Investor A manages a portfolio of bonds with duration of $10$ years. Investor B man$-$

ages a portfolio of bonds with duration of $20$ years. In all other dimensions, the two

portfolios are identical. If interest rates go up next year $($and nothing else changes$),$

what will happen to the value of these portfolios:

A$.$ Both portfolios will suffer a loss and the percentage decline in value will be the

same across the two portfolios

B$.$ Both portfolios will suffer a loss and the percentage decline in value will be stronger

for portfolio $A$

C$.$ Both portfolios will suffer a loss and the percentage decline in value will be stronger

for portfolio B

D$.$ Both portfolios will suffer a loss but we do not know which portfolio will have the

stronger percentage decline in value