# Bank duration measure

Rules: LADG = Duration of Assets - Leveaged Duration of Liabilities. If LADG>0 then for an increase in interest rates, the market value of equity goes down. Issue: If you have a greater duration of assets over liabilities I’m thinking that an increase in interest rates is a positive thing. Can anyone explain this more in depth?

In your example, the value of your assets will decline more than the value of your liabilities. How is that a good thing? It’s great a in a decreasing interest rate environment, but not increasing.

I see what my issue was. For some reason I was thinking of assets from a floating rate perspective. But I suppose you should consider them as fixed. Ok now I can get on with my day.

In an extreme case, what if (Assets-Liabilities)<0, like those banks in 2008? But I think A > L if not mentioned in the exam. if L > A and LADG < 0, then the opposite is true, an increase in interest rate helps your overall position. think of something like an underfunded pension plan for this sort of scenario…

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.