Sample Question #224 (finance – bond pricing)

Explain the difference between a bond’s yield and its rate of return. How do you calculate them?

(Comment: the funny thing about bond pricing is that, as long as you understand the concept of NPV, you should be able to derive a lot of pricing formulas without even knowing much about the bond itself — and many quant interviewers expect you to do so. In other words, it doesn’t pay to memorize what you study; you should always thoroughly understand it.)

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ANSWER

Yield is short for yield to maturity; it’s the return (relative to the price you pay for the bond) from the coupon payments, compounded at the ongoing interest rate, when you hold the bond to maturity. It’s also the bond’s internal rate of return.

Rate of return is a more general concept, and you can calculate it even if you don’t hold the bond to maturity.

Ok, since you deleted my last rude response, I’ll keep this one nicer.YTM is not the return if held to maturity. And even if it was, it wouldn’t be the return if coupons were reinvested at ongoing interest rates.The only way YTM would equal return if held to maturity is if coupons could be reinvsted at the yield calculated at time 0. To see this, take the bond pricing formula and multiply both sides by (1+y)^n.

Thanks for the constructive input! 🙂

I believe YTM assumes you’ll reinvest the coupon payments you receive at the same rate as the bond coupon rate. More generally, YTM is an interest rate concept that assumes you hold the bond to maturity; of course in reality you may not. The advantage of knowing the YTM (yield) is you can compare bonds of different maturities based on their annualized yields.

-brett

Yield is a more general concept than YTM; you can calculate yield to any endpoint, not just maturity. I just checked Fabozzi’s book and he treats yield as a general "internal rate of return" while states that YTM is calculated "by holding the bond to maturity" [p.74]. My original answer was suggested by a fixed income guy at Citigroup.

So in terms of scope, it’s like YTM < yield < rate of return.

Your constructive comments are welcome.

Check this alternative source for discussion of yield vs. YTM:

http://www.riskglossary.com/link/yield.htm

They equate YTM with internal rate of return, a treatment different from Fabozzi’s.

If you’re asked this question at an interview by a fixed income guy, maybe it’s best to write down your formulas to let him know what you mean… But in general, I think it’s okay to say something like "the rate of return is a more general concept than yield; some people define yield without taking into account capital gains or losses but the rate of return is always calculated taking such gains or losses into account."

-brett

"I believe YTM assumes you’ll reinvest the coupon payments you receive at the same rate as the bond coupon rate. "YTM is the internal rate of return if you hypothetically held the bond to maturity and were able to reinvest coupons at the calculated YTM, not the coupon rate or the current yield (i.e. coupon/price). It’s a theoretic number that doesn’t tell you all that much by itself. Given both the coupon rates and YTM, you could draw some relative conclusions about things like duration.You can’t really use YTM to compare different bonds of different maturities nor can you draw conclusions using YTM to compare bonds of even the same maturity. Think of a coupon bond as a portfolio of zeros, YTM represents a weighted average of the various zero coupon yields. If someone asked you to compare two portfolios of zeros knowing nothing but the maturity of the longest zero in the portfolio and a weighted average of the component yields, what conclusion could you possibly draw?The realized yield is a function of what you can do with the coupons at the prevailing spot rates at coupon dates and how long you hold the bond. The only thing you can really say about YTM is that it represents the actual yield for a time period if the YTM does not change during that time period.I think the original question was probably asking what’s the difference between YTM (rate of return) and realized yield. The answer would be the rate at which coupons were reinvested and value at redemption or sale.

Thanks, "MoronFisher"!

-brett