Bond Duration, Yield, and Interest Rate Sensitivity
Summary
The document raises foundational questions about how yield relates to duration and discounting. It distinguishes Macaulay duration, the present-value-weighted average timing of a bond’s cash flows, from the bond’s final maturity. A bond with duration shorter than maturity pays some cash flows earlier, so duration can describe the timing of value recovery without implying that all principal is returned at that point. This concept also motivates duration matching in portfolio immunization, where matching asset and liability sensitivity can help reduce the effect of rate changes.
The questions explore which yield is used in duration calculations, what “interest rates” means when bond prices move, and how modified duration estimates price sensitivity. They also ask why a simple one-for-one price adjustment for a yield change is insufficient. The document itself is a set of questions rather than a worked explanation, so it provides no derivations or numerical examples resolving these points. Its learning value lies in identifying the distinctions a bond investor needs to understand: yield convention, cash-flow timing, market discount rates, and the approximate nature of duration-based price estimates.
Key ideas
- Macaulay duration is the present-value-weighted timing of a bond’s cash flows.
- Duration can be shorter than maturity because a bond may pay cash flows before principal repayment.
- Duration matching is used to align portfolio sensitivity with liabilities for immunization.
- Modified duration expresses approximate bond price sensitivity to changes in yield.
- Duration-based estimates are an approximation and do not replace repricing cash flows.
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Full text
# Duration and yield # Duration and yield I have some basic questions about mainly duration and yield. 1) Almost no-one defines what yield they are talking about when talking about duration and discount rate, I've seen some talk about interest rate some yield etc I'm assuming (from wiki on duration also) that usually people are talking about yield to maturity. Is this the same for general yield curves also do they mean yield to maturity? 2) I'm aware that Macaulay duration is the weighted present value time to receipt of cash flows but I'm unsure as to what that actually means from a practical stand point. Say a maturity is 5 years and the duration is 4.5 what does that actually tell me, I'm slightly confused as i believe it means that it would effectively take 4.5 years to earn the present value of all cash flows but i will only earn all the money back at maturity as the final payment is the biggest. Maybe an example of portfolio immunization might help here , why is it better to match durations over maturity for example? 3) When we say that bond prices rise when interest rates fall, are we talking about the base rates, like the bank of England rate rising? 4) For modified duration I'm unsure as to how this measures the sensitivity in price to interest rates. I've looked at many pages but they just put the equation and say it does, Wikipedia is quite good but I'm still unsure as to how exactly dividing through by 1 plus the rate gives you sensitivity to the interest rate. I really want to know the mechanics behind it however 5) I've read examples explaining that when interest rates rise for example 1% for example, the price must fall to increase the yield by 1% in order to make up for it. If this is the case then surely we can just work out the price from that, how does duration play into it or is this just a too simple example. I realise these are very basic questions but I'd like to know how these all fit together as opposed to just learning the equations and i find some definitions on the internet very confusing. Sorry if some are difficult questions to understand.
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