Question

Campbell's father holds just 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 more diversified. Campbell obtained the following returns data shown 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 50% ECB and the remainder in WCB? Enter your answer rounded to two decimal places. Do not enter % in the answer box. For example, if your answer is 0.12345 or 12.345% then enter as 12.35 in the answer box.

Year         ECD                WCD

2014       20.00%        25.00%

2015       -10.00%          15.00%

2016        35.00%          -5.00%

2017      -5.00%           -10.00%

2018      15.00%         35.00%

Answer 1

The mean, standard deviation and covariance of the companies are calculated as follows:

In the excel, the following calculations are made:

Option 1: 100% amount invested in East Coast Bank (ECB) stock

Risk for holding only the stocks of East Coast Bank (ECB) = Standard deviation of the returns of ECB

= 18.51%

Option 2: The portfolio consists of 50% investment in East Coast Bank (ECB) and 50% investment in West Coast Bank (WCB)

Standard Deviation of Portfolio with 2 Assets is calculated as:

where, weight of ECB (Wa) = 50% = 0.5

Weight of WCB (Wb) = 50% = 0.5

Standard deviation of returns of ECB, σ(Ka) = 18.51%

Standard deviation of returns of WCB, σ(Kb)= 19.24%

Covariance of the returns of two stocks, Cov(Ka, Kb) = 0.23%

Puuting the values in the formula we get

σ(P)^2 = (0.5*18.51%)^2 + (0.5*19.24%)^2 + 2*0.5*0.5*0.23%

σ(P)^2 = 0.008566 + 0.009254 + 0.00115 = 0.01897

σ(P) = sqrt(0.01897) = 0.137731 = 13.77%

With the addition of WCB, the portfolio risk lowered by = 18.51% -  13.77% = 4.74%