Question

In: Finance

The following data is provided for the S&P 500 Index: Year Total Return Year Total Return...

The following data is provided for the S&P 500 Index:

Year Total Return Year Total Return
1988 16.81% 1998 28.58%
1989 31.49% 1999 21.04%
1990 -3.17% 2000 -9.11%
1991 30.55% 2001 -11.88%
1992 7.67% 2002 -22.10%
1993 9.99% 2003 28.70%
1994 1.31% 2004 10.87%
1995 37.43% 2005 4.91%
1996 23.07% 2006 15.80%
1997 33.36% 2007 5.49%

Refer to the information above. Calculate the 20-year arithmetic average annual rate of return on the S&P 500 Index.

Question 22 options:

13.04%

11.81%

10.56%

none of the above

Solutions

Expert Solution

Solution:
Answer is 1st option 13.04%
Working Notes:
Arithmetic average annual rate of return on the S&P 500 Index, is Arithmetic mean in simple language, which we compute with this formula
Arithmetic average annual rate of return = Mean = (sum of returns)/ number returns considered
=(sum of returns)/no of returns
=[16.81%+31.49%+(-3.17%)+30.55%+7.67%+9.99%+1.31%+37.43%+23.07%+33.36%+28.58%+21.04%+(-9.11%)+(-11.88%)+(-22.10%)+28.70%+10.87%+4.91%+15.80%+5.49%]/20
=260.81%/20
=13.0405%
=13.04%
Notes: Arithmetic average (mean) is a better measure of average performance over single period. It is best estimate of the expected return for next period.
Please feel free to ask if anything about above solution in comment section of the question.

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