Development of the initial benchmark portfolio
The initial benchmark portfolio of January 2, 2001 consists of an initial (fictitious) investment in each of the last 13 issues of 91-day Québec Treasury bills (“QTB 91”). Consequently, these investments have the following features:
a) Issue date = “t”
= October 6, 2000 November 3, 2000 December 1, 2000
October 13, 2000 November 10, 2000 December 8, 2000
October 20, 2000 November 17, 2000 December 15, 2000
October 27, 2000 November 24, 2000 December 22, 2000
December 29, 2000
b) Maturity date = “t+91 days”
c) Purchase price = Pt
= (Fictitious) amount disbursed to purchase the QTB 91 issued on date “t”
= $1 000 000
d) Value at maturity = VMt
= Value at maturity date “t+91 days” of the QTB 91 issued on date “t”
= Pt x (1+ Yt) where Yt = average yield to maturity1 of QTB 91s actually issued on date “t”
|
For instance, the QTB 91 issued on October 6, 2000 had an average yield to maturity, for a period of 91 days, of 1.4199% (Y2000/10/06 = 0.014199). The value at maturity, on January 5, 2001, of the QTB 91 issued on October 6, 2000 is therefore:
VM2000/10/06 = P2000/10/06 × (1 + Y2000/10/06)
= $1 000 000 × (1 + 0,014199)
= $1 014 199$
The values at maturity of the QTB 91s for issues ranging from October 13 to December 29, 2000 are obtained in a similar way. The first line of Diagram I represents the values at maturity or the monetary flows of the benchmark portfolio as that portfolio was immediately after issue of the QTB 91 of December 29, 2000. This portfolio remained unchanged until January 2 inclusively. At such date, it constituted the “initial benchmark portfolio”.
|
Updating the initial portfolio
The portfolio is changed on each QTB 91 auction date (normally, on Thursday2 of each week). On the day of the auction, the decision is taken to purchase (fictitious), on the issue date relating to such auction (normally, on the Friday following the auction), a new QTB 91 with the following features:
Purchase price = amount that, in the benchmark portfolio, matures on the issue date of the new auction; this is the maturity value of the QTB 91 issued 13 weeks earlier;
Maturity date = on the Friday of the 13th week following the issue date of the new auction;
Yield to maturity = average yield to maturity of new QTB 91s, published on the auction date.
|
For instance, following the January 3, 2001 auction, the yield on QTB 91s that will be issued on January 5, 2001 and will mature on April 6, 2001 is released. In point of fact, this yield, indicated as Y2001/01/05, was 1.3855%.
We also know that on January 5, 2001, the QTB 91 issued on October 6, 2000 will mature; this amount at maturity, determined in the preceding section and indicated by VM2000/10/06, is $1 014 199.
Immediately after the January 3, 2001 auction, the initial portfolio is changed as follows: the amount maturing on January 5 is used to purchase a new QTB 91, to be issued on January 5, at the yield of the January 3 auction. If VM2001/01/05 indicates the value at maturity of this new QTB 91 issued on January 5, 2001, then:
VM2001/01/05 = VM2000/10/06 x ( 1+Y2001/01/05)
= $1 014 199 x 1.013855
= $1 028 251
The second line of Diagram I represents the monetary flows arising from the decision taken on January 3, 2001 to use the value at maturity of the QTB 91 issued on October 6 to purchase, on January 5, 2001, a new QTB 91 maturing on April 6, 2001.
The third line of Diagram I represents all the monetary flows of the portfolio as it exists after the January 3, 2001 auction. This portfolio remains unchanged until the auction of Wednesday, January 10.
|
If the Thursday of a given week is a holiday, the auction date is moved to the preceding Wednesday or, if that Wednesday is also a holiday, to the preceding Tuesday. The maturity date of the issue, 13 weeks later, remains the Friday.
If the Friday that is 13 weeks after a given auction date is a holiday, the maturity date of the issue relating to such auction is brought forward to Thursday or, if that Thursday is also a holiday, to Wednesday. The new auction held in the week of such earlier maturity will have as the issue date for the new QTB 91s the Wednesday or Thursday rather than the Friday of that week.
|
For instance, the QTB 91s issued on January 10, 2001 matured on Thursday, April 12 because Friday, April 13 was a holiday; the issue date relating to the auction of Wednesday, April 11 was therefore Thursday, April 12 and the maturity date of this issue was, according to the usual rules, Friday, July 13
|
As a result of the practice described above, the issue date of new QTB 91s always coincides with the maturity date of the QTB 91s issued 13 weeks earlier. However, there can be exceptions to this rule, for instance the week of the events of September 11, 2001. How such exceptional situations are taken into account in the benchmark portfolio is dealt with in the Explanatory notes section.
When the Ministère des Finances du Québec does not auction 91-day Québec Treasury bills, a matured Treasury bill is reinvested in a theoretical security of the same term so that there are always 13 securities in the portfolio. The theoretical security’s yield then corresponds to that of a Québec government security with a similar term to maturity. At maturity, the Québec government theoretical security is reinvested in Treasury bills auctioned by the Ministère des Finances du Québec, or in another theoretical security, as applicable.
Monetary flows of the benchmark portfolio
As described above, the benchmark portfolio always consists of 13 QTB 91s. Since QTB 91s have no coupon, their only monetary flow is the amount payable at maturity. Accordingly, at a given valuation date, the portfolio has 13 future monetary flows, namely the 13 values at maturity relating to the 13 QTB 91 issues immediately preceding the valuation date. Note that on the day of the auction, i.e. normally on a Thursday, the monetary flow maturing the next day is replaced, in the benchmark portfolio, by the monetary flow maturing on Friday, 13 weeks and one day later. This substitution is carried out on the day of the auction because it is already known at what rate of yield to maturity the amount maturing one day after the auction will be reinvested for a period of thirteen weeks. While the new QTB 91 does not bear interest between the auction date and the issue date, it is exposed to the risk of fluctuations in interest rates, which is taken into account by the method used.
|
To illustrate, suppose the valuation is carried out on Wednesday, January 10, 2001, immediately after the weekly auction of QTB 91s. The 13 monetary flows that make up the benchmark portfolio then fall, as shown in Table I, on Friday, January 19, January 26, … , April 6, and April 12,3 2001. These monetary flows stem from the QTB 91s issued respectively on Friday, October 20, October 27, … , January 5, and January 12, 2001. At the time of the valuation on January 10, the value maturing on January 12 constitutes a positive monetary flow for the portfolio, but the use of this same amount to purchase a QTB 91 on January 12 constitutes a negative monetary flow of equal value; the net monetary flow for that day is therefore zero. As a result of the purchase of the QTB 91 on January 12, there is a new positive monetary flow, i.e. the value maturing on April 12, 2001. These 13 monetary flows make up the benchmark portfolio on January 10, 2001, which portfolio remains unchanged until the next auction, on January 17.
|
TABLE I
Monetary Flows
Making up the Benchmark Portfolio on January 10, 2001
|
Issue date
of the
QTB 91
|
Maturity date
of the
QTB 91
|
Monetary flow
of the portfolio
|
|
2000/10/20
|
2001/01/19
|
$1 014 297
|
|
2000/10/27
|
2001/01/26
|
$1 014 333
|
|
2000/03/11
|
2001/02/02
|
$1 014 312
|
|
2000/11/10
|
2001/02/09
|
$1 014 440
|
|
2000/11/17
|
2001/02/16
|
$1 014 507
|
|
2000/11/24
|
2001/02/23
|
$1 014 477
|
|
2000/12/01
|
2001/03/02
|
$1 014 391
|
|
2000/12/08
|
2001/03/09
|
$1 014 206
|
|
2000/12/15
|
2001/03/16
|
$1 014 126
|
|
2000/12/22
|
2001/03/23
|
$1 014 020
|
|
2000/12/29
|
2001/03/30
|
$1 014 026
|
|
2001/01/05
|
2001/04/06
|
$1 028 251
|
|
2001/01/12
|
2001/04/12
|
$1 027 632
|
DIAGRAM I
|
Maturity: 2000/01/05 2000/01/12 … 2001/03/30 2001/04/06
|
Initial portfolio just before the auction on January 3, 2001:
|
Monetary flow:
|
$1 014 199 $1 014 252
|
…
|
$1 014 026 Zero
|
|
|
|
(VM 2000/10/06) (VM2000/10/13)
|
|
(VM2000/12/29)
|
|
Effect of the auction on January 3, 2001:
|
Monetary flow:
|
$1 014 199
|
|
|
|
|
Monetary flow:
|
|
|
$1 028 251
|
|
Portfolio resulting from the auction on January 3, 2001:
|
Monetary flow:
|
Zero $1 014 252
|
…
|
$1 014 026 $1 028 251
|
|
1 The rate of return is equal to the yield to maturity when the security is held to maturity, but the latter is used to avoid any confusion.
2 Auction date has been moved from Wednesdays to Thursdays in 2013.
3 Since Friday, April 13 is a holiday, the issue date is brought forward to Thursday, April 12.