [[Patent]] |
| The forward yield is also known as the [[Forward rate]] or (sometimes) the Forward forward rate.
| | * [[Proprietary]] |
| | | * [[Real property]] |
| (The [[forward forward rate]] is technically slightly different.)
| | * [[Research & development]] |
| | | * [[Royalty]] |
| | | * [[Tangible asset]] |
| '''Conversion'''
| | * [[Trademark]] |
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| If we know the forward yield, we can calculate both the [[zero coupon yield]] and the [[par yield]] for the same maturities and risk class.
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| The conversion process and calculation stems from the '[[no-arbitrage]]' relationship between the related yield curves.
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| '''Example 2'''
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| Periodic forward yields ('''f''') are:
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| f<sub>0-1</sub> = 0.02 per period (2%)
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| f<sub>1-2</sub> = 0.04 per period (4%)
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| The total accumulated cash at Time 2 periods hence, from investing £1m at Time 0 is:
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| £1m x 1.02 x 1.04
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| = £'''1.0608m'''
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| Under no-abitrage pricing conditions, the identical cash flows arise from investing in an outright zero coupon investment of two periods maturity, at the rate of '''z<sub>0-2</sub>''' per period, as follows:
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| £1m x (1 + z<sub>0-2</sub>)<sup>2</sup> = £'''1.0608m'''
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| Using this information, we can calculate the zero coupon rate for two periods' maturity.
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| (1 + z<sub>0-2</sub>)<sup>2</sup> = 1.0608
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| 1 + z<sub>0-2</sub> = 1.0608<sup>(1/2)</sup>
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| z<sub>0-2</sub> = 1.0608<sup>(1/2)</sup> - 1
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| = 0.029951 per period (= 2.9951%)
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| Investing the same £1m in the two-periods maturity zero coupon instrument on these terms would return the same terminal cash flow of £1.0608m as the forward investments, as follows:
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| £1m x (1.029951)<sup>2</sup>
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| = £'''1.0608m'''
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| '''Example 3'''
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| Now using the zero coupon rates ('''z'''), the par rates ('''p''') can also be calculated in turn.
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| The periodic zero coupon yields ('''f''') are:
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| z<sub>0-1</sub> = 0.02 per period (2%)
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| z<sub>0-2</sub> = 0.029951 per period (2.9951%)
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| The no-arbitrage relationship between par rates and zero coupon rates is summarised in the formula:
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| p<sub>0-n</sub> = (1 - DF<sub>n</sub>) / CumDF<sub>n</sub>
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| ''Where:''
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| p<sub>0-n</sub> = the par rate for maturity n periods, starting now
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| DF<sub>n</sub>) = the discount factor for 'n' periods maturity, calculated from the zero coupon rate (z<sub>n</sub>)
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| CumDF<sub>n</sub>) = the total of the discount factors for maturities 1 to 'n' periods maturity, again calculated from the zero coupon rates (z<sub>1</sub> to z<sub>n</sub>)
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| ''Applying the formula:''
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| p<sub>0-2</sub> = (1 - DF<sub>2</sub>) / CumDF<sub>2</sub>
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| p<sub>0-2</sub> = (1 - 1.029951<sup>-2</sup>) / (1.02<sup>-1</sup> + 1.029951<sup>-2</sup>)
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| = 0.029803 (= 2.9803% per period)
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| This is the fair (no-arbitrage) market price for the par instrument, which will produce the identical terminal cash flow of £1.0608m as follows:
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| Cash flows from the two period par instrument, paying periodic interest of 2.9803% per period, assuming an initial investment of £1m:
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| Interest coupon at Time 1 period = £1m x 0.029803 = £0.029803m
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| Principal + interest at Time 2 periods = £1m + 0.029803m = £1.029803m
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| The coupon receivable at Time 1 period is reinvested at the pre-agreed forward rate of 4% (0.04) for the maturity 1-2 periods.
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| So the Time 2 proceeds from the reinvested coupon received at Time 1 are:
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| £0.029803 x 1.04
| | [[Category:The_business_context]] |
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| = £0.030995 at Time 2
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| The total terminal value at Time 2 periods is:
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| 0.030995 + 1.029803
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| = £'''1.0608m''' (as before)
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| == See also ==
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| * [[Yield curve]]
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| * [[Par yield]]
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| * [[Zero coupon yield]]
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| * [[Forward rate agreement]]
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| * [[Periodic yield]]
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| * [[Discount factor]]
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| * [[Coupon]]
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