Question

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

Answer 1

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