u/Embarrassed-Ad5667

Hi - I know this title is a little inflammatory but wanted to get a conversation going on the topic.

See attached image for reference.

I wanted to refresh my understanding of discounting cashflows. So, I pulled together some basic bond terms and evaluated the returns. I thought about keeping things simple and holding everything constant in a normal economic environment. That environment being an upward sloping yield curve. I understand that rates obviously change as time goes on, but I wanted to not deal with that complexity to start.

In this scenario, the YTM is not the true realized return an investor experience (it's super close though).

Just thought it is interesting that the quoted number (YTM) is not the number you will actually earn if absolutely nothing changes and you reinvest your coupons over time at those spot rates. To reiterate, if the most common curve (an upward sloping one) does not change at all through time (no shifts, no slope changes, nothing)... the state of rates when your bond matures is identical to when you invested, you will not earn the stated YTM. But it will be super close to that.

Just found that to be an interesting quark in how rates are quoted.

The YTM is the true realized return when the yield curve is perfectly flat and stays that way through time, so you can keep reinvesting the coupons at that rate.

Let me know if you disagree or found and error and respond back with some work to show please.

Original Reddit Post

Help, I'm confused. I need to understand a concept with YTM and realized return.

Is it possible, in an upward sloping yield curve (that stays exactly the same through time), for the initial stated YTM at bond issuance (assume a semi‑annual, government, risk‑free, coupon‑paying bond issued at par) to differ from the ultimate realized return experienced by the bondholder upon maturity?

To clarify: can the stated YTM differ from the actual realized return upon maturity?

I want to think in terms of both dollars and percent

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Said differently:

There are two time periods I care about:

1. At the start of the investment (“expected” return) At t = 0, I want to know how much money I expect to have at maturity under different scenarios: For each of these, what is the expected return? How should I think about the “expected” return at this stage?
   • No reinvestment of coupons
   • Reinvestment of coupons at a static upward‑sloping yield curve (term structure is fixed over time)
   • Reinvestment of coupons in a changing yield curve (Assume some expectation of rate change that the investor has. I care less about this line for now and more about the first two)
2. At the end of the investment (“realized” return) At maturity, I will actually know the full cash‑flow path and the exact amount of money I have earned under each scenario. This is the ex‑post, realized return.

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Main question:

How does the “expected” return at t = 0 differ from its corresponding “realized” return at maturity, and why (in both dollar and % terms)? In particular:

• In which cases did I end up earning exactly the stated YTM?
• In which cases did I not earn the YTM, and what is the precise reason?

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Workbook:

Here is a link to my workbook:
https://docs.google.com/spreadsheets/d/1THmJHKbDhxD2_2i4POPm8pDOqPLSwxaJ/edit?usp=sharing&ouid=112251604062566371150&rtpof=true&sd=true

Notes on the workbook:

• You'll have to download it and open in excel as I use some dynamic array functions
• This is very much a workbook of my thinking, not a proof of any final realization. I’ve been spinning my wheels and got frustrated, so I wanted to include what I have done so far. Sorry if it’s a bit messy. Let me know if you have questions
• Please respond with questions and, if you have a better way of thinking about it, with a workbook/model of your own.
• Most of the meat is in the “Bond Details” tab.