Which of the following has a higher duration?

Duration measures the sensitivity of a bond's price to changes in interest rates, and it reflects the weighted average time until cash flows are received.

A bond with a longer maturity typically has a higher duration because for longer maturities, cash flows extend over a longer period of time. As a result, the present value of these cash flows is more sensitive to changes in interest rates. The rationale is that the longer the duration, the greater the potential change in price relative to interest rate movement. Thus, among the choices given, a bond that has a longer maturity tends to have a higher duration compared to counterparts with shorter maturities, regardless of coupon or yield.

While a bond with a higher coupon might provide more cash flows upfront, which reduces duration, and a higher market yield generally results in lower duration due to increased discounting effects, the fundamental principle here is that maturity is the dominant factor in determining duration. Likewise, bonds with embedded options may have modified durations that vary depending on the likelihood of the option being exercised. Thus, the focus on maturity clearly indicates that a bond with a longer maturity will have a higher duration compared to the others listed.