Question

Historical Realized Rates of Return

You are considering an investment in either individual stocks or a portfolio of stocks. The two stocks you are researching, Stocks A and B have the following historical returns:

Year
2011	-15.00%	-15.80%
2012	24.25	24.90
2013	15.75	22.90
2014	-2.00	-7.60
2015	23.75	22.35

1. Calculate the average rate of return for each stock during the 5-year period. Round your answers to two decimal places.

   Stock A	%
   Stock B	%

2. Suppose you had held a portfolio consisting of 50% of Stock A and 50% of Stock B. What would have been the realized rate of return on the portfolio in each year? What would have been the average return on the portfolio during this period? Round your answers to two decimal places.

   Year	Portfolio
   2011	%
   2012	%
   2013	%
   2014	%
   2015	%
   Average return	%

3. Calculate the standard deviation of returns for each stock and for the portfolio. Round your answers to two decimal places. Enter negative returns with a minus sign.

   	rA	rB	Portfolio
   Std. Dev.	%	%	%

Answer 1

a. Average Return of Stock A =(-15%+24.25%+15.75%-2%+23.75%)/5 =9.35%
Average Return of Stock B =(-15.80%+24.90%+22.90%-7.60%+22.35%)/5 =9.35%

b. In Year 2011 Average return =50%*-15%+50%*-15.80% =-15.40%
In Year 2012 Average return =50%*24.25%+50%*24.90% =24.575% or 24.58%
In Year 2013 Average return =50%*15.75%+50%*22.90% =19.325% or 19.33%
In Year 2014 Average return =50%*-2%+50%*-7.60% =-4.80% or -4.80%
In Year 2015 Average return =50%*23.75%+50%*22.35% =23.05%
average return of Portfolio =(-15.40%+24.575%+19.325%-4.80%+23.05%)/5 =9.35%

c. Standard Deviation of Stock A =(((-15%-9.35%)^2+(24.25%-9.35%)^2+(15.75%-9.35%)^2+(-2%-9.35%)^2+(23.75%-9.35%)^2)/(5-1))^0.5=17.26%
Standard Deviation of Stock A =(((-15.80%-9.35%)^2+(24.90%-9.35%)^2+(22.90%-9.35%)^2+(-7.60%-9.35%)^2+(22.35%-9.35%)^2)/(5-1))^0.5=19.46%

Standard Deviation of Portfolio =(((-15.40%-12.34%)^2+(24.575%-12.34%)^2+(19.325%-12.34%)^2+(-4.80%-12.34%)^2+(23.05%-12.34%)^2)/(5-1))^0.5 =18.25%