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Problem #1: Geometric Mean Returns Here are the total returns for the S&P500 for the first ten years of this century. Year Re

8. What was the arithmetic average return for the 10-year period? %. The arithmetic average return was Show work here or abov
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Answer #1
Answer 1
Year Return (%) worth of one dollar at the end of the year
2001 -11.85 0.8815
2002 -21.97 0.6618
2003 28.36 0.9454
2004 10.74 1.0528
2005 4.83 1.1011
2006 15.61 1.2572
2007 5.48 1.312
2008 -36.55 0.9465
2009 26.94 1.2159
2010 18 1.3959

From the above calculation it is stated that Investment in one dollar on January 2001 will become 1.3959 dollar ten years later.

2. Geometric Average Return
Year Return (%) 1+R (1+R1)(1+R2)………..(1+R10) [(1+R1)(1+R2)………..(1+R10)]^(1/n)
2001 -11.85 0.8815 1.187904116 1.01736815
2002 -21.97 0.7803
2003 28.36 1.2836
2004 10.74 1.1074
2005 4.83 1.0483
2006 15.61 1.1561
2007 5.48 1.0548
2008 -36.55 0.6345
2009 26.94 1.2694
2010 18 1.18

Geometric Average return for the 10 years is 1.73% per year.

3. Arithmetic Average Return
Year Return (%) Total return Average Annual Return
2001 -11.85 39.59 3.959
2002 -21.97
2003 28.36
2004 10.74
2005 4.83
2006 15.61
2007 5.48
2008 -36.55
2009 26.94
2010 18

Arithmetic Average return for 10 years 3.959%

4. Standard Deviation
Year Return (%) R-R Bar Square
2001 -11.85 -15.809 249.924481
2002 -21.97 -25.929 672.313041
2003 28.36 24.401 595.408801
2004 10.74 10.74 115.3476
2005 4.83 4.83 23.3289
2006 15.61 15.61 243.6721
2007 5.48 5.48 30.0304
2008 -36.55 -36.55 1335.9025
2009 26.94 26.94 725.7636
2010 18 18 324
Sum 4315.691423
Variance 479.5212692
Standard Deviation 21.89797409

Answer 5.dintributed of If tums 5C Anthmat Mean Retuom 3.959 Stondand olevlahon 21.9349 C-2 8975 Z> X-4 0-3.959 21.8979 Atea of lo Z 0

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