Question

(1). Calculate the gross annual return on this stock and report the number in a separate column.

Date Price before Dividend Dividend 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 742.5 758.8 742.9 697.7 744.9 693 735.7 692 768.7 767 12.6 11.1 15.6 18.2 18 19.7 19.2 21.1 20.5 21.5 22.4 23 23.3 24.1 25 784.5 758 796.7 823.2

(2). Calculate the sample mean for the gross return.

(3). Calculate the sample standard deviation for the gross return.

(4). Assume the risk-free rate is 0.02. Estimate the risk premium.

(5). Estimate the sharp ratio.

Answer 1

1) Gross Annual Return

Gross Annual Return = Dividend/Price * 100

Year	Price	Dividend	Annual Return
2000	742.5	12.6	1.70%
2001	758.8	11.1	1.46%
2002	742.90	15.6	2.10%
2003	697.7	18.2	2.61%
2004	744.9	18	2.42%
2005	693	19.7	2.84%
2006	735.7	19.2	2.61%
2007	692	21.1	3.05%
2008	768.7	20.5	2.67%
2009	767	21.5	2.80%
2010	777.2	22	2.83%
2011	784.5	22.4	2.85%
2012	758	23	3.03%
2013	771.8	23.3	3.02%
2014	796.7	24.1	3.02%
2015	823.2	25	3.04%

2.

Sample Mean of Gross Return

= (1.7+1.46+2.10+2.61+2.42+2.84+2.61+3.05+2.67+2.80+2.83+2.85+3.03+3.02+3.02+3.04)/16

= 42.05/16

= 2.63%

3. Sample Standard Deviation

= (Annual Return - Mean Return)^2

= 3.52

= 3.52/16

= 0.22

Under root of 0.22

= 0.47%

Standard deviation = 0.47%

5. Sharpe ratio = (Mean portfolio return − Risk-free rate)/Standard deviation of portfolio return

= (0.0263 - 0.02)/0.0047

= 1.34

4. Risk Premium

The estimated stock return minus the risk free rate equals the estimated risk premium.

= Mean - Risk free rate

= 0.0263 - 0.02

= 0.63% or 0.0063