For those who are interested I was just having a discussion with a friend re: LADG and we think we may have come up with a simple way of viewing this formula. I found the Schweser notes don’t really offer any detail and I can’t stand reading the dribble from the CFA material. In simple terms a banks liabilities are its borrowings (deposits, bond issuance etc); it’s assets are it’s loans. The forumla measures the gap in duration b/w to the two adjusted for leverage. The relationship states that if LADG is <0 in an environment of increasing interest rates the MV of equity increases. Looking at this intuitively, for the LADG to be less than zero the duration of the liabilities is greater than the assets. Put another way, the banks borrowings have greater price sensitivity to changes in interest rates thus an increase in rates will decrease the value of the debt, the bank has borrowed at a cheaper rate than the current market offers. The assets (loans) have a smaller duration thus this is good from the banks perspective because as they mature they can reinvest at higher rates. A - L = E. For a given increase in rates L will decrease by a relatively greater proportion than A thus increasing E. The LADG captures this relationship. If LADG is <0 as rates are decreasing the inverse applies. Value of liabilities increase by a greater rate due to higher duration when compared to the banks assets, therefore equity decreases.
This is super helpful. Thanks:)
If you think of your assets and liabilities as a (single) portfolio, the duration of that portfolio is the weighted-average duration of the constituents: the weight (value) of the assets times the assets’ duration plus the weight (value) of the liabilities times the liabilities’ duration; the key is that the weight (value) of the liabilities is negative.
If the portfolio has a positive duration, its value (hence, the value of equity) will decrease when interest rates rise and increase when interest rates fall; should the portfolio have a negative duration, the opposite effect obtains.
LADG is nothing more than the duration of this portfolio.