Question

Year Stock A Returns Stock B Returns

2008 -18.00% -14.50%

2009 33.00 21.80

2010 15.00 30.50

2011 -0.50 -7.60

2012 27.00 26.30

1. Calculate the average rate of return for each stock during the period 2008–2012.
2. Assume that someone held a portfolio consisting of 50 percent Stock A and 50 percent Stock B. What would have been the realized rate of return on the portfolio in each year from 2008 through 2012? What would have been the average return on the portfolio during this period?
3. 1. Calculate the standard deviation of returns for each stock and for the portfolio.
   2. Calculate the coefficient of variation for each stock and for the portfolio. If you are a risk-averse investor, would you prefer to hold Stock A, Stock B, or the portfolio? Why?
4. Assume a third stock, Stock C, is available for inclusion in the portfolio. Stock C produced the following returns during the 2008-2012 period

Year   Stock C

2008                                          32.00%

2009                                        –11.75

2010                                          10.75

2011                                          32.25

2012                                          –6.75

6. Calculate (or read from the computer screen) the average return, standard deviation, and coefficient of variation for Stock C.
7. Assume that the portfolio now consists of 33.33 percent Stock A, 33.33 percent Stock B, and 33.33 percent Stock C. How does this composition affect the portfolio return, standard deviation, and coefficient of variation versus when 50 percent was invested in A and in B

Answer 1

Year	A	B
2008	(18.00)	(14.50)
2009	33.00	21.80
2010	15.00	30.50
2011	(0.50)	(7.60)
2012	27.00	26.30
Total	56.50	56.50

(a) Average Return (MeanA)= ∑A/n

=56.5/5

=11.30

Average Return (MeanB)= ∑B/n

=56.5/5

=11.30

(b) Portfolio of 50% A and 50% B

Year	A	Weight A	B	Weight B	P
2008	(18.00)	50.00%	(14.50)	50.00%	(16.25)
2009	33.00	50.00%	21.80	50.00%	27.40
2010	15.00	50.00%	30.50	50.00%	22.75
2011	(0.50)	50.00%	(7.60)	50.00%	(4.05)
2012	27.00	50.00%	26.30	50.00%	26.65
Total	56.50		56.50		56.50

) Average Return of Portfolio (MeanP)= ∑P/n

=56.5/5

=11.30

(a) The standard deviation of returns for each stock and for the portfolio

Year	da=A-MeanA	da2	db=B-MeanB	db2	dp=P-MeanP	dp2
2008	(29.30)	858.49	(25.80)	665.64	(27.55)	759.00
2009	21.70	470.89	10.50	110.25	16.10	259.21
2010	3.70	13.69	19.20	368.64	11.45	131.10
2011	(11.80)	139.24	(18.90)	357.21	(15.35)	235.62
2012	15.70	246.49	15.00	225.00	15.35	235.62
Total		1,728.80		1,726.74		1,620.56

Standard Deviation A = √ ( da2/ n )

=√ (1,728.80 / 5 )

= 18.595

Standard Deviation B = √ ( db2/ n )

=√ (1,726.74 / 5 )

= 18.587

Standard Deviation P = √ ( dp2/ n )

=√ (1,620.56 / 5 )

= 18.00

(b) Calculation of the coefficient of variation for each stock and for the portfolio.

Coefficient of variation( CV)= Standard Deviation / Mean

CV of A= 18.60/11.3

= 1.65

CV of B = 18.59 /11.3

= 1.64

CV of P = 18 / 11.3

= 1.59

(a)average return, standard deviation, and coefficient of variation for Stock C.

Year	C	dc= C - MeanC	dc2
2008	32.00	20.70	428.49
2009	-11.75	-23.05	531.30
2010	10.75	-0.55	0.30
2011	32.25	20.95	438.90
2012	-6.75	-18.05	325.80
Total	56.50		1,724.80

Average Return (MeanC)= ∑C/n

=56.5/5

=11.30

Standard Deviation C = √ ( dC2/ n )

=√ (1,724.80 / 5 )

= 18.573

CV of C = 18.573/11.3

= 1.643

( b )The portfolio now consists of 33.33 % Stock A, 33.33 % Stock B, and 33.33 % Stock C.

C	Weight C	A	Weight A	B	Weight B	P2	dp2	(dp2)2
32.00	0.33	(18.00)	0.33	(14.50)	0.33	(0.17)	(11.47)	131.48
(11.75)	0.33	33.00	0.33	21.80	0.33	14.35	3.05	9.30
10.75	0.33	15.00	0.33	30.50	0.33	18.75	7.45	55.50
32.25	0.33	(0.50)	0.33	(7.60)	0.33	8.05	(3.25)	10.56
(6.75)	0.33	27.00	0.33	26.30	0.33	15.52	4.22	17.78
						56.50		224.63

Average Return (MeanP2)= ∑P2/n

  =56.5/5

  =11.30

Standard Deviation P2 = √ ( dP22/ n )

=√ (224.63 / 5 )

= 6.7  

  CV of P2 = 6.7/11.3

= 0.593

If A, B, C, are invested equally the standard deviation decreases to 6.7. It becomes a safer investment even when the return is the same.