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In: Finance

Assume that your uncle holds just one stock, East Coast Bank (ECB), which he thinks has...

Assume that your uncle holds just one stock, East Coast Bank (ECB), which he thinks has very little risk. You agree that the stock is relatively safe, but you want to demonstrate that his risk would be even lower if he were more diversified. You obtain the following returns data for West Coast Bank (WCB). Both banks have had less variability than most other stocks over the past 5 years.

Year                 ECB                  WCB

2004                 40.00%            40.00%

2005 -              10.00%            15.00%

2006                 35.00%            -5.00%

2007                 -5.00%             -10.00%

2008                 15.00%            35.00%

a. What is the expected return and risk of each stock?

b. Measured by the standard deviation of returns, by how much would your uncle's risk have been reduced if he had held a portfolio consisting of 60% in ECB and the remainder in WCB? In other words, what is the difference between portfolio's standard deviation and weighted average of components' standard deviations? (Hint: check the example on page 11-12 on my note).

If this problem can be done using excel, in a way that I can understand the steps I need to take as I go.

Solutions

Expert Solution

(a)

(b)

Portfolio Weight of ECB = 60 % and Portfolio Weight of WCB = 40 %

Standard Deviation of Portfolio = [{0.6 x 16.55}^(2) + {0.4 x 20.25}^(2) + {2 x 0.6 x 0.4 x 16.55 x 20.25 x 0.4326}]^(1/2) = 15.2907 % ~ 15.29 %

Weighted Standard Deviation = 0.6 x 16.55 + 0.4 x 20.25 = 18.03 %

Difference in Risk Level = 18.03 - 15.29 = 2.74 %

jeff jeffy answered 1 year ago
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