In: Finance
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 |
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. |