Question

Stocks A and B have the following historical returns:

Year	Stock A's Returns, rA	Stock B's Returns, rB
2011	- 22.40%	- 15.60%
2012	27.75	19.70
2013	10.00	37.00
2014	- 5.00	- 9.90
2015	23.75	2.90

a. Calculate the average rate of return for stock A during the period 2011 through 2015. Round your answer to two decimal places.
%_________

Calculate the average rate of return for stock B during the period 2011 through 2015. 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. Enter a negative answer with a minus sign.

Year	Portfolio
2011	%_____
2012	%_____
2013	%_____
2014	%_____
2015	%_____

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	_______	_______	________

e. Assuming you are a risk-averse investor, would you prefer to hold Stock A, Stock B, or the portfolio?
I.Stock A

II.Stock B

III. Portfolio

Answer 1

1)Calculation of average return, standard deviation and coefficient of variation for each stock and for the portfolio

-Stock A

Year	Return(%)	Deviation form avearge return (D)	D^2
2011	-22.40	-29.22	853.81
2012	27.75	20.93	438.06
2013	10.00	3.18	10.11
2014	-5.00	-11.82	139.71
2015	23.75	16.93	286.62

Average Return = sum of returns/no. of returns

=( -22.4+27.75+10-5+23.75)/5

= 34.10/5

= 6.82 %

Variance = D^2 /n

= (853.81+438.06+10.11+139.71+286.62)/5

= 1728.32/5

= 345.664

Standard Deviation = Variance

= 345.664

= 18.59%

Coefficient of variation =Standard Deviation / Average Return

= 18.59/6.82

= 2.73

-Stock B

Year	Return(%)	Deviation form avearge return (D)	D^2
2011	-15.60	-22.42	502.66
2012	19.70	12.88	165.89
2013	37.00	30.18	910.83
2014	-9.90	-16.72	279.56
2015	2.90	-3.92	15.37

Average Return = sum of returns/no. of returns

=(-15.6+19.7+37-9.9+2.9)/5

= 34.10/5

= 6.82 %

Variance = D^2 /n

= (502.66+165.89+910.83+279.56+15.37)/5

= 1874.31/5

= 374.862

Standard Deviation = Variance

= 374.862

= 19.36%

Coefficient of variation =Standard Deviation / Average Return

= 19.36/6.82

= 2.84

- Portfolio

Year	Calculation	realized rate of return
2011	-22.4*0.5+-15.6*0.5	-19.00
2012	27.75*.5+19.7*.5	23.73
2013	10*.5+37*.5	23.50
2014	-5*0.5+-9.9*0.5	-7.45
2015	23.75*.5+2.9*.5	13.33
Average Return	(-19+23.73+23.5-7.45+13.33)/5	6.82

Year	Return(%)	Deviation form avearge return (D)	D^2
2011	-19.00	-25.82	666.67
2012	23.73	16.91	285.78
2013	23.50	16.68	278.22
2014	-7.45	-14.27	203.63
2015	13.33	6.51	42.32

Variance = D^2 /n

= (666.67+285.78+278.22+203.63+42.32)/5

= 1476.62/5

= 295.324

Standard Deviation = Variance

= 295.324

= 17.18%

Coefficient of variation =Standard Deviation / Average Return

= 17.18/6.82

= 2.52

A risk-averse investor, also called as conservative investor will prefer low risk stock out of similar return stocks. Here portfolio has lower risk, to be selected.