Question

Consider the following realized annual returns: Year End Index Realized Return Stock A Realized Return 2006 23.6% 46.3% 2007 24.7% 26.7% 2008 30.5% 86.9% 2009 9.0% 23.1% 2010 -2.0% 0.2% 2011 -17.3% -3.2% 2012 -24.3% -27.0% 2013 32.2% 27.9% 2014 4.4% -5.1% 2015 7.4% -11.3% The average annual return on the Index from 2006 to 2015 is closest to: 8.75% 7.10% 9.75% 4.00%

Answer 1

Formula used to calculate average annual return is:
Average annual return=[(1+r1)x(1+r2)x...x(1+rn)]^(1/n) -1
Where r1, r2, rn are the returns starting from year 1 to year n.
Using the values of index returns as given in the question, we get
Average annual return=[(1+23.6%)*(1+24.7%)*(1+30.5%)*(1+9.0%)*(1-2.0%)*(1-17.3%)*(1-24.3%)*(1+32.2%)*(1+4.4%)*(1+7.4%)]^1/10 -1
=[(1.236)*(1.247)*(1.305)*(1.09)*(0.98)*(0.827)*(0.757)*(1.322)*(1.044)*(1.074)]^1/10 -1
=(1.993818557)^1/10 -1
=(1.993818557)^1/10 -1
=1.071441746-1
=0.071441746 or 7.14%
The closest value available in the options is 7.10%, so the correct option is 7.10%