Holding Period Return Formula

A security has seen the following returns over the past three years: | Year | Return | |---|---| | 1 | 8.5% | | 2 | 11.7% | | 3 | 4.1% | Which of the following is _closest_ to the three-year holding period return (HPR)?

Correct! This is an example of the concept of compounding. The holding period return is the total return over a period in which an asset is held. When this occurs over multiple concurrent periods, the formula is as follows. $$\displaystyle HPR = (1 + R_1)(1 + R_2)(1 + R_3) - 1 $$ So, in this case: $$ HPR = (1 + 0.085)(1 + 0.117)(1 + 0.041) - 1 = 0.2616 $$, or close to 26%. This allows you to take compounding returns into account and accurately represent the difference in the money that you would have at the beginning and end of the three-year period.

Incorrect. This answer is what you get when you add the individual returns. This ignores the effects of compounding interests, which is an incredibly valuable component of the time value of money. In order to fully compound the returns to find the three-year holding period return, you must use the following formula. $$\displaystyle HPR = (1 + R_1)(1 + R_2)(1 + R_3) - 1 $$

Incorrect. This problem is an example of compounding over multiple time periods. Compounding allows for compound interest to be incorporated throughout the time period of investment. The HPR of this three-year period needs to be calculated using the geometric cumulative return formula, which looks like the following. $$\displaystyle HPR = (1 + R_1)(1 + R_2)(1 + R_3) - 1 $$

18%

24%

26%