Assume that your uncle holds just one stock, East Coast Bank (ECB), which he thi
ID: 2622769 • 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. 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.)
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%
Average return =
15.00%
15.00%
Standard deviation =
22.64%
22.64%
a.
3.29%
b.
3.46%
c.
3.65%
d.
3.84%
e.
4.03%
Explanation / Answer
Calculate the five annual returns as (.6 * ECB) + ( .4 * WCB )
40, 0, 19, -7, 23
Calculate the standard deviation. With only 5 items, you could do it by hand, but I used Excel.
Standard deviation = 18.80
Risk reduction = (old risk - new risk) / old risk = (22.64 - 18.80 ) / 22.64 = .1696 or about 17%