Consider a security with annual cash flows of $100,000 and a time to maturity of 9 years. The current interest rate is 9% p.a.. Which of the following would unconditionally increase its duration?
考虑年现金流为 100,000 美元且到期时间为 9 年的证券。目前的利率为每年 9%。以下哪项会无条件地增加其持续时间？

Question

Consider a security with annual cash flows of $100,000 and a time to maturity of 9 years. The current interest rate is 9% p.a.. Which of the following would unconditionally increase its duration?
考虑年现金流为 100,000 美元且到期时间为 9 年的证券。目前的利率为每年 9%。 以下哪项会无条件地增加其持续时间？

BlackTom AI · Accepted Answer

Question restatement: A security pays annual cash flows of $100,000 with a time to maturity of 9 years. The current yield is 9% per annum. Which of the following would unconditionally increase its duration?

Option 1: A decrease in maturity and a decrease in its annual cash flows.
- With both maturity and cash flows reduced, the weighted average time to receipt of cash flows tends to shift toward earlier payments and shorten the duration. Since duration generally rises with longer time to cash flow and is dampened by larger, earlier payments, this combination is unlikely to increase duration; it would more likely decrease duration.

Option 2: A decrease in maturity and an increase in its annual cash flows.
- Here, shorter time to receive cash flows tends to reduce duration, even though larger cash flows do not increase the time axis. The net effect is typically a reduction in duration because the remaining payments are sooner. Therefore, this option would not unconditionally increase duration.

Option 3: An increase in maturity only.
- Extending the time to maturity increases the weighted average timing of cash flows. All else equal, longer maturities push more cash flow weight further into the future, which raises the Macaulay duration. Since the yield is held constant at 9%, the present value weights still reflect the later cash flows, leading to a higher duration as maturity grows. This option is a classic way to increase duration unconditionally.

Option 4: An increase in maturity and an increase in its annual cash flows.
- Increasing both maturity and cash flows could have opposing effects on duration: longer maturity tends to raise duration, but larger near-term cash flows can pull the average payment date earlier, potentially reducing duration. The net effect is ambiguous and not guaranteed to increase duration unconditionally, since the extra near-term cash flows may offset the benefit of a longer horizon depending on their timing and size. Therefore, this option does not unconditionally increase duration.

In summary, concepts at play include how Macaulay duration responds to changes in time to maturity and the timing/size of cash flows. Longer maturities generally raise duration, while earlier or larger near-term payments tend to shorten it. The only option that unambiguously pushes duration upward across all else being equal is an increase in maturity only.

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