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School of Administrative Studies
Faculty of Liberal Arts and Professional Studies
York University
AP/ADMS4504
Fixed Income Securities and Risk Management
Fall 2010
Final Exam Formula Sheet
Duration
is computed as:
)
y
(
V
2
V
V
0
Δ
−
+
−
, and
convexity
,
)
y
(
V
2
V
2
V
V
2
0
0
Δ
−
+
=
−
+
where
Δ
y
= change in
yields in decimal,
V
0
= initial price,
V

= price if yields decline by
y
, and
V
+
= price if yields
increase by
y
The traditional approach to bond valuation:
price of a bond = PV (coupons) + PV (face value) =
t
t
)
r
1
(
)
r
1
(
r
1
r
1
C
+
+
⎥
⎦
⎤
⎢
⎣
⎡
+
−
×
value
Face
PV of an annuity =
⎥
⎦
⎤
⎢
⎣
⎡
+
−
×
t
)
r
1
(
r
1
r
1
C
;
FV of an annuity =
⎥
⎦
⎤
⎢
⎣
⎡
−
+
×
r
1
)
r
1
(
C
t
The floating rate payment on an interest rate swap is calculated as:
360
quarter
in
days
of
number
rate)
(floating
amount
notional
×
×
The fixed rate payment on an interest rate swap is calculated as:
360
quarter
in
days
of
number
rate)
(swap
amount
notional
×
×
The
sample variance
of daily interest rates (or yields) is calculated as:
,
1
)
(
Variance
1
2
−
−
=
∑
=
T
X
X
T
t
t
and
standard deviation =
,
Variance where
X
t
= percentage
change in yields on Day
t
, i.e.,
)],
y
y
[ln(
100
X
1
t
t
t
−
=
where
y
t
is the yield on Day
t
;
X
= the
sample mean for variable
X
t
; and
T
is the number of observations for the daily percentage
change in yields in the sample
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Annual standard deviation
=
year
a
in
days
of
number
deviation
standard
daily
×
Using “moving average” to forecast yield standard deviation (or yield volatility) assuming
X
=
0:
variance with equal weights =
;
1
T
X
T
1
t
2
t
−
∑
=
variance with unequal weights =
,
1
T
X
W
T
1
t
2
t
t
−
∑
=
where
the sum of the weights
W
t
is equal to
T
Price of callable bond = price of option free bond – price of embedded call option
Price of putable bond = price of option free bond + price of embedded put option
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This note was uploaded on 12/17/2010 for the course ATKINSON adms 4504 taught by Professor Nabil during the Fall '10 term at York University.
 Fall '10
 Nabil

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