In: Finance
Stocks A and B have the following historical returns:
Year | Stock A's Returns, rA | Stock B's Returns, rB |
2013 | - 23.10% | - 16.70% |
2014 | 39.25 | 28.30 |
2015 | 16.50 | 37.90 |
2016 | - 1.75 | - 7.70 |
2017 | 26.25 | 15.35 |
a Calculate the average rate of return for stock A during the
period 2013 through 2017. Round your answer to two decimal
places.
Calculate the average rate of return for stock B
during the period 2013 through 2017. Round your answer to two
decimal places.
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? Round your answers to two decimal places. Negative values should be indicated by a minus sign.
Year | Portfolio |
2013 | % |
2014 | |
2015 | |
2016 | |
2017 |
What would the average return on the portfolio have been during this period? Round your answer to two decimal places
c. Calculate the standard deviation of returns for each stock
and for the portfolio. Round your answers to two decimal
places.
Stock A | Stock B | Portfolio | |
Standard Deviation | % | % | % |
d. Calculate the coefficient of variation for each stock and for
the portfolio. Round your answers to two decimal places.
Stock A | Stock B | Portfolio | |
CV |
Assuming you are a risk-averse investor, would you prefer to hold Stock A, Stock B, or the portfolio?
A. Average Return of Stock A
=(-23.10%+39.25%+16.50%-1.75%+26.25%)/5 =11.43%
Average Return of Stock B =(-16.70%+28.30%+37.90%-7.70%+15.35%)/5
=11.43%
B. In Year 2013 Average return =50%*-23.10%+50%*-16.70%
=-19.90%
In Year 2014 Average return =50%*39.25%+50%*28.30% =33.775% or
33.78%
In Year 2016 Average return =50%*16.50%+50%*37.90% =27.20%
In Year 2017 Average return =50%*-1.75%+50%*-7.70% =-4.725% or
-4.73%
In Year 2018 Average return =50%*26.25%+50%*15.35% =20.80%
average return of Portfolio
=(-19.90%+33.775%+27.20%-4.725%+20.80%)/5 =11.43%
c. Standard Deviation of Stock
A=(((-23.10%-11.42%)^2+(39.25%-11.42%)^2+(16.50%-11.42%)^2+(-1.75%-11.42%)^2+(26.25%-11.42%)^2)/(5-1))^0.5
=24.42%
Standard Deviation of Stock
B=(((-16.70%-11.43%)^2+(28.30%-11.43%)^2+(37.90%-11.43%)^2+(-7.70%-11.43%)^2+(15.35%-11.43%)^2)/(5-1))^0.5
=23.23%
Standard Deviation of Portfolio
=(((-19.90%-11.43%)^2+(33.775%-11.43%)^2+(27.20%-11.43%)^2+(-4.725%-11.43%)^2+(20.80%-11.43%)^2)/(5-1))^0.5=22.79%
d. Coefficient of Stock A =Standard Deviation of A/Expected Return
of A =24.42%/11.43% =2.14
Coefficient of Stock B =Standard Deviation of B/Expected Return of
B =23.23%/11.43% =2.03
Coefficient of Stock B =Standard Deviation of C/Expected Return of
C =22.79%/11.43% =1.99
e. A risk averse investor would prefer to hold portfolio.