Answer:
Year Stock A's Returns (rA) Stock B's Returns (rB)
2014 (19.80%) (16.10%)
2015 28.75% 17.80%
2016 14.50% 30.60%
2017 (3.00%) (8.90%)
2018 22.75% 19.80%
a) Calculate the average rate of return for each stock during the period 2014 through 2018.
Average rate of return of each stock will be calculated by taking an aggregate for all the returns of each stock and dividing it by 5, which is the total number of years.
a) The average rate of return for Stock A during the period 2014 through 2015 is given by
,
Average Return = ( -19.80 + 28.75 + 14.50 – 3.00 +22.75)/5 = 8.64%
The average rate of return for Stock b during the period 2014 through 2015 is given by
,
Average Return = ( -16.10 + 17.80 + 30.60 – 8.90 +19.80)/5 = 8.64%
b) Assume that someone held a portfolio consisting of 50% of Stock A and 50% of Stock B. What would the realized rate of return on the portfolio have been each year?
Since the investment in the portfolio created by stock A and stock B is 50-50, we will calculate portfolio return each year by multiplying each return with it's weight in the portfolio (50%) to find out the realized rate of return each year and then take an average to find out the average return of the portfolio during these 5 years
Realized Return for 2014:
= 0.5*(-19.80) + 0.5*(-16.10%) = -17.95%
Realized Return for 2015:
= 0.5*(28.75)+ 0.5*(17.80)= 23.27%
Realized Return for 2016:
= 0.5*(14.50) + 0.5*(30.60) = 22.55%
Realized Return for 2017:
= 0.5*(-3.0) + 0.5*(-8.90) = -5.95%
Realized Return for 2018:
= 0.5*(22.75)+ 0.5*(19.8) = 21.27%
The average return on the portfolio have been during this period is given by
,
Realized Rate of Return = ( - 17.95% + 23.27% + 22.55% - 5.95% + 21.27%
)/5 = 8.638%
