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My question is quick and simple. However, I would like to use this answer to further my understanding of bonds and yields.

If the YTM on a 10yr Note yesterday was 1.00% and the YTM on the same 10yr Note today is 1.10%, did the yield increase by:

  1. 0.10%, i.e. (1.10% - 1.00% = 0.10% ?
  2. 10.0%, i.e. (1.10%/1.00% - 1) = 10% ?

What I am looking to get out of an answer to this question:

  1. What does yield actually represent? We look at stock returns during a holding period as in terms of the current price and purchase price (basis). How can we look at stock returns in terms of yield?
  2. THE THING I DO NOT UNDERSTAND ABOUT BONDS (chicken or egg). Do traders who trade bonds trade the yield or the face value? Does the yield go up because bond prices go down or do bond prices go down because yields go up

Thank you for taking the time to answer this seemingly trivial question. However, this is a major blockage point in my studies for the CFA and Finance in general.

TL;DR: If the YTM on a 10yr Note yesterday was 1.00% Yesterday and the YTM on the same 10yr Note Today is 1.10%, did the yield increase by:

  1. 0.10%, i.e. (1.10% - 1.00% = 0.10% ?
  2. 10.0%, i.e. (1.10%/1.00% - 1) = 10% ?
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  • $\begingroup$ Yield is more intuitive (especially for people who are not professional bond traders), but your doubts about how to measure a yield change are precisely why traders sometimes measure market changes by $\Delta P/P$, especially when dealing with bonds of very different maturities. So both $P$ and $y$ are useful. $\endgroup$
    – noob2
    Feb 25 at 21:12
  • $\begingroup$ Usually people quote nominal changes in yield, i.e. 1. You may be interested in total return calculation where you have your change in price plus accrued interest to get you a percent that can compare you to another asset (say, stock). Keep in mind that yield cuts are selling (ie higher yields) and bumps are buying (lower yields). I would say 10s sold off 10 bps in that scenario. $\endgroup$
    – Kch
    Feb 25 at 23:10
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This is a very profound question, actually.

Definitely not 2. This breaks when rates become zero and negative. This works for prices, not for rates. (I wrote more on it here.)

In practice, most people use 1: the yield changed by 0.10% (10 basis points).

This is not ideal either, because what if you're trying to compare this change to a historical change when the yield changed from 10% to 11% - which of these was a bigger change?

Some people compare the changes in log(1 + rate), or some variant of it. This does not seem as intuitive, but gets around some of these problems.

A somewhat relevant paper is: Nick Guillaume,Riccardo Rebonato, Andrei Pogudin. The Nature of the Dependence of Magnitude of Rate Moves on the Rates Levels: A Universal Relationship (2015).

Edit: you asked what a yield is. A yield is one number that aims to summarize multiple numbers - the price you pay for the bond now, and the cash flows that you are promised to be paid in the future. You lose some details but gain the convenience of seeing just one number. If you are trying to decide whether one bond is rich or cheap in comparison with another, then you probably need to look at a lot more than their yield.

For dividend-paying stocks, there is a similar concept of dividend yield - the amount of dividend you expect divided by the price.

Edit: you also asked, do traders trade face value. A bond trade ticket (try BXT on Bloomberg) always has the price (usually clean) and the face value. Most investment grade bonds are quoted as yield, but the yield is translated into price for the trade ticket. The decision how much face value to do depends on what you want with the bond. For example, if you want to be paid the face value (+coupon) at maturity (not a very usual reason to buy a bond), then you'd buy this much face value. If you want a certain dollar amount of dv01, then you figure out how much face value has this much dv01 and trade this face amount. If you want to spend a particular dollar amount on a particular bond (not very usual), then you buy whatever face value this money buys at the price you see.

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What does yield actually represent? - it's just the return on the bond subject to a number of (unrealistic) assumptions. Perhaps a better way to think about it is as a quotation convention like implied volatility.

As an aside, people who think about bonds in price terms are generally those trading credit risky bonds, in my experience.

And as to normal vs. lognormal - it is standard to quote changes in terms of basis points, not percentage changes. [edit for clarity: as rates went negative post-GFC, option pricing moved from lognormal to either shifted lognormal or normal, and thinking about changes in rates in bp changes rather than % changes became standard]

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