Question

# The table below displays returns associated with a company's shares over the last 15 years. Year...

The table below displays returns associated with a company's shares over the last 15 years.

Year Return
(% pa)
2005 23
2006 17
2007 11
2008 15
2009 12
Year Return
(% pa)
2010 31
2011 2
2012 16
2013 8
2014 31
Year Return
(% pa)
2015 29
2016 5
2017 26
2018 6
2019 1

Based on this historic data, calculate the expected return on the shares and its standard deviation. Give your answers as a percentage per annum to 2 decimal places.

a)Expected return =  % pa

b)Standard deviation =  % pa

 Year Return Weight based on years Return*Weight Return - Expected return (Return - Expected return)^2 X X-X' (X-X')^2 2005 23 15 345 6.4 40.96 2006 17 14 238 0.4 0.16 2007 11 13 143 -5.6 31.36 2008 15 12 180 -1.6 2.56 2009 12 11 132 -4.6 21.16 2010 31 10 310 14.4 207.36 2011 2 9 18 -14.6 213.16 2012 16 8 128 -0.6 0.36 2013 8 7 56 -8.6 73.96 2014 31 6 186 14.4 207.36 2015 29 5 145 12.4 153.76 2016 5 4 20 -11.6 134.56 2017 26 3 78 9.4 88.36 2018 6 2 12 -10.6 112.36 2019 1 1 1 -15.6 243.36 Total 120 1992 1530.8
 Expected return                            = 1992/120 = 16.6

Variance = Σ(X-X')^2 / n-1

= 1530.8 / 15-1

= 109.34

Standard deviation = √Variance

= √109.34

= 10.46

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