Lecture_7 - FINN 3225 Commercial Bank Management Lecture 7...

FINN 3225 - Commercial Bank
Management
Lecture 7 - Managing IRR: Economic Value of Equity
UNC Charlotte
October 1st, 2014
(UNC Charlotte) FINN 3225 - Commercial Bank Management October 1st, 2014 1 / 23

Duration Gap Analysis
We use duration gap to try to estimate changes in a
bank’s economic value of equity or EVE
EVE is just the market value of assets minus the market
value of liabilities
A bank with $ 100M in market value of assets and $ 90M
in market value of liabilities has EVE of $ 10M
If rates increase and market value of assets drops to
$ 96M and market value of liabilities drops to $ 88M, then
EVE will drop to $ 8M
(UNC Charlotte) FINN 3225 - Commercial Bank Management October 1st, 2014 2 / 23

Duration Gap Analysis (cont’d)
Three different measures of duration:
1
Macaulay’s duration
D =
n
∑
t
[ CF
t
/ ( 1 + i )
t
] × t
P *
Δ P
P
≈ -
D
( 1 + i )
× Δ i
2
Modified duration
D / ( 1 + i )
3
Effective duration
Eff Dur =
P
i -
- P
i +
P
0
( i + - i - )
P
i -
is price if rates fall, P
i +
is price of rates increase, P
0
is
current price, i + is initial rate plus increase, i - is initial
rate minus fall
Helpful for bonds with embedded options
(UNC Charlotte) FINN 3225 - Commercial Bank Management October 1st, 2014 3 / 23

Duration Gap Analysis (cont’d)
To conduct duration gap analysis, we:
1
forecast interest rates
2
estimate the market value of all bank assets, liabilities,
and EVE
3
estimate the weighted average duration of assets and
weighted average duration of liabilities; use these to
estimate duration gap
4
forecast changes in EVE across different interest rate
environments
(UNC Charlotte) FINN 3225 - Commercial Bank Management October 1st, 2014 4 / 23

Duration Gap Analysis (cont’d)
Duration of assets:
DA =
n ∑
i
w
i
D
a
i
w
i
= A
i
/ MVA : weight for asset i is the size of asset i
relative to total market value of n total assets
D
a
i
is duration of asset i
Duration of liabilities:
DL =
m ∑
j
w
j
D
l
j
w
j
= L
j
/ MVL : weight for liability j is the size of liability
j relative to total market value of m total liabilities
D
l
j
is duration of asset j
(UNC Charlotte) FINN 3225 - Commercial Bank Management October 1st, 2014 5 / 23

Duration Gap Analysis (cont’d)
Once we calculate EVE, we can get the change in
EVE as Δ EVE = Δ MVA - Δ MVL
We can estimate the change in the market value of