YIELD TO MATURITY ACCRUED INTEREST QUOTED PRICE …
[Pages:28]YIELD TO MATURITY ACCRUED INTEREST
QUOTED PRICE INVOICE PRICE
September 1999
Quoted Rate Treasury Bills [Called Banker's Discount Rate]
d = [ P1 - P0 ] * [ 360 ]
P1
N
d = Bankers discount yield
P1 = face value P 0 = Price N = number of days until maturity
P1* N * d = P1 -1
P0 360
P0
1 +
P 1 P0
d* N 360
=
P1 P0
=
holding
period
return
2
The invoice on a bond (what you pay) is quoted price plus accrued interest.
3
Government Bonds and Notes
Calculating Accrued Interest
Accrued interest is actual days/actual days
Last coupon date
settlement date
next coupon date
x
y
Accrued interest = x/y times interest payment
Example:
(1) 10% coupon (2) $100 interest annually or $50 semi-annual per
$1000 face
y = 183 x = 100
100 [50] = $27.32 183
4
Yield To Maturity
1. One coupon left [like T bill]
2. At coupon paying date
0
1
2
3
4
C Po
C
C
C
C + Prin
P0
=
C [1 + r
]
+
C [1 + r
]2
+
C [1 + r
]3
+
C + Prin [1 + r ]4
2
2
2
2
3. Between Coupon Dates
P0
+
A
=
C [1 + r
]w
+
[1 +
C r ]1+ w
+
[1 +
C r ]2+w
+
C + prin [1 + r ] 3+w
2
2
2
2
5
w = fraction of year to first coupon actual days over actual days
0
1
2
3
4
w
Note:
Ignore that intervals may be of uneven size because of Saturdays or end of month.
6
Eurobonds - will examine only bonds issued in dollars - interest paid annually usually
Calculating accrued interest
uses 30 day months 360 day years
Example 1:
1. Issue date 2. Settlement date
January 28 March 5
days
January [29, 30]
2
February 30 day
30
March
[1,2,3,4,5]
5
37
37 x interest = accrued interest 360
7
Example 2: 1. May 14 issue date 2. Sept 17 settlement date May 16
J, Ju Aug 90 Sept 17 123
The 31st is the same as the 30th.
123 x interest = accrued interest 360
8
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