Quantitative Methods - Quantitative Methods Section 1

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 Observation 1 2 3 4 5 Value 13 - 5 1 3 - 8

• Option : C
• Explanation : The sample variance is given by s2 = 264.8/5-1 = 66.2 The sample standard deviation is simple the square root of the sample variance. The sample standard deviation is 8.13.

 Year Return (%) 2009 -12 2010 10 2011 15 2012 17 2013 19

• Option : A
• Explanation : The Mean Absolute Deviation (MAD) is calculated through the following formula: Mean = (-12+10+15+17+19)/5 = 9.8% MAD = (|-12 - 9.8| + |10 - 9.8| + |15 – 9.8| + |17 – 9.8| + |19 – 9.8|)/5=8.72%.

 Year Portfolio return 2008 7.5% 2009 9.0% 2010 11.5% 2011 -5.3% 2012 9.7%

• Option : B
• Explanation : Compute the mean: (7.5 + 9.0 + 11.5 – 5.3 + 9.7) / 5 = 6.48% and compute MAD, (|7.5 – 6.48| + |9.0 – 6.48| + |11.5 – 6.48| + | –5.3 – 6.48| + |9.7 – 6.48|) / 5 = 4.71%.Compute the mean: (7.5 + 9.0 + 11.5 – 5.3 + 9.7) / 5 = 6.48% and compute MAD, (|7.5 – 6.48| + |9.0 – 6.48| + |11.5 – 6.48| + | –5.3 – 6.48| + |9.7 – 6.48|) / 5 = 4.71%.

 Year Return % 2009 5.0 2010 -3.2 2011 6.1 2012 4.5 2013 1.3

• Option : B
• Explanation : Mean is 2.74. MAD is the mean of the absolute deviations from 2.74: (2.26 + 5.94 + 3.36 + 1.76 + 1.44) / 5 = 2.95.