Yield to Maturity as an Annualized Bond Return

Summary

This explanation distinguishes a return from the amount of interest paid. Return is defined as the gain relative to the original investment, so receiving the same amount invested produces no return, while receiving more produces a positive return. The examples use a $100 investment to illustrate this proportional measure.

The explanation then accounts for how long it takes to earn that return by expressing it on a yearly basis. It describes dividing a period return by the fraction of a year, so an equal gain over a shorter period corresponds to a larger simple annualized rate. It flags that day-count conventions and compounding also affect the calculation, but does not explain them. For bonds, this provides an introductory way to understand yield to maturity as a rate of return rather than a cash amount of interest; the short explanation does not cover the full bond cash-flow calculation or reinvestment assumptions.

Key ideas

• Return measures the gain relative to the amount invested.
• A zero gain relative to the investment corresponds to a zero return.
• Annualizing a return requires accounting for the length of the investment period.
• Day-count conventions and compounding affect yield calculations.

Tags

# Does YTM represent interest?


# Does YTM represent interest?












Does a bond's Yield to Maturity represent the amount of interest one gets at maturity even though it's expressed as a percentage? I read that it is a rate of return on a bond at maturity, but what is the "return"?

## Answer by Rustam (score 1)

https://quant.stackexchange.com/a/8286

Simply speaking, return means relative amount of extra money earned after investing of some amount of money: Return = $\frac{Received}{Invested}-1$.

If you invested \$100 and received \$100, this means you have zero return (\$100/\$100-1).

If you invested \$100 and received \$110, your return in 10% (\$110/\$100-1 = 1.1-1 = 0.1 = 10%).

Next step is account for term in which you received this return, and here comes a concept of yearly return. Formula is $1+r_y f = 1+r$ or $r_t = r/f$, where $r_y$ is year return, $f$ is fraction of a year, and $r$ is your previously calculated absolute return.

If you earned 10% in one year, it is your yearly return.

If you earned 10% in half year, then your yearly return is 10%/0.5 = 20%.

Next step is account for Day count convention and Compounding but it would be a long story.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.