# Holding period return and YTM

Suppose I purchased a 2 year bond at par \$1000 paying 10% annually. Then the YTM is 10% but the holding period return would be 20%. Shouldn't those 2 values be the same since I am holding the bond to its maturity?

When calculating holding period return for any time period why do we not discount the future cash values so we can compare the return in terms of today's value of money?

The term commonly used for "holding period return" is "cumulative return".

The issue is that you're comparing two different formulas for return and mistaking them for interchangeable values.

Yield to maturity (YTM) is annualized (it's also forward looking).

Cumulative return is a historical measure of how much money an investment has earned for an investor during a historical time period and is not annualized. Annualized performance shows what the average annual return was for this historical period.

• Cumulative Performance formula = (Initial Purchase + Gains) / (Initial Purchase)-1
• Annualized Performance formula = ((Initial Purchase + Gains) / (Initial Purchase)) ^ (1/N)-1

(where "N" is the number of years.)

• Cumulative performance for your scenario is 20%
• Annualized performance for your scenario is 10%

YTM is typically presented as an annual number.

To your second point, returns don't typically include separate inflation adjustments or discounts. Those factors would already be considered in the yield the market is willing to pay.