It depends how quickly a company/ individual/ country rolls over their debt.
Imagine you have a mortgage that has an interest rate that is indexed to fed funds rate, you'll instantly feel the rate increase and you will instantly start trying to balance your books(austerity). Compared to if you have a 20 year fixed mortgage where you don't really care what the rate does. You have a lot of certainty with your cash flow.
Bonds are a bit different because you pay the interest then finish off the bond by paying back the principle amount and a lot of debt is 'rolled over' meaning you renew your debt and get the new interest rate. A lot of corporate debt is also indexed to LIBOR so rates are updated automatically.
To model this really well you'd want to look at the raw data and see when these roll overs/principle repayments are due and do some scenario analysis to get a fell for how this would look.
The big boys at investment banks/hedge funds already had this priced in before you were born so good luck trading on it!!!