Bank's LADG

[BN]

Schweser has the following about Leverage adjusted duration gap (LADG) for banks:
For an increase in interest rate,
If LADG < 0, market value of equity Increases
If LADG > 0, market value of equity Decreases
If LADG = 0, market value of equity is unchanged (immunized)
Can someone explain why this is the case…?
thanks,
- BN

 

[strikershank]

For instance.
Duration Assets = 6, duration labilities = 4, price = $1000 in each case so equity = 0.
Dollar duration value for a 1% rise in rates:
- (6*1000*0.01 - 4*1000*0.01) = equity value decreases by = -(60 - 40) = -$20.
you can see that now if the duration of your liabilities is greater than the duration of your assets and rates rise, that the decrease in the value of the liabilities will be greater relative to the decrease in the value of the assets for the same rise in rates.