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This section outlines pricing formulae and market conventions for standard fixed income securities. Many of these formulae are provided by the RBA to ensure calculations are generic. You may also wish to visit the Practices, Standards, and Documentation pages at the Australian Financial Markets Association (AFMA) website for in-depth documentation on market conventions for these and other fixed income securities.
Each section on this page also includes a working calculator for the security described.
On this page
Cash (Simple Interest-at-Maturity)
Discount Securities
Fixed Coupon Bonds
Floating Rate Notes
Capital Indexed Bonds
Inflation Index Annuities
Cash (Simple Interest-at-Maturity)
At-call deposits, term deposits
The general formula for calculating the simple interest amount is:
I = P * r * (d / 365)
where:
P = principle amount or present value
r = rate of interest per annum
d = number of days
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Discount Securities
Bank Accepted Bills, Negotiable Certificates of Deposit, Promissory Notes, Treasury Notes
The general formula for calculating the present (discounted) value of a discount security is:
PV = FV / [1 + r * (d/365)]
where:
FV = Face (future) value of the security
r = per annum yield to maturity
d = number of days
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Fixed Coupon Bonds (RBA Formula)
Most Government, Semi-Government, and Corporate Benchmark bonds
Basic formula:
P = v^(f/d) * (g * (x + a) + 100*v^n)
Near-maturing securities (in final coupon period):
P = (100 + g) / [1 + (f / 365) * i]
where:
P = price per $100 face value; rounded to three decimal places
f = number of days from the settlement date to the next coupon date
d = the number of days in the half year ending on the next coupon date
g = the half-yearly rate of coupon payment per $100 face value
x = 1 if the security is cum-interest; 0 if the security is ex-interest
a = (1 - v^n) / i
n = the number of half-years from the next coupon date to maturity
v = 1 / (1 + i)
i = yield to maturity (half-yearly in the 1st formula; annual in the 2nd formula)
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Floating Rate Notes
Some collateralised debt obligations (mortgage-backed, asset-backed) may also be priced as FRNs. Refer to the particular issue for details of pricing for these securities.
Prices are based on information available on the day the deal is struck
Basic formula:
P = { [ Z * (b + im) * d/365 + ( (im-tm) / k ) * a + 1 ] / [ 1 + (r + tm) * f/365 ] }* 100
where:
P = price per $100 face value; rounded to three decimal places
Z = 1 if the security is cum-interest; 0 if the security is ex-interest
b = the reference rate from last interest reset date to next interest rate date
d = the number of days from the last coupon date to the next coupon date
im = interest margin (as a percentage) paid over or under the reference rate
tm = trading margin (as a percentage) paid over or under the reference rate
r = the reference rate to the next interest rate reset date
f = number of days from the settlement date to the next coupon date
a = [ 1 - (1+i)^(-n) ] / i
i = (s + tm)/k
k = payment frequency (1=annual, 2=semiannual, 4=quarterly, 12=monthly)
s = yield from settlement to the maturity of the FRN (with frequency k)
n = the number of whole coupon periods remaining to maturity (or call/put) date
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Capital Indexed Bonds
CIB's feature quarterly indexation of the outstanding capital or principal value, which is repaid in full at maturity. The indexation factor is usually based on the rate of consumer price inflation represented by the Australian Bureau of Statistics' CPI, although other price and wage indices are used. A coupon interest rate on the bond is set at issue. Interest payments will vary over time in line with the indexed capital or principal value.
Basic formula:
P = v^(f/d) * [ g * (Z + a) + 100 * v^n ] * Kt * (1+cdelta)^(-f/d) / 100
where:
P = price per $100 face value
Kt = the nominal value of the principal at the next interest payment date
Kt = K(t-1) * (1 + cdelta) rounded to two decimal places, where K(t-1) is the nominal value of the principal at the previous interest payment date. K(t-1) is equal to $100 (the face value of the stock) at the interest payment date on or prior to the earliest date on which the stock may be settled at their first issue.
cdelta = the average percentage change in the Consumer Price Index over the two quarters ending in the quarter which is two quarters prior to that in which the next interest payment falls (eg: if the next interest payment is in November, p is based on the average movement in the CPI over the two quarters ended in the June quarter preceding).
cdelta = [ ( CPI(t) / CPI(t-2) ) - 1] / 2
i = real yield
f = the number of days from the date of settlement to the next interest payment date
d = the number of days in the quarter ending on the next interest payment date
g = the fixed quarterly coupon rate payable (equal to the annual fixed rate divided by 4)
a = (1 - v^n) / i
n = the number of full quarters between the next interest payment date and the date of maturity
v = 1 / (1 + i)
Z = 1 if security is cum interest; 0 if the security is ex interest
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Inflation Index Annuities
An Inflation Indexed Annuity is a stream of regular payments that are adjusted with reference to the inflation rate to protect the real value of the payments from being eroded over time. The relevant inflation index is almost always the one quarter lagging CPI.
*FIIG Securities Limited makes no guarantee as to the accuracy of these formulae and accepts no responsibility for losses occurring, directly or indirectly, as a result of their use.
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