Question

https://d.pr/i/d79jej

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. 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 46% in ECB and the remainder in WCB? (Hint: Use the sample standard deviation formula.)

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%

https://d.pr/i/d79jej

Average return = 15.00% 15.00%

Standard deviation = 22.64% 22.64%

Answer 1

compute the reduction in risk:

The portfolio percentage is computed as ECB divided by WCB

Year ECB     WCB Portfolio ECB/WCB

2004 40% 40% 100.00%

2005 10% 15% 66.67%

2006 35% 5% 7.00%

2007 5% 10% 50.00%

2008 15% 35% 42.86%

Average return 15% 15% 15.00%

Standard deviation(SD) 22.64% 22.64% 16.81%

The iinvestment made in ECB is 46% while the remaining 54% made in WCB.

Use the portfolio standard deviation formula to compute the standard deviation of portfolio.

CALCULATION OF STANDARD DEVIATION

To calculate standard deviation ,the variance has to be found out.The standard deviation has to be determined to calculate variance.

Formula :   σp = sd(portfolio) = √​​​​​​​var(portfolio)

σp2(square) = 0.46*0,46*0.2264*0.2264+0.54*0.54+2*0.46*0.54*0.2264*0.2264*0.4

= 0.0108+0.0149+0.0101

= 0.0358

when you take the square other side,it will become square root.

σA =√​​​​​​​0.0358

σA = 0.189 OR 18.9%

standard deviation of portfolio is 19.00%

Therefore, the reduction in risk of the portfolio is (22..64% - 19.00%) = 3.64%