Andrew plans to retire in 40 years. He is thinking of investing his retirement f
ID: 3131407 • Letter: A
Question
Andrew plans to retire in 40 years. He is thinking of investing his retirement funds in stocks, so he seeks out information on past returns. He learns that over the 101 years from 1900 to 2000, the real (that is, adjusted for inflation) returns on U.S. common stocks had mean 8.7% and standard deviation 20.2%. The distribution of annual returns on common stocks is roughly symmetric. What sample mean annual return (sample mean for the next 40 years before Andrew retires) would be higher than 80% of all sample mean annual returns? Choose the answer that is closest to your answer.
Explanation / Answer
Andrew plans to retire in 40 years. He is thinking of investing his retirement funds in stocks, so he seeks out information on past returns. He learns that over the 101 years from 1900 to 2000, the real (that is, adjusted for inflation) returns on U.S. common stocks had mean 8.7% and standard deviation 20.2%. The distribution of annual returns on common stocks is roughly symmetric. What sample mean annual return (sample mean for the next 40 years before Andrew retires) would be higher than 80% of all sample mean annual returns?
Standard error = sd /sqrt(n) =20.2/sqrt(40) =3.1939
Z value for top top 20%(higher than 80%) =0.842
The required sample mean
= 8.7+0.842*3.1939
= 11.3892638
Answer : 11.39%