Time-Weighted Return

kschuster · February 5, 2017, 10:42pm

I was going though a practice problem using the wiley study material and I had a question about the solution:

Why are the two holding periods raised to the .5 power?

Thanks in advance.

An investor purchases a share for $50 today. At the end of the year, she purchases another share for $60. At the end of Year 2, she sells the shares for $65 each. At the end of each year in the holding period, she also receives $1 per share as dividend. What is her time-weighted rate of return?

Solution

Step 2 : Calculate the HPY for each period.

HPY₁ = [(60 + 1)/50] − 1 = 22%

HPY₂ = [130 + 2)/120] − 1 = 10%

Step 3 : Finally, calculate the compounded annual rate that would produce the same return as the investment over the two-year period.

(1 + time-weighted rate of return)² = (1 + HPY₁)(1 + HPY₂) = (1.22)(1.10) Time-weighted rate of return = [(1.22) (1.10)]^0.5 − 1 = 15.84%.

kevinsfl · February 8, 2017, 11:02am

Because you are ANNUALIZING the time-weighted return. Before raising to the power of 0.5, the time-weighted return is based on 2 years. You have to bring that time-weighted return to 1 year, i.e. raising to the power of 1/2 = 0.5.

For 3 years, raise to the power of 1/3 = 0.333.

Hope it helps

kschuster · February 9, 2017, 5:32pm

Excellent!

This was helpful, thanks!