Question

Shares for Deloitte plc and PWC ltd have the following historical dividends and price data

companies	DELOITE PLC			PWC LTD
	dividends	year end price		dividends	year end price
Year
2001		22.50			43.75
2002	2.0	16.00		3.4	35.50
2003	2.2	17.00		3.65	38.78
2004	2.4	20.25		3.9	51.75
2005	2.6	17.25		4.15	44.50
2006	3.0	18.75		4.25	45.25

Required:

(a) Calculate the realized rate of return (or holding period return) for each share in each year. Assume an equally weighted portfolio. What would the realized rate of return on the portfolio be in each year from 2001 through to 2006? What are the average returns for each share and for the portfolio?

(b) Calculate the standard deviation of returns for each share and for the portfolio.

(c) Based on the extent to which the portfolio has a lower risk than the shares held individually, would you assess that the correlation co-efficient between returns on the two shares is closer to 0.9, 0.0 or -0.9?

(d) If you added more shares at random to the portfolio, what is the most accurate statement of what would happen to σp?

σp would remain constant

σp would decline to somewhere in the vicinity of 15%, or

σp would decline to zero if enough shares were included

Answer 1

		RealizedReturn in Year( N+1)=(Dividend(YearN+1)+(Price (YearN+1))-Price (YearN))/(Price YearN)
		For Example: Return of Deolite in Year 2002=(2+(16-22.5))/22.5=		-0.20	-20%
		Rate of Return of Portfolio=w1*R1+w2*R2
		w1=Weight of Deolite, R1=Return of Deolite
		w2=Weight of PWC, R2=Return of PWC
		w1=w2=0.5
		Portfolio Return =0.5*R1+0.5*R2=0.5*(R1+R2)
			N	A	B		C	D	R1	R2	Rp=0.5*(R1+R2)
				DELOITE PLC			PWC LTD		DEOLITE	PWC LTD	PORTFOLIO
				dividends	year end price		dividends	year end price	Realized Return (%)	RealizedReturn(%)	Realized Return (%)
			Year
			2001		22.5			43.75
			2002	2	16		3.4	35.5	-20.00	-11.09	-15.54
			2003	2.2	17		3.65	38.78	20.00	19.52	19.76
			2004	2.4	20.25		3.9	51.75	33.24	43.50	38.37
			2005	2.6	17.25		4.15	44.5	-1.98	-5.99	-3.98
			2006	3	18.75		4.25	45.25	26.09	11.24	18.66
								TOTAL	57.35	57.18	57.26
		Average Return of DEOLITE=57.35/5=	11.47	%
		Average Return of PWC=57.18/5=	11.44	%
		Average Return of DEOKITE=57.26/5=	11.45	%
		STANDARD DEVIATION OF RETURNS
			R1	R2	Rp	D1=R1-11.47	D2=R2-11.44	DP=Rp-11.45	E1=D1^2	E2=D2^2	Ep=Dp^2
			DEOLITE	PWC LTD	PORTFOLIO	DEOLITE	PWC LTD	PORTFOLIO	DEOLITE	PWC LTD	PORTFOLIO
			Realized Return (%)	RealizedReturn(%)	Realized Return (%)	Deviation From Mean	Deviation From Mean	Deviation From Mean	Deviation Squared	Deviation Squared	Deviation Squared
			-20.00	-11.09	-15.54	-31.4694	-22.5223	-26.9959	990.32	507.2546	728.7763
			20.00	19.52	19.76	8.5306	8.0845	8.3076	72.77	65.3596	69.0156
			33.24	43.50	38.37	21.7659	32.0652	26.9155	473.75	1028.1774	724.4468
			-1.98	-5.99	-3.98	-13.4447	-17.4269	-15.4358	180.76	303.6982	238.2646
			26.09	11.24	18.66	14.6176	-0.2006	7.2085	213.67	0.0403	51.9618
								TOTAL	1931.28	1904.53	1812.47
		Standard Deviation of DEOLITE=SQRT(1931.28)	43.95
		Standard Deviation of PWC=SQRT(1904.53)	43.640921
		Standard Deviation of PORTFOLIO=SQRT(1812.47)	42.573057
	c)	Correlation is closer to 0.9
		Because , there is not much reduction in Portfolio Standard Deviation
		Returns of the two shares are highly correlated
	d)	If we added shares at random to the portfolio
		Standard Deviation would reduce significantly
		σp would decline to somewhere in the vicinity of 15%,