Determining Bond and Treasury Bill Prices and Yields (Government of Canada Securities)
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Government of Canada Securities
- Technical Guide -
Determining Bond and Treasury Bill Prices and
Yields
Bonds
In general, there are two parameters that are needed to describe fully the cash
flows on a bond. The first is the maturity date of the bond, at which time the
principal, or face amount of the bond is paid and the bond retired. The second
parameter need to describe a bond is the coupon rate. A Government of
Canada bond issued in the domestic market pays one-half of its coupon rate
times its principal value every six months up to and including the maturity date.
Thus, a bond with an 8 per cent coupon maturing on December 1, 2005 will
make future coupon payments of 4 per cent of principal value on each June 1
and December 1 between the purchase date and the maturity date.
The price of the bond is found by discounting future cash flows back to their
present value as indicated in the following formula:
where
P
N
y
= price
= number of semi-annual periods
= yield to maturity (expressed in percentage points). The yield is divided
by 200 to convert the yield to a percentage on a semi-annual basis.
CF = cash flow in a given semi-annual period (coupon/2) and at maturity
(coupon/2) + 100
This may be better understood by considering the following example, which
shows the price per $100 that would equate a 2-year bond with an 8 per cent
coupon to a 6 per cent yield to maturity.
N
= 4 (two semi-annual payment in each of the two years)
coupon = 8% ( CF = 8/2 = 4 and at maturity CF = 4 +100 =104)
y
= 6% (yield to maturity)
If the bond is purchased between coupon payment dates, the price must be
http://www.fin.gc.ca/invest/bondprice-e.html
10/11/2008
Determining Bond and Treasury Bill Prices and Yields (Government of Canada Securities)
Page 2 of 3
adjusted for accrued interest that is owed to the seller of the bond.
Treasury Bills
Treasury bills are priced at a discount. The return to the investor is the
difference between the purchase price and the par value. The rate of return is
calculated by dividing this difference by the purchase price and expressing the
result as an annual percentage rate, using a 365-day year. For example, a
price of $990.13 per $1,000 of face amount for a 91-day bill would produce an
annualised rate of return equal to 4.00 per cent, computed as follows:
per cent
Market Convention for Quoting Bond and
Treasury Bill Prices and Yields in the Secondary
Market
Bonds
Bond prices are quoted as a percentage of the bond’s par or face value and
exclude accrued interest; e.g. if a nominal fixed coupon bond is quoted as
101.59, then the price of that bond is 101.59% or 1.0159 times the value of the
bond at maturity.
When an investor buys a bond between coupon payments, the investor must
compensate the seller of the bond for the coupon interest earned from the time
of the last coupon payment to the settlement date of the bond. This amount is
called accrued interest. Accrued interest for Government of Canada bonds are
calculated as follows:
C/2 × actual number of days from the last coupon payment to settlement date
actual number of days in coupon period
where C = coupon payment
The market convention for calculating accrued interest on Government of
Canada bonds is known as actual over actual basis since the actual day
counts are used.
Bond yields are quoted as the yield to maturity; i.e. the quoted yield is the yield
necessary to make the present value of the bond's cash flow equal to the
current market price. However, as previously mentioned, the quoted price and,
consequently, the quoted yield-to-maturity excludes accrued interest.
Therefore, the yield-to-maturity is determined by solving for y in the following
equation:
where
http://www.fin.gc.ca/invest/bondprice-e.html
10/11/2008
Determining Bond and Treasury Bill Prices and Yields (Government of Canada Securities)
P
N
y
CF
Page 3 of 3
= current price
= number of semi-annual periods left until maturity
= yield to maturity (expressed in percentage points).
= cash flow in a given semi-annual period (coupon payment/2) and at
maturity (coupon payment/2) + 100
Treasury Bills
The convention in Canada is to quote Treasury bills in yield terms. . The yield is
calculated as follows:
where
Y=
F=
P=
t=
quoted value
face value of the Treasury Bill
price
actual number of days remaining to maturity
The price of the Treasury bill can be determined by rearranging the above
equation and solving for (F-P)/P and then given F, solving for P.
- Technical Guide -
Last Updated: 2007-12-11
http://www.fin.gc.ca/invest/bondprice-e.html
Important Notices
10/11/2008