Using the five years of returns from 6-1, assume that one of the five years during the second half of the decade, 2015–2019, shows a loss of 10 percent. What would the geometric mean of the remaining four years have to be for the decade as a whole to average the 10 percent return for the S&P 500 Index?
Answer the question up please.
First, convert the TRs to Return Relatives: 1.1506, .901, 1.161, .803, and 1.107.
Multiply these RRs together to obtain 1.0699, the cumulative wealth for the first 5 years.
A geometric mean of 10% for the decade results in a cumulative wealth of (1.10)10 = 2.594. Divide 2.594 by 1.0699 to obtain 2.424. The fifth root of 2.424 is 19.37%.
Thus, the geometric mean for the last 5 years must be 19.37% if the entire decade is to have a geometric mean of 10%.