Final answer:
The 30-year treasury bond has the longest duration because it has the longest time to maturity of the options provided. Duration estimates how long it takes to be repaid a bond's price by its cash flows, and longer-term bonds have longer durations.
Step-by-step explanation:
When comparing different debt instruments, duration is a financial concept that describes how long it takes for an investor to be repaid the bond's price by the bond's total cash flows. Generally, the longer the time to maturity, the longer the duration of a bond. This is because investors have to wait longer to receive the principal and interest payments, which are received over a longer period.
In the question asked, the options are a one-year government bond, a five-year corporate bond, a 10-year mortgage-backed security, and a 30-year treasury bond. Of these, the 30-year treasury bond has the longest duration. This is because the 30-year bond has the longest time to maturity, which means the investor waits the longest time to receive all interest and principal payments compared to the other options listed.
Treasury notes and bonds are known for their safety since they are backed by the full faith and credit of the U.S. government. Their interest rates are typically lower than corporate bonds, which compensate for higher risk with higher interest rates. However, the 30-year treasury bond will still have the longest duration because duration is primarily determined by the length of time until maturity.