Question

Please help with part C, D, and E. Thank you!

Stocks A and B have the following historical returns: Stock B's Returns, le (13.40%) Year Stock A's Returns, A 2014 (21.50%) 2015 39.75 2016 11.25 2017 (1.00) 2018 26.25 a. Calculate the average rate of return for each stock during the period 2014 through 2018. Round your answers to two decimal places. Stock A: 10.95 % Stock B: 10.95 % 26.30 25.80 (13.30) 29.35 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 2014 » % » 2015 2016 2017 Portfolio -17.45 33.03 18.53 -2.15 27.8 » % % » 2018 » % What would the average return on the portfolio have been during this period? Round your answer to two decimal places. 10.95 % C. Calculate the standard deviation of returns for each stock and for the portfolio. Round your answers to two decimal places. Stock A Stock Portfolio Standard Deviation 33.46 % 33.02 % 73.82 % 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 3.06 3.02 6.74 e. Assuming you are a risk-averse investor, would you prefer to hold Stock A, Stock B, or the portfolio?

Answer 1

c. standard deviation = √(sum of (( actual return-mean return)² /(n-1)))

so here,

	Actual return		Mean return		s= (Given return - mean)^2
year	A	B	A	B	A	B
2014	-21.50	-13.40	10.95	10.95	1,053.00	592.92
2015	39.75	26.30	10.95	10.95	829.44	235.62
2016	11.25	25.80	10.95	10.95	0.09	220.52
2017	-1.00	-13.30	10.95	10.95	142.80	588.06
2018	26.25	29.35	10.95	10.95	234.09	338.56
		Total			2,259.43	1,975.69

So for 2014, for A, S= (-21.50-10.95)^2

And for B, S= (-13.40-10.95)^2

And so on

Now,

Std. dev= (s/(n-1))^1/2

For A= (2259.43/4)^1/2

= 564.86^1/2

= 23.77%

For B= (1975.69/4)^1/2

= 493.92^1/2

= 22.22%

Now, for the portfolio:

	Portfolio return	mean return	s= (Given return - mean)^2
year			A
2014	-17.45	10.95	806.56
2015	33.03	10.95	487.31
2016	18.53	10.95	57.38
2017	-7.15	10.95	327.61
2018	27.80	10.95	283.92
		Total	1,962.78

Std. dev= (s/(n-1))^1/2

= (1962.78/4)^1/2

= 490.69^1/2

= 22.15%

d. Coefficient of variation:

Coefficient of variation (COV)= standard deviation/ expected return rate or mean

for A:

SD= 23.77

Mean= 10.95

COV= 23.77/10.95

= 2.17

for B:

SD= 22.22

Expected return = 10.95

COV= 22.22/10.95

=2.03

For the portfolio:

SD= 22.15

Mean= 10.95

COV= 22.15/10.95

= 2.02

e. as a risk aversive investor, we will look into the stock that has the minimum deviation from the expected return , that is we will go for the portfolio of 50% A and 50% B.