Question

2.

2. Calculate the standard deviation and return of portfolio consisting of 60% of Security A and 40% of Security B. Assume correlation coefficient between stock A and stock B is 0.55. Interpret the benefit of portfolio over individual stock investment (in case of security A and B). Year Security A return(% Security B return(%) 20 2015 2016 2017 2018 2019

Answer 1

Ans. 2	For Calculating the Standard Deviation and Return of Portfolio we have to find out return and SD of individual Stock.
	Year	Return of Security A i.e. RA	Return of Security B i.e. RB	RA-Mean of RA	RA-Mean of RA	(RA-Mean of RA)^2	(RA-Mean of RA)^2
	2015	20	15	2.8	3.2	7.84	10.24
	2016	22	12	4.8	0.2	23.04	0.04
	2017	18	11	0.8	-0.8	0.64	0.64
	2018	15	10	-2.2	-1.8	4.84	3.24
	2019	11	11	-6.2	-0.8	38.44	0.64
	TOTAL	86	59	0	-0.00	74.80	14.80
	For Security A
	∑RA=	86
	Mean of RA=	∑RA/n
	Where n = Numbers of years i.e. 5
	So,
	Mean of RA=	86/5
		17.2
	i.e Expected rate of return from security A = 17.20%
	For Security B
	∑RB=	59
	Mean of RB=	∑RB/n
		59/5
		11.8
	i.e Expected rate of return from security B = 11.80%
	For Security A
	Standard Deviation (σA)= (∑(RA-Mean of RA)^2)/n)^1/2
	σA=	(74.80/5)^1/2
		3.87
	For Security B
	Standard Deviation (σB)= (∑(RB-Mean of RB)^2)/n)^1/2
	σB=	(14.80/5)^1/2
		1.72
	As we know that portfolio consisting of 60% of Security A and 40% of Security B
	So,
	WA=60% i.e. 0.60
	WB=40% i.e. 0.40
	Mean of RA (i.e. Return from Security A)=	17.2
	Mean of RB (i.e. Return from Security B)=	11.8
	rAB=0.55
	Now
	Expected Return of Portfolio = WA*Mean of RA+WB*Mean of RB
		= 0.6*17.2+0.4*11.8
		15.04	Ans
	Expected SD of Portfolio = ( WA*σA)^2+( WB*σB)^2+2*WA*WB*σA*σB*rAB
		= ((0.60)^2*3.87^2+(0.40)^2*1.72^2+2*0.60*0.40*3.87*1.72*0.55)^1/2
		=(7.6223176)^1/2
		2.76	Ans

Selecting the portfolio over the individuals stock is better as it wolud reduce the unsysmatic risk.