Campbell\'s father holds just only one stock, East Coast Bank (ECB), which he th

Question

Campbell's father holds just only one stock, East Coast Bank (ECB), which he thinks is a very low-risk security. Campbell agrees that the stock is relatively safe, but he wants to demonstrate that his father's risk would be even lower if he were diversified. Campbell obtained the following returns data for West Coast Bank (WCB). Both have had less variability than most other stocks over the past 5 years. Measured by the standard deviation of returns, by how much would his father's historical risk have been reduced if he had held a portfolio consisting of 60% ECB and the remainder in WCB? Please show work step by step.

Year             ECB                  WCB

2010             20.00%             25.00%

2011          -10.00%             15.00%

2012           35.00%             -5.00%

2013           -5.00%              -10.00%

2014           15.00%               35.00%

Explanation / Answer

1. Standard deviation of ECB alone : under rood of [sigma (X - M)2/n-1]

where M = Mean, N = Numbers of value

M = Sum of X values / N(Number of values)

M = (20 + -10 + 35 + -5 + 15)/5

M = 11

X - M = 20 - 11 = 9

= -10 - 11 = -21

= 35 - 11 = 24

= -5 - 11 = -16

= 15 - 11 = 4

(X - M)2 = (9)2 = 81, (-21)2 = 441, (24)2 = 576, (-16)2 = 256, (4)2 = 16

Sigma of (X - M)2 =81+441+576+256+16 = 1370

= 1370/n -1 = 1370/5-1 = 1370/4 = 342.5

Variance = 342.5

Standard Deviation = under rood of variance

SD = Under rood of 342.5 = 18.507

2. Standard deviation of ECB & WCB : under rood of [sigma (X - M)2/n-1]

Year ECB*60% WCB*40% Composite Return(ECB + WCB)

2010 20%*60% = 12% 25%*40% = 10% = 12% + 10% = 22%

2011 -10%*60% = -6% 15%*40% = 6% = - 6% + 6% = Nil

2012 35%*60% = 21% -5%*40% = -2% = 21% + -2% = 19%

2013 -5%*60% = -3% -10%*40% = -4% = -3% + -4% = -7%

2014 15%*60% = 9% 35%*40% = 14% = 9% + 14% = 23%

where M = Mean, N = Numbers of value

M = Sum of X values / N(Number of values)

M = (22 + 0 + 19 + -7 + 23)/5

M = 11.4

X - M = 22 - 11.4 = 10.6

= 0 - 11.4 = -11.4

= 19 - 11.4 = 7.6

= -7 - 11.4 = -18.4

= 23 - 11.4 = 11.6

(X - M)2 = (10.6)2 = 112.36, (-11.4)2 = 129.96, (7.6)2 = 57.6, (-18.4)2 = 338.56, (11.4)2 = 129.96

Sigma of (X - M)2 =112.36+129.96+57.6+338.56+129.96 = 768.44

= 768.44/n -1 = 768.44/5-1 = 768.44/4 = 192.11

Variance = 192.11

Standard Deviation = under rood of variance

SD = Under rood of 192.11 = 13.86

hence it is proved that after considering both investment option Combell's father will reduce his risk with safe return hence combell is giving good advise to his father

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