The
Heriot-Watt University/Institute and Faculty of Actuaries
British
Government Securities Database
constructed
by:
Dr
Andrew Cairns and Professor David Wilkie
sponsored
by:
The
Department of Actuarial Mathematics and Statistics,
The
Revision
1.10 June 2011
Five
files are available on this database.
Apart from this ReadMe text/html file, they are all Excel 2003
Workbooks. Anyone may download them
free. Whilst we believe the data to be
correct (subject to the caveats and explanations below), their accuracy is not
warranted, and we can take no responsibility for any use that may be made of
the figures. In particular they do not
indicate that any actual transactions took place at those prices on the dates in
question; indeed since many of the prices are constructed by averaging
quotations from different market-makers, they would hardly ever be the prices
of actual trades.
In
September 2005 a new style of index-linked stock was issued (1¼% Index-linked
2055). The indexing for this and
subsequent stocks is different from the older ones, and the lag is no longer an
exact eight months, but varies between two and three months. These stocks are described in Section F.
If
any user observes errors in our data, or has additional information or other
observations, we should be very pleased to hear from them, at A.J.G.Cairns @hw.ac.uk.
The
Excel files are:
A BGSDetails.xls
B BGSAmounts.xls
C BGSPrices.xls
D BGSIndices.xls
These
are available also as csv (comma separated variable) files:
A BGSDetailsCSV.csv
B BGSAmountsCSV.csv
C BGSPricesCSV.csv
D BGSIndicesCSV.csv
The
Excel files have several worksheets in each workbook. The csv files have the contents of all worksheets
in one file, so if they are read into an Excel file, all the data appears in
one worksheet. The top of each worksheet
is easily identified. The data on each
line ends with the word "END" so that all the lines have the same
number of commas in them, thus forming a fully rectangular array.
The
files are also available in two zipped files:
BGSExcel.zip
BGSCSV.zip
each
of which contains all the Excel or csv files together with this ReadMe file in
both text and html format. This may be
the most convenient way to download all the files.
The
files and their contents are described below.
A BGSDetails.xls
A1 This file contains details of all the
British Government Securities that we believe have been in issue between March
1964 and the present date. Stocks
included are: conventional gilts, floating rate stocks, index-linked stocks,
STRIPS and some government guaranteed stocks.
Stocks not included are: Treasury Bills, non-sterling issues (e.g.
stocks denominated in Dollars, Ecus or Euros). Incomplete data is recorded for floating rate
or variable rate stocks (e.g. the coupons paid are not shown). Incomplete data is given for convertibles
(e.g. the conversion terms).
A2 Three worksheets are included in the file:
"Codes", which explains the
abbreviations used on the other worksheets
"Details" for conventional
stocks
"IL Details" for
index-linked stocks
“STRIPS” for STRIPS
A3 The data for each stock lies in one
row. The fields listed below are shown
for conventional stocks. Note that dates
are displayed as Excel "d mm yyyy" format,
i.e. the day, the first three letters of the month and the four-digit year,
e.g. 1 Jul 1966. This can easily be
changed by the user in their own copy of the
file. Note that Excel records dates
accurately only from 1 March 1900 (it erroneously allows 29 Feb 1900), and does
not record dates prior to 1 Jan 1900.
The issue dates of some very old stocks are therefore shown as "1
Jan 1900". The columns are the same
for conventional stocks, index-linked stocks and STRIPS, although some columns
are applicable only to one of these categories of stock. For STRIPS, rather little data is relevant or
necessary.
A Sequence:
this is our (arbitrary) sequence number, starting initially at 100 and
increasing by steps of 100, so that there is plenty of space to insert future
issues. Stocks are identified uniquely
in other workbooks through this sequence number. Conventional stocks start at 100, index-linked
at 50000 and STRIPS at 60000.
B Inst
Code: the abbreviation used by the Debt Management Office (DMO) for the
stock. This is in a coded form, with
coupon, name, dates and suffix in sequence.
Coupon is given as a digit
and possibly a letter, the digit representing the integral rate per cent, the
fraction, if any, denoted by a letter:
H = 1/2
Q = 1/4
T = 3/4
A = 1/8
B = 3/8
C = 5/8
D = 7/8
Name codes are a two or three
letter abbreviation and are shown in the worksheet "Codes". The DMO uses:
AN Annuities
CL Consolidated
CV Conversion
EX Exchequer
FD Funding
FR Floating Rate
IL Index Linked
ILC Index Linked Convertible
TY Treasury or Treasury Gilts (as stocks issued
in 2005 and later are called)
TYC Treasury Convertible
WR War Stock
to
which we have added, for stocks now redeemed:
BE British Electric
BEA BEA
BO BOAC
BT British Transport
EG Exchequer Gas
EXC Exchequer Convertible
RD Redemption
SB Savings Bonds
VY Victory
VR Variable Rate
Dates: the
two digits giving the last two digits of the last or only year of redemption,
or four digits giving the first two digits of the first and last redemption
years.
Suffix: "A",
"B", etc for an A, B stock, i.e. a new tranche of a stock issued at a
later date
Example: 8HTY8082A
representing 8 1/2% Treasury 1980-82 "A".
The coding for STRIPS is less
condensed, and quite explicit. Thus,
e.g. UKT07JUN2002C represents the coupon strip (C)
maturing on 7 June 2002, and UK7TO7JUN2002P represents the principal strip (P)
for 7% Treasury 2002 also maturing on 7 Jun 2002.
C %:
percentage coupon, i.e. the rate of interest per £100 nominal paid per year.
D Name:
name of the stock.
E Suffix:
"A", "B", ... to identify further
tranches A, B, ... of each stock.
F Special
features: comments relevant to the stock.
"Small" indicates a small issue, for which we have incomplete
details (and no prices). There are also
other notes.
G First
year: earliest year of redemption; blank if there is only one year of
redemption, as for index-linked.
H Last
year: latest or only year of redemption.
Blank for "irredeemables".
I Issue
date: date (day-month-year) of issue.
This may be inaccurate by one or two days, because it has not always
been easy to see whether the recorded date is the actual issue date or the
first day of dealing; practice seems to have changed over the years.
J First
coupon payable on date: the date of payment of the first interest payment.
K Earliest
redemption: the date (day month year) of the first possible redemption date, or
blank if there is only one redemption date.
L Latest
redemption: the date (day month year) of the last or only redemption date. The first redemption date, if any, always has
the same month and year as the last. For
irredeemables it is blank.
M A
(B, C ) stock merged on date: the date on which an
"A" (B, C, ...) stock was amalgamated with the main stock; normally
this is the xd date of the first interest payment of
the A stock. An "A" stock
typically has an irregular first interest payment, and is therefore not
fungible with the main stock until after this payment has gone xd.
N Actually
redeemed: the date on which stocks that have been redeemed were in fact
redeemed.
O Frequency:
frequency of interest payments; 2 for all stocks except for the following
stocks which are payable quarterly: 2½% Consols, 2½% Annuities, 2¾% Annuities
and floating rate stocks.
P-S Payment
dates 1, 2, 3 and 4, in sequence within the calendar year.
T First
coupon: amount of first (possibly irregular) interest payment, per £100
nominal. This amount is calculated on
the basis of the annual coupon, the number of days from the issue day to the
first interest payment date, the convention applicable at the time for counting
days in the year and the convention applicable at the time for the number of
decimal places to which it is quoted and the way it is rounded. The amount is given in the prospectus for
each stock. Since the conventions have
varied from time to time, it has not been possible to check the exact accuracy
of the figures we have given.
U Last
coupon: amount of last interest payment, if this is irregular. This can only apply to “double-dated” stocks
(including irredeemables) if they are redeemed on a day other than an interest
payment date. So far it has applied only
to 3½% Funding 1999-2004, which will be (was) redeemed on 6 June 2003, with a
final interest payment of £1.382597 per £100 nominal.
X Indexing
lag: (for index-linked only): number of months lag for indexing, which is 8 for
all index-linked stocks issued before 2005.
For new-style index-linked this is left blank.
Y Base
month: (for index-linked only): the month eight months before the issue date,
on the basis of which indexing is calculated.
For new-style index-linked this is left blank.
Z Base
RPI: (for index-linked only): the value of the Retail Prices Index (adjusted as
necessary for rebasing of the RPI) for the base month for the stock. For new-style index-linked this is the
applicable interpolated RPI for the issue date.
AA Number
of calls: for stocks where the issue price has been paid in instalments, by
"calls", the number of such calls.
This column (and the next following columns) are
blank where the issue price was paid in one instalment; the amount of the issue
price is not recorded. The number of
calls, if given, is therefore at least 2, and may be as many as 4. Details of the calls are given in the
following columns.
AB, AD, AF, AH Call payment 1, 2, 3, 4: the amount of each call per £100
nominal.
AC, AE, AG, AI due on: the date on which each call was payable.
B BGSAmounts.xls
B1 This file contains the amounts in issue of
each BGS stock, including conventional and index-linked stocks, but not STRIPS,
at the end of each month from March 1964 to the latest date.
There
are (so far) three worksheets:
Monthly1964to1979
Monthly1980to1999
Monthly2000to2019
Index-linked
stocks are included only from March 1981, when they were first issued. The last month on each completed worksheet
(e.g. Dec 1979, Dec 1999) is repeated on the next worksheet.
B2 Each month gets one column, and each stock
one row. Identifying data for each stock
is given in the first few columns. This
should match up exactly with what is shown in the Details Workbook and in the
Prices Workbook.
A Sequence:
the unique sequence number used to identify the stock
B %:
coupon per cent
C Stock
name
D Suffix:
A, B, C, etc for subsequent tranches of the stock
E First
year: first possible redemption year (even for index-linked although it is
always blank)
F Last
year: last or only redemption year; blank for irredeemables
G Issue
date
H Last
redemption date
I Actually redeemed or amalgamated: for "A" stocks
the date of amalgamation is shown; for other stocks the actual redemption date
is shown.
J Special
features
Amount (in £ millions) in issue for
each stock for which the amount was non-zero on that date. The word "Redeemed" or
"Amalgamated" appears at the end of the month in which it was
redeemed or amalgamated.
B3 We have shown data for amounts from March
1964 because it is readily available from the Annual Reports, and it is
possible that the price data might be extended back towards that date (perhaps
even by someone other than us!).
C BGSPrices.xls
C1 This file contains the quoted prices of
each BGS stock, including conventional and index-linked stocks and also STRIPS,
at the end of each month from November 1975 to the latest date shown.
There
are (so far) three worksheets:
Monthly1975to1979
Monthly1980to1999
Monthly2000to2019
Index-linked stocks are included only from March 1981 and STRIPS
from December 1997. The last month on each completed worksheet
(e.g. Dec 1979, Dec 1999) is repeated on the next worksheet.
C2 Each month gets one column, and each stock
one row. Identifying data for each stock
is given in the first few columns. This
should match up exactly with what is shown in the Details Workbook and in the
Amounts Workbook.
A Sequence:
the unique sequence number used to identify the stock
B %:
coupon per cent
C Stock
name; for STRIPS the Inst Code is shown.
D Suffix:
A, B, C, etc for subsequent tranches of the stock
E First
year: first possible redemption year (even for index-linked although it is
always blank)
F Last
year: last or only redemption year (blank for irredeemables)
G Issue
date
H Last
redemption date
I Actually redeemed or amalgamated: for "A" stocks
the date of amalgamation is shown; for other stocks the actual redemption date
is shown.
J Special
features
C3 The data given for each date is:
Date of last working day of each month
Day of the week of the above
Settlement date corresponding to the
last working day
Day of week of the above
Price (in £ per cent nominal) for each
stock for which the price was available on that date.
C4 The following points should be noted:
C5 The prices are given to different accuracy
at different dates:
From November 1975 to June
1996 they are given in binary fractions (1/2, 1/4, etc, down to 1/32), which
was the method of quotation at the time.
From July 1996 onwards they
are given in decimals, but with varying numbers of decimal places.
C6 The prices come from different sources.
C6.1 Conventional
gilts:
From November 1975 to May
1984 they are derived from the prices collected by A. D. Wilkie while he was
responsible for checking, by parallel running, the then Financial-Times–Actuaries
Indices.
From June 1984 to April 1988
they have been transcribed from printouts of the microfilm versions of The
Financial Times, held in Edinburgh Public Library. These are not always clear; some end-of-month
dates are so obscure that they have been deduced with the aid of the prices for
the following working day and the day's change shown. Two months (April 1987 and November 1987) are
so obscure for several days in succession that we cannot read them at all. If anyone has a suitable and legible source,
such as a copy of the relevant section of The Financial Times, we would
be pleased to hear from them
From May 1988 to June 1996
they have been transcribed from photocopies of The Financial Times held
by Watson Wyatt Partners.
From July 1996 to March 2001
they are derived from disks provided by the DMO.
From April 2001 to the latest
date shown they have been taken from the DMO website.
C6.2 Index-linked
stocks:
From May 1981 to December
1984 they are derived from the prices collected by A. D. Wilkie while he was
responsible for checking, by parallel running, the then Financial Times–Actuaries
Indices.
From January 1985 to April
1988 they have been transcribed from printouts of the microfilm versions of The
Financial Times, held in Edinburgh Public Library. These are not always clear; some end-of-month
dates are so obscure that they have been deduced with the aid of the prices for
the following working day and the day's change shown. Two months (April 1987 and November 1987) are
so obscure for several days in succession that we cannot read them at all.
From May 1988 to November
1992 they have been transcribed from photocopies of The Financial Times
held by Watson Wyatt Partners.
From December 1992 to June
1996 they are derived from the prices collected by A. D. Wilkie while he was
responsible for checking, by parallel running, the index-linked section of the
FTSE-Actuaries Indices.
From July 1996 to March 2001
they are derived from disks provided by the DMO.
From April 2001 to the latest
date shown they have been taken from the DMO website.
C7 The prices are "clean" or
"dirty" depending on the class of stock and the date.
C7.1
"Clean" means that
there is no allowance for accrued interest in the quoted price; accrued
interest has to be calculated separately and added (or deducted) from the
quoted price to get the actual price per cent payable.
"Dirty" means that
accrued interest is included in the quoted price, and there is no separate
calculation of accrued interest. The
dirty price is the actual price per cent payable.
C7.2
Up to 28 February 1986 the
prices for stocks with a maturity date greater than five years were dirty,
while the prices for stocks with a maturity date less than five years were
clean.
From March 1986 to the latest
date the prices for all stocks are clean.
C7.3
The way in which accrued
interest has been calculated has varied from time to time. The indices have followed the market
convention at the time. Up to 30 October
1998 the basis was "Actual/365"; from 31 October 1998 onwards it has
been "Actual/Actual".
How the "ex div"
(strictly "ex interest") date is determined has also varied from time
to time. Up to 31 December 1995 it was
37 calendar days before the due date, except for 2 1/2% Consols, which is
payable on 5 January, 5 April, 5 July and 5 October, and for which the ex div
dates were 1 December, 1 March, 1 June and 1 September. From 1 January 1996 onwards the ex div date
has been 7 working days before the due date, except for 3 1/2% War Stock (Loan)
for which it is 10 working days.
C8 Prices are missing for some stocks for
dates close to the redemption date, and for others for the whole of the last
year of the stock. Prices for some “A”
stocks are missing because they did not appear in The Financial Times.
D BGSIndices.xls
D1 Values of the FTSE-Actuaries British
Government Securities Indices (formerly the Financial Times–Actuaries
BGS Indices) are given for the last working day of each month from 31 December
1975 to the most recent date. The data
is all on one worksheet, called "BGSIndices1975Onwards".
D2 One row is used for each date. One column is used for each index item. Note that this is transposed from the other
workbooks, but it allows all the data to go onto one worksheet. The index items included have varied with
time. The main sections are:
1 Gilts
(i.e. conventional BGS), which have existed for the full period since 31
December 1975.
2 Debentures
and Loan Stocks, which commenced on 30 December 1977 and ceased on 30 December
1994.
3 Preference
Shares, which commenced on 30 December 1977 and ceased on 30 November 1990.
4 Index-linked
Stocks, which commenced 31 May 1981 (after the first such stock became fully
paid).
5 Bank
Base Rate, commencing 31 December 1975, together with a Total Return Index
based on Bank Base Rate; see Section G.
Each of the sections contains price
indices and yield indices.
D3 The items included in each of the indices
has varied from time to time. We have
followed whatever was published at the date, except that we have derived our
information for earlier years from the series of articles by A. D. Wilkie
published in Journal of the Institute of Actuaries and in Transactions
of the Faculty of Actuaries covering the years from 1976 to 1984.
D4 Particular changes to be noted are:
1 Irredeemables yield: from December 1975
to December 1977 this was calculated as the “long” point of the high coupon
yield curve; from December 1977 onwards it was calculated as the average
(aggregate) yield of the irredeemable stocks.
2 25/20 years yield, for Low, Medium and
High Coupon bands: from December 1975 to March 1991 this was the 25 years yield
from the calculated yield curves; from April 1991 to October 1998 it was the 20
years yield; the series ceased in October 1998.
3 Number of stocks in each sector and
Accrued Interest commenced in December 1990 (though the number of stocks is
available sporadically before that date), for both BGS and Index-linked.
4 For BGS the 5-10 and 10-15 year sectors,
Total Return Indices, and the Yield, Duration and Weight for each sector
commenced in November 1998.
5 The Low, Medium and High coupon bands
ceased in November 1998, except that Medium and High 15-year yields continued
until May 1999.
6 Preference indices commenced in December
1977 and ceased in November 1990
7 Debenture and Loan Stock indices
commenced in December 1977 and ceased in December 1994.
8 Index-linked indices commenced in May
1981 with an All Stocks sector.
9 For index-linked Up to 5 years and Over
5 years indices commenced in January 1986; 5-15 years and Over 15 years indices commenced in November 1998, along with Total
Return Indices and Weights for each sector.
10 For index-linked yields on the basis of 5%
and 10% inflation were given from May 1981 to October 1998; yields and also
duration on the basis of 0% and 5% inflation are given from November 1998 onwards.
11 For index-linked duration on the basis of
0% inflation ceased in August 2005, but has been reinstated when available from
time to time since then..
12 For both conventionals
and index-linked all the calculations of yield and duration omitted stocks with
less than one year to maturity prior to 3 May 2011, but after that date these
stocks have been included. Note that
this change makes only a small difference to the yields for the “Under 5 years”
and “All stocks” sectors, but makes a quite large difference to the duration,
especially for the index-linked.
D5 It sometimes occurs that an error is made
in the calculation of the indices for a particular day, which may be noted and
corrected by The Financial Times or by FTSE International in the following
day's newspaper, or in a later day's. If
such an error occurred in the month-end indices, we may not have noticed its
subsequent correction, since in general we have used the newspaper for the day
following the last working day of each month.
If any such errors are drawn to our attention, we shall be please to
correct them.
E Monthly list of events and major changes
(routine changes like adding a further month’s data not noted)
E1 May 2003: Redemption
of 9¾% Conversion 2003 (£12mn).
Redemption of 2½% Index-linked 2003 (£2,734mn nominal).
Issue of
new stock: 4% Treasury 2009 (£3,500mn).
Issue of
further tranche of 4¼% Treasury 2036 (£2,250mn, making £5,000mn), and whole
stock made strippable, with extra strips:
Coupons:
7 September 2025, 7 March 2026, …, 7 March 2036.
Principal:
7 March 2036.
Addition of a column in BGSIndices
showing Bank Base Rate at the end of each month from December 1975.
This
report of monthly changes has not been continued.
F Technical features of “new-style”
index-linked gilts with three-month lag and “old-style” with eight-month lag
F1 The indexing method for “new-style” index
linked gilts, those issued from September 2005 (1¼% Index-linked 2055), differs
from the “old-style” index-linked gilts, those issued from March 1981 (2%
Index-linked 1996) to July 2002 (2% Index-linked 2035). The five differences are:
(i) indexing of coupon and redemption amounts (see ¶F2 and ¶F3);
(ii) calculation of first coupon (see ¶¶F4,
F5 and F6);
(iii) calculation of price (see ¶F7);
(iv) calculation of accrued interest (see ¶F8
and ¶F9);
(v) calculation of current indexed nominal
(see ¶F10).
F2 For old-style index-linked indexation of
coupon and redemption amounts was based on the values of the Retail Prices
Index (RPI) for the month eight months prior to the date of payment and the
value of the RPI eight months prior to the issue date (the Base RPI). Thus for 2% Index-linked 2035, issued in July
2002, the Base RPI is the value of the RPI for November 2001 (eight months
before July 2002), which is173.6. The
coupon due on 26 January 2006, at the rate of 1% before indexing, is calculated
using the value of the RPI for May 2005 (eight months before January 2006), which
is 192.0. The coupon, per £100 nominal,
is therefore calculated as 1% × 192.0 / 173.6 = £1.105991. For this stock the coupon is rounded to the
nearer £0.000001, and this is the only stock to which this rule applies. For other stocks the rounding rules
differ. For the earliest-issued stocks
the coupons and redemption amounts per £100 nominal were rounded down to
£0.01. The stocks to which this rule
applies are (were):
2% Index-linked 1996
2% Index-linked 2006
2½% Index-linked 2011
For
later stocks the coupons and redemption amounts per £100 nominal were rounded
down to £0.0001. The stocks to which
this rule applies are (were):
2% Index-linked 1988
2% Index-linked 1990
2% Index-linked 1992
2% Index-linked 1994
4⅝% Index-linked 1998
2½% Index-linked Convertible
1999
2½% Index-linked 2001
2½% Index-linked 2003
4⅜% Index-linked 2004
2½% Index-linked 2009
2½% Index-linked 2013
2½% Index-linked 2016
2½% Index-linked 2020
2½% Index-linked 2024
4⅛% Index-linked 2030
For
the last old-style index linked stock, 2% Index-linked 2035, the rule is to
calculate the coupons and redemption amounts per £100 nominal to the nearer
£0.000001.
Thus
when 4⅜% Index-linked 2004 reached its redemption date of 21 October 2004
the redemption amount per £100 nominal was calculated from the Base RPI (that
for January 1992, eight months before the issue date of 22 September 1992)
which was 135.6 and the value of the RPI for February 2004 (eight months before
October 2004) which was 183.8. The
calculation gave £100 × 183.8 / 135.6 = £135.5457 (rounded down). The last coupon payment was indexed similarly
and was calculated as 4⅜ /2 × 183.8 / 135.6 = £2.9650 (also rounded
down).
F3 For new-style index-linked the “Reference
RPI” changes each day. On the first day
of each month it is the value of the RPI for the month three months
previously. For intermediate dates it is
calculated for the day by linear interpolation.
Thus 1¼% Index-linked 2055 was issued with settlement on 23 September
2005. The Reference RPI for 1 September
2005 is that for June 2005, whose value is 192.2; the Reference RPI for 1
October 2005 is that for July 2005, whose value is also 192.2. The Base RPI is therefore calculated as (22 ×
192.2 (the later one) + 8 × 192.2 (the earlier one)) / 30 = 192.2 exactly. Normally the Reference RPI would be rounded
to the nearer 5th decimal place. The
first coupon for this stock is due on 22 May 2006, and the Reference RPI will
be calculated as: (21 × RPI for March 2006 + 10 × RPI for February 2006) / 31
and the “RPI Ratio” for that date will be calculated as this value divided by
the Base RPI (=192.2) rounded to the nearer 5th decimal place.
F4 For most gilts
(unless issued on a coupon date) the first coupon is an irregular one, and
depends on the number of days between the issue date and the date of payment of
the first coupon. The period until the
first coupon is paid may be shorter or longer than half a year and the
calculation is slightly different in each case.
Consider again 2% Index-linked 2035, an “old-style” index-linked, issued
on 11 July 2002 with the first coupon payable on 26 January 2003. Normal coupons are payable on 26 January
and 26 July each year, and these dates are treated as “pseudo-coupon days” even
when no coupon is payable on them. The
period for the first coupon is counted as interest for 15 days (from
11 July 2002 to 26 July 2002) plus one half year (from 26 July 2002 to 26
January 2003). There are 181 days from
26 January 2002 to 26 July 2002 (it was not a leap year) so the non-indexed
coupon per £100 nominal would be calculated as 2% × (15/181 + 1) × ½ = 1.0828729...
. The extra dots after this number
indicate that there are more decimal digits, not shown. However, this now needs to be indexed, and
the indexation can be calculated at the time the stock is issued, because the
values of the RPI for the relevant dates, November 2001 (eight months before
the issue date) and May 2002 (eight months before the first coupon date) are
known. They were 173.6 and 176.2
respectively. The indexed first coupon
was therefore 1.0828729 × 176.2 / 173.6 = 1.099091, rounded to the nearer
£0.000001. This indexed first coupon
could therefore be announced when the stock was first issued, and the indexed
accrued interest could be calculated from the issue date.
F5 For stocks with short first period the
calculation depends only on the number of days in the period, and there is no
addition of one half a year.
F6 For “new-style” index-linked the
calculations are in principle the same, but the indexed amount is not known at
the issue date. 1¼% Index-linked 2055
was issued 23 September 2005 with coupons payable on 22 May 2006. The long first period is counted in two
parts, 60 days from 23 September 2005 to 22 November 2005 and one half-year
from 22 November 2005 to 22 May 2006.
The non-indexed first coupon per £100 nominal is calculated as 1.25 ×
(60/184 + 1) × ½ = 0.828804… . This number will in due course be multiplied
by the RPI Ratio for 22 May 2006, as described in ¶F3, which will be known
about the middle of April 2006, and which will be rounded to the nearer 5th
decimal place; the resulting product will then be rounded to the nearer 6th
decimal place of £1.
F7 For old-style index-linked gilts the quoted
price per £100 nominal is the actual price, and includes such indexation as the
market thinks fit. For new-style
index-linked the quoted price is a notional “real” price, and needs to be
indexed to the settlement date to get the actual price. The quoted price for 1¼% Index-linked 2055 on
Friday, 30 September 2005 was 106.48 per £100 nominal. Settlement was on Monday, 3 October
2005. The Reference RPI for 3 October
2005 is calculated from the values for the RPI for July 2005 (192.2) and August
2005 (192.6) and its value is: (2 × 192.6 + 29 × 192.2) / 31 = 192.22581
(rounded to the nearer 5th decimal place).
The RPI Ratio for 3 October 2005 is calculated as the Reference RPI for
that date divided by the Reference RPI for the base date, 192.2, as shown in
¶F3, which comes to 192.22581 / 192.2 = 1.00013 (rounded to the nearer 5th
decimal place). The indexed (clean)
price for 30 September is therefore calculated as 106.48 × 1.00013 = 106.493842… . This is left
unrounded at this stage.
F8 Accrued interest on old-style index-linked
is calculated as for conventional (unindexed) gilts. The amount of the next coupon payment is
known at the beginning of the interest period, so the accrued interest can be
calculated on the “actual/actual” basis from the start of the period. The actual quoted price of 2% Index-linked 2035
on 30 September 2005 was 128.22. The
coupon due on 26 January 2006 is 1.105991, calculated as one half of 2% × RPI
for May 2005 / Base RPI, that for November 2001 = ½ × 2 × 192.0 / 173.6. The accrued interest for the settlement date
of 3 October 2005 was 0.414747…, and the “dirty” price (including accrued
interest) was 128.22 + 0.414747… = 128.634747… .
F9 Accrued interest on new-style index-linked
is calculated in the opposite order.
First, the unindexed amount is calculated, and then this is indexed up
to the settlement date. We return to 1¼%
Index-linked 2055. On 30 September 2005,
with a settlement date of 3 October the unindexed accrued interest, based on
the irregular long first period, is calculated counting 10 days from 23
September 2005 to 3 October 2005 as 1.25 /2 × 10/184 = 0.033967… . We now index this in the same way as the
clean price (see ¶F7) by multiplying by the RPI ratio of 1.00013, giving
0.033972… . This is added to
the clean price, 106.493842…, giving a dirty price per £100 nominal of 106.527814… . This is finally multiplied by the size of the
deal and rounded to pennies for payment.
F10 In the BGSAmounts
file the unindexed nominal amounts for each stock, as the end of each month,
are shown, and for index-linked stocks also the indexed amounts. For old-style gilts this is the unindexed
amount multiplied by the value of the RPI for the month eight months prior to
the given month and divided by the Base RPI.
For new-style index-linked it is the unindexed amount multiplied by the
RPI for two months prior to the given month and divided by the Base RPI; this
has the effect of indexing the amount to the first day of the month following
the given month.
F11 In the BGSDetails
file the unindexed first coupon is shown; the fields showing the rounding and
lag are blank, as is the Base Month, and the Base RPI is shown, rounded to the
5th decimal place. In the BGSPrices file the unindexed quoted price is shown for
new-style index-linked.
G Calculation of the Total Return Index
based on Bank Base Rate
G1 In the BGSIndices
file, column GN shows the value of Bank Base Rate (in the past also known as
Bank Rate and Minimum Lending Rate), on the last working day of each
month. Column GO shows a Total Return
Index (TRI) calculated on the basis of this interest rate in the following
way. The index is calculated as at the
last working day of each month (as shown in Column B), and is compounded
monthly. Interest is credited on a daily
basis, taking account of the values of Bank Base rate on each day. (We have the dates of change recorded in a
separate file, but they are not shown here.)
In a leap year interest is credited for 29 February, but calculated throughout
the year by dividing by 365 not 366. The
base of the index is 100.00 on 31 December 1975.
Acknowledgments
The
help of the Debt Management Office, FTSE International, Watson Wyatt Partners
and also David Jones and Craig MacLean, students from the Department of
Actuarial Mathematics and Statistics at
David
Wilkie and Andrew
First
edition: April 2002
Last
revision: March 2014