# Impact of interest rates on assets and liability value

If interest rates rise (given that duration of assets is larger than duration of liabilities) assets lose more value than liabilities, reducing the value of the firm’s equity. If interest rates fall, assets gain more value than liabilities, increasing the value of the firm’s equity. When interest rates rise, why do assets lose more value than liabilities?

D(A) > D(L)

when interest rates change - rise e.g.

Change in value of Assets = -D(A) * Change in Rate

Change in value of liabilities = -D(L) * Change in Rate

Since D(A) > D(L)

Change in value of Assets > Change in Value of Liabilties (and this is a negative change, remember)

hence Value of Assets < Value of Liabilities

You were going so strong until you hit that last line; I wish that you hadn’t written it.

Obviously, it ain’t necessarily true; indeed, it’s pretty darned hard for it to be true, as that would imply negative equity.

understood - thanks for the correction.

It’s not like you to make mistakes.

Must have been early in the morning or late at night.

When interest rates rise (and duration of assets is larger than duration of liabilities):

• Higher discount rate means lower asset value, meaning lower NPV - Higher discount rate means lower liability value, meaning higher NPV - Assets lose more than liabilities since assets duration > liabilities duration When interest rates rise (and duration of liabilities is larger than duration of assets): - Higher discount rate means lower asset value, meaning lower NPV - Higher discount rate means lower liability value, meaning higher NPV - Liabilities lose more than assets since liabilities duration > assets duration

Is that conceptually corect?

That’s correct from my understanding.

I like to think in terms of what’s repricing and placing A/L’s on a timeline:

Duration:

Assets

Liabs.

1month 2 3 4 5 6

Since assets reprice fast (shorter duration), then will perform better when rates rise and vice versa.

If you’re asset sensitive, you’re assets reprice faster than liabilities and you increase value of equity when rates rise.

If you’re liability sensitive, you’re liabilities reprice faster than your assets and you increase value of equity when rates fall.

That simple.

D(E) = [(A)*D(A) - (L)*D(L)]/E

where Assets (A) = Liabilities (L) + Equity (E) ; D( ) represents duration (% change in value)

A>L (for solvent firm)

if D(A) > D(L), sign of D(E) will be +ve

rates rise = value of equity falls and vice versa

its obviously different for the case where A