Assume that your uncle holds just one stock, East Coast Bank (ECB), which he thi
ID: 2665669 • Letter: A
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.
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?
Explanation / Answer
a. E(e) = Expected return on east bank E(w) = Expected return on west bank Since no information was given, we must assume that each yearly percentage has an equal probability of occurring. Therefore, the expected return is simply equal to the average or mean of each bank. E(e) = (40-10+35-5+15)/5 = 75/5 = 15% E(w) = (40+15-5-10+35)/5 = 75/5 = 15% So the expected return on each stock is 15%. b. If each year's return results have the same probability of occurring, then there would be no difference between the standard deviations of the two portfolios. As I said before I would consult your teacher because the question seems to be lacking poorly worded.