Question

You invest in a stock over a 5-year period. The returns in each of the 5 years are: 10%, 1%, -12%, 4%, and 20%. For all questions, answer should be given in terms of %, and rounded to one decimal place.

1) What is the 5-year Holding Period Return (HPR) of your stock investment?  (in %, 1 decimal place)

2) What is the compound annual growth rate of the investment over the 5-year period?   (in %, 1 decimal place)

Answer 1

1)

Holding Period Return = [(1 + R1)(1 +R2)(1 + R3)(1 + R4)(1 + R5)] - 1

Holding Period Return = [(1 + 0.1)(1 +0.01)(1 - 0.12)(1 + 0.04)(1 + 0.2)] - 1

Holding Period Return = [1.1 * 1.01 * 0.88 * 1.04 * 1.2] - 1

Holding Period Return = [1.220145] - 1

Holding Period Return = 0.220 or 22.0%

2)

compound annual growth rate = [(1 + R1)(1 +R2)(1 + R3)(1 + R4)(1 + R5)]^1/n - 1

compound annual growth rate = [(1 + 0.1)(1 +0.01)(1 - 0.12)(1 + 0.04)(1 + 0.2)]^1/5 - 1

compound annual growth rate = [1.1 * 1.01 * 0.88 * 1.04 * 1.2]^1/5 - 1

compound annual growth rate = [1.220145]^1/5 - 1

compound annual growth rate = 1.0406 - 1

compound annual growth rate = 0.041 or 4.1%