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Formulas for Test 2: FINA 465
Chapter 8
1) Change in interest rate in the
i
th bucket:
∆
NII
i
= (GAP
i
)
∆
R
i
= (RSA
i
 RSL
i
)
∆
R
i
Chapter 9
2) The price of a bond is the present discounted value of all future cash flows.
P =
Σ
n
t=1
[CF
t
/(1+R)
t
]
3) The duration of any fixedincome security that pays interest annually is given by:
D = Σ
n
t=1
[CF
t
• t/(1+R)
t
] / Σ
n
t=1
[CF
t
/(1+R)
t
] =>
D = Σ
n
t=1
[PV
t
• t] / Σ
n
t=1
[PV
t
]
D = duration measured in years
CF
t
= cash flow received at the end of period
t
n = last period in which cashflow is received
R = is the annual yield or current level of interest rates in the market
PV
t
= present value of the cash flow from period
t
4) The change in price for a small change in interest rate:
ΔP = D[ΔR/(1+R)]P
5) Duration of assets:
D
A
= X
1A
D
1A
+ X
2A
D
2A
+ … + X
n
A
D
n
A
Duration of liabilities:
D
L
= X
1L
D
1L
+ X
2L
D
2L
+ … + X
m
L
D
m
L
Where X
i
A
and X
i
L
are the market value proportions of each asset or liability held in the
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 Spring '11
 Berger
 Interest, Interest Rate

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