Question

Given the year end prices of the following stocks, estimate the standard deviation of the returns of a portfolio of 30% AAA and 70% BBB. Enter your answer as a percent without the % sign. Round your final answer to two decimals.

Year	AAA	BBB
2006	100	55
2007	105	65
2008	120	60
2009	110	70
2010	130	65
2011	160	80

Answer 1

First we will Calculate Return of AAA and BBB by following formula              
rate of return = (closing price -opening price)/Opening price              
First year 2007 AAA Return = (105-100)/105 = 5%              
BBB Return =(65-55)/55=       18.1818%      

Then we will calculate Combined Portfolio Return year wise              
return of portfolio = (return of AAA * Weight AAA) + ( Return of BBB* weight BBB)              
Year 2007 Return = (5%*30%)+(18.1818%*70%)=       14.2273%      
year   AAA   BBB   Portfolio Return   (Return - ER)^2
              
              
2007   5.0000%   18.1818%   14.2273%   0.2562%
2008   14.2857%   -7.6923%   -1.0989%   1.0535%
2009   -8.3333%   16.6667%   9.1667%   0.0000%
2010   18.1818%   -7.1429%   0.4545%   0.7588%
2011   23.0769%   23.0769%   23.0769%   1.9353%
              
Total            45.8265%   4.0039%
ER=           9.17%  
Expected return = total /number of years              
              
Standard deviation = √ (∑ (Return-Average or Expected return)^2)/(no. of periods - 1))              
√(4.0039%/(5-1))              
10.00%              
              

Standard deviation of portfolio is 10%