Forward yield and Listing Rules: Difference between pages

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imported>Doug Williamson
(Add second example and link with No arbitrage conditions and No arbitrage pages.)
 
imported>Doug Williamson
(Add quote. Source: ACT ESG blog 19 Feb 2021 https://www.treasurers.org/hub/blog/ESG/Update-February-2021)
 
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The rate of return in the market today for a notional or actual deposit or borrowing:
''London Stock Exchange''
#Starting at a fixed future date; and
#Ending on a later fixed future date.


The Listing Rules are regulations which apply to all companies with a Main Market listing - or seeking a Main Market listing - on the London Stock Exchange.


'''Example 1'''
The Listing Rules are not mandatory for Alternative Investment Market (AIM) companies.


The forward yield for the maturity 2-3 periods is 3% per period.
However, some AIM-listed companies, and other companies, choose to follow the Listing Rules on a voluntary basis.


This means that a deposit of £1,000,000 at Time 2 periods would return:


£1,000,000 x 1.03
The Listing Rules are published by the UK's Financial Conduct Authority.


= £1,030,000 at Time 3 periods.


:<span style="color:#4B0082">'''''Climate risk disclosures'''''</span>


A common application of forward yields is the pricing of forward rate agreements.
:"The Financial Conduct Authority (FCA) implemented a new Listing Rule applicable to premium listed commercial companies designed to help users understand how they are managing climate-related risks.  


:The new Rule (LR 9.8.6(8)) does this by requiring disclosures in annual reports consistent with the recommendations and recommended disclosures of the Task Force on Climate-related Disclosures (TCFD).


:The Rule will apply to accounting periods beginning on or after 1 January 2021 with the first annual financial reports under the new rule will be published in the spring of 2022. "


The forward yield is also known as the [[Forward rate]] or (sometimes) the Forward forward rate.
:''ACT blog, 19 February 2021 - Naresh Aggarwal, Associate Director, Policy & Technical.''


(The [[forward forward rate]] is technically slightly different.)


== See also ==
* [[Alternative Investment Market]]
* [[De-listing]]
* [[Disclosure and Transparency Rules]]
* [[Financial Conduct Authority]]
* [[Initial public offering ]]
* [[Introduction]]
* [[Listing]]
* [[Listing particulars]]
* [[London Stock Exchange]]
* [[Premium Listing]]
* [[Private placement]]
* [[Security]]
* [[Standard Listing]]
* [[Stock]]
* [[Task Force on Climate-related Financial Disclosures]]


'''Conversion'''
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.
The conversion process and calculation stems from the '[[no-arbitrage]]' relationship between the related yield curves.
'''Example 2'''
Periodic forward yields ('''f''') are:
f<sub>0-1</sub> = 0.02 per period (2%)
f<sub>1-2</sub> = 0.04 per period (4%)
The total accumulated cash at Time 2 periods hence, from investing £1m at Time 0 is:
£1m x 1.02 x 1.04
= £'''1.0608m'''
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:
£1m x (1 + z<sub>0-2</sub>)<sup>2</sup> = £'''1.0608m'''
Using this information, we can calculate the zero coupon rate for two periods' maturity.
(1 + z<sub>0-2</sub>)<sup>2</sup> = 1.0608
1 + z<sub>0-2</sub> = 1.0608<sup>(1/2)</sup>
z<sub>0-2</sub> = 1.0608<sup>(1/2)</sup> - 1
= 0.029951 per period (= 2.9951%)
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:
£1m x (1.029951)<sup>2</sup>
= £'''1.0608m'''
'''Example 3'''
Now using the zero coupon rates ('''z'''), the par rates ('''p''') can also be calculated in turn.
The periodic zero coupon yields ('''f''') are:
z<sub>0-1</sub> = 0.02 per period (2%)
z<sub>0-2</sub> = 0.029951 per period (2.9951%)
The no-arbitrage relationship between par rates and zero coupon rates is summarised in the formula:
p<sub>0-n</sub> = (1 - DF<sub>n</sub>) / CumDF<sub>n</sub>
''Where:''
p<sub>0-n</sub> = the par rate for maturity n periods, starting now
DF<sub>n</sub>) = the discount factor for 'n' periods maturity, calculated from the zero coupon rate (z<sub>n</sub>)
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>)
''Applying the formula:''
p<sub>0-2</sub> = (1 - DF<sub>2</sub>) / CumDF<sub>2</sub>
p<sub>0-2</sub> = (1 - 1.029951<sup>-2</sup>) / (1.02<sup>-1</sup> + 1.029951<sup>-2</sup>)
= 0.029803 (= 2.9803% per period)


===Other links===
[http://www.treasurers.org/node/10045 Make a debut, David Tilston, The Treasurer April 2014]


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:
[[Category:Corporate_finance]]
 
Cash flows from the two period par instrument, paying periodic interest of 2.9803% per period, assuming an initial investment of £1m:
 
 
Interest coupon at Time 1 period = £1m x 0.029803 = £0.029803m
 
Principal + interest at Time 2 periods = £1m + 0.029803m = £1.029803m
 
 
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.
 
So the Time 2 proceeds from the reinvested coupon received at Time 1 are:
 
£0.029803 x 1.04
 
= £0.030995 at Time 2
 
 
The total terminal value at Time 2 periods is:
 
0.030995 + 1.029803
 
= £'''1.0608m''' (as before)
 
 
== See also ==
* [[Yield curve]]
* [[Par yield]]
* [[Zero coupon yield]]
* [[Forward rate agreement]]
* [[Periodic yield]]
* [[Discount factor]]
* [[Coupon]]

Revision as of 11:01, 11 March 2021

London Stock Exchange

The Listing Rules are regulations which apply to all companies with a Main Market listing - or seeking a Main Market listing - on the London Stock Exchange.

The Listing Rules are not mandatory for Alternative Investment Market (AIM) companies.

However, some AIM-listed companies, and other companies, choose to follow the Listing Rules on a voluntary basis.


The Listing Rules are published by the UK's Financial Conduct Authority.


Climate risk disclosures
"The Financial Conduct Authority (FCA) implemented a new Listing Rule applicable to premium listed commercial companies designed to help users understand how they are managing climate-related risks.
The new Rule (LR 9.8.6(8)) does this by requiring disclosures in annual reports consistent with the recommendations and recommended disclosures of the Task Force on Climate-related Disclosures (TCFD).
The Rule will apply to accounting periods beginning on or after 1 January 2021 with the first annual financial reports under the new rule will be published in the spring of 2022. "
ACT blog, 19 February 2021 - Naresh Aggarwal, Associate Director, Policy & Technical.


See also


Other links

Make a debut, David Tilston, The Treasurer April 2014

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