Interest rate effect on assets and liabilities

How do you determine the effect on interest rate on asset and liability duration for ALM matching?

My understanding is : if asset duration is greater than liability duration, and if there is a rise in interest rates, asset values will fall more than than the decline in value of liabilities. If the interest rates decline, the asset values will rise more than the rise in liabilities.

The opposite happens when asset duration is lower than liability duration, if interest rates rise, the fall in value of assets will be less than fall in value of liabilities. If interest rates fall, the rise in asset values will be less than rise in liability values.

Am I correct?

Yes, with a parallel shift in interest rates.