Yield to Maturity Interpretations (FRM T3-10)

[my xls is here trtl.bz/2HifflO] Superficially, the yield to maturity (YTM, aka yield) simply inverts the usual time value of money (TVM) inputs by solving for the yield as a function of four inputs: face (future) value, coupon (payment), maturity (time), and current price (present value). But in terms of interpretation, I share four ways to think about yield: 1. Yield is the SINGLE discount rate that solves the present value to match the current price and consequently graphs a horizontal line; 2. Yield is an internal rate of return (IRR) which expects and reflects a "realistic" price input; 3. Yield is a complex average of the spot rates; e.g., if the theoretical price is the input, it will be close to the final spot rate; and 4. Due to reinvestment risk and interest rate risk (aka, duration risk), the yield (YTM) will only be the REALIZED yield if the bond is held to maturity AND the coupons happen to be reinvested at the same yield. Discuss this video here in our FRM forum: trtl.bz/2YwCOfm.

[@crystalife]

Thank you very much for making these amazing videos. It helps a lot!

[@FRANTAJE1]

Your videos are amazing and I enjoy every one of them. Would you please consider making some videos, or video, on stochastic interest rates? I think there is so much intuition hiden in this topic that when explained properly, which is something you absolutely excel at, many would appreciate. Its quite hard topic, especialy the intuition behind martingale measures and whatnot. Just for your consideration. Many thanks to you nevertheless.

[@58raza]

how are the coupon payments reinvested at the yield to maturity in your 4th point? also please can you explain what is reinvestment risk?

[@Jupiter1423]

properly priced bonds are zero npv projects

[@bhdkid1]

Hi there, thanks for your great work.
Upon reading about interest rates and bonds, there seems to be confusion about yield to maturity and the reinvestment rate assumption (citations to some papers posted below, there are many others saying similar things- YT won't let me post links to them but they are all free and easy to find on google). The question I have for you is does the YTM (and therefore IRR) assume that all intermediate cash flows are reinvested at the YTM rate (or IRR rate)? As when I get into the research on it, it seems like there are 2 groups that oppose each other on this fact.
Arjunan, Kannapiran and Kannapiran, Karthi, The Controversial Reinvestment Assumption in IRR and NPV Estimates: New Evidence against Reinvestment Assumption (February 16, 2017). Cost‐benefit Analysis and the Controversial Reinvestment Assumption in IRR and NPV Estimates: Some New Evidence against Reinvestment Assumption, Economic Papers, 36 ( 3), 351- 63, 2017.
Shawn M. Forbes, John J. Hatem, and Chris Paul. (Summer 2008). Yield-to-Maturity and the Reinvestment of Coupon Payments. JOURNAL OF ECONOMICS AND FINANCE EDUCATION • Volume 7 • Number 1.
Richard J. Cebula and Bill Z. Yang. (Summer 2008). Yield to Maturity Is Always Received as Promised. JOURNAL OF ECONOMICS AND FINANCE EDUCATION • Volume 7 • Number 1.

[@bionicturtle]

Sure thing. Per my point #2, yield (YTM) is an IRR that makes no reinvestment assumption for the coupons; this is a mathematical fact based on it being a solution to a given vector that includes coupons (aka, return on capital) and final principal (aka, return of capital) but not coupon reinvestment. Put another way, the yield calculation obviously does not include a "return on the return on" capital". Per my point #4, the cumulative future realized return will happen to equal the initial (ex ante) yield if the coupons are reinvested at the same yield, but this is a DIFFERENT fact (and highly unlikely to coincidentally occur!) that reminds us the the (ex ante) yield is hardly a guarantee of the future, realized yield at the bond's maturity, as coupon's do need to get reinvested (or at least they incur an opportunity cost). Yield is an IRR that reconciles TODAY's bond price with the future cash flow stream--it is makes no assumption about the FUTURE's realized yield as it makes no coupon reinvestment assumption(s). I hope that helps,

[@bhdkid1]

@@bionicturtle Thanks for the detailed answer and great help!