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 60% in ECB and the remainder in WCB? (Hint: Use the sample standard deviation formula.)

Question

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 60% in ECB and the remainder in WCB? (Hint: Use the sample standard deviation formula.)
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Quizplus · Accepted Answer

We can use the formula for portfolio standard deviation:
σp = √[w1^2σ1^2 + w2^2σ2^2 + 2w1w2ρ12σ1σ2]

where w1 and w2 are the portfolio weights, σ1 and σ2 are the standard deviations of returns for ECB and WCB respectively, and ρ12 is the correlation coefficient between the two stocks.

Assuming a correlation coefficient of 0 (which means the stocks move independently of each other), and using the given standard deviations of returns, we get:

σp = √[(0.6^2)(0.055^2) + (0.4^2)(0.045^2) + 2(0.6)(0.4)(0)(0.055)(0.045)]

σp = 0.0335 or 3.35%

Compared to the standard deviation of returns for ECB alone (0.055), this represents a reduction in risk of:

(0.055 - 0.0335)/0.055 = 0.384 or 3.84%

Therefore, the correct answer is D) 3.84%.

Assume That Your Uncle Holds Just One Stock,East Coast Bank