Question

Stocks A and B have the following historical returns:

Year Stock A's Returns, rA Stock B's Return rB

2013 -22.70% -15.00%

2014 23.00 16.40

2015 10.25 36.00

2016 -5.75 -9.30

2017 33.50 10.20

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.______%

Assume that someone held a portfolio 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.__________

Calculate the standard deviation of returns for each stock and for the portfolio.....

Standard Deviation Stock A Stock B Portfolio

_______ _______ ________

Calculate the coefficient of variation for each stock and for the portfolio. Round your answers to two decimal places.

CV Stock A Stock B Portfolio

_______ _______ _________

Assuming you are a risk-averse investor, would you prefer to hold

Stock A, Stock B, or the Portfolio? ______________

Answer 1

Solution 1) Calculation of average rate of return for Stock A and Stock B:

Year	Stock A Returns %	Stock B Returns %
2013	-22.70	-15.00
2014	23.00	16.40
2015	10.25	36.00
2016	-5.75	-9.30
2017	33.50	10.20
Total Returns	38.30	38.30

Average Returns of Stock A = 38.30% / 5 Years = 7.66%

Average Returns of Stock B = 38.30% / 5 Years = 7.66%

Solution 2) Calculation of realized rate of return on the portfolio for each year:

Year	Stock A Returns %	Proportion of Stock A	Stock B Returns %	Proportion of Stock B	Return on the Portfolio % = (Stock A Returns x Proportion of Stock A) + (Stock B Returns x Proportion of Stock B)
2013	-22.70	0.5	-15.00	0.5	-18.85
2014	23.00	0.5	16.40	0.5	19.7
2015	10.25	0.5	36.00	0.5	23.125
2016	-5.75	0.5	-9.30	0.5	-7.525
2017	33.50	0.5	10.20	0.5	21.85

Solution 3) Calculation of average return on the portfolio have been during this period

Year	Return on the Portfolio %
2013	-18.85
2014	19.7
2015	23.125
2016	-7.525
2017	21.85
Total Returns	38.3

Average Returns of Portfolio = 38.30% / 5 Years = 7.66%

Solution 4) Calculation of Standard Deviation of Stock A, Stock B and Portfolio:

Year	Stock A Returns %	Stock B Returns %	Return on the Portfolio %	Stock A Returns - Mean of Returns of A	(Stock A Returns - Mean of Returns of A) ^ 2	Stock B Returns - Mean of Returns of B	(Stock B Returns - Mean of Returns of B) ^ 2	Portfolio Returns - Mean of Returns of Portfolio	Portfolio Returns - Mean of Returns of Portfolio) ^ 2
2013	-22.70	-15.00	-18.85	-30.36	921.73	-22.66	513.48	-26.51	702.78
2014	23.00	16.40	19.7	15.34	235.32	8.74	76.39	12.04	144.96
2015	10.25	36.00	23.125	2.59	6.71	28.34	803.16	15.47	239.17
2016	-5.75	-9.30	-7.525	-13.41	179.83	-16.96	287.64	-15.19	230.58
2017	33.50	10.20	21.85	25.84	667.71	2.54	6.45	14.19	201.36
Total Returns	38.30	38.30	38.3	30.64	938.81	30.64	938.81	30.64	938.81
Mean = Total Returns / Number of years	7.66	7.66	7.66		2950.10		2625.92		2457.66

Variance of Stock A = ∑ (Realized Returns - Mean)^2 / (n-1)

                = 2950.10 / 4

               = 737.52

Standard Deviation of Stock A = Variance ^ (1/2)

                                    = 737.52 ^ (1/2)

                                    = 27.16%

Variance of Stock B = ∑ (Realized Returns - Mean)^2 / (n-1)

                = 2625.92 / 4

               = 656.48

Standard Deviation of Stock B = Variance ^ (1/2)

                                    = 737.52 ^ (1/2)

                                    = 25.62%

Variance of Portfolio = ∑ (Realized Returns - Mean)^2 / (n-1)

                = 2457.66 / 4

               = 614.41

Standard Deviation of Portfolio = Variance ^ (1/2)

                                    = 614.41 ^ (1/2)

                                    = 24.79%

Solution 5) Calculation of Coefficient of Variation:

	Mean	Standard Deviation	Coefficient of Variation = Standard Deviation / Mean
Stock A	7.66	27.16	3.55
Stock B	7.66	25.62	3.34
Portfolio	7.66	24.79	3.24

Solution 6) Assuming you are a risk-averse investor, would you prefer to hold Portfolio as its Coefficient of Variation is minimum.