Question

You are planning to make investment into three stocks, stock A, stock B and stock C. If the following information is given for them (KA: Rate of return of stock A): Variance(KA)=120 Variance(KB)=286 Variance(KC)=125 Covariance(KA, KB)= - 98 Covariance (KA, Kc)=260 Covariance (KC, KB)= - 40 If you form a portfolio investing 5% of your savings into stock A (WA=5%), 5% of your savings into stock B (WB=5%) and 90% of your savings into stock C (WC=90%), what will be the standard deviation of rate of return of your portfolio?

Answer 1

weight of staock A = 5% = 0.05

weight of staock B = 5% = 0.05

weight of staock C = 90% = 0.9

by using the variances given in the question prepare variance covariance matrics

variance co variance matrics
weight	security	A	B	C
0.05	A	120	-98	260
0.05	B	-98	286	-40
0.9	C	260	-40	125

the question clearly mention variance and covariances of each security

portfolio variance with 3 securities (A,B and C)

portfolio variance = summation of variances of all combinations

portfolio variance
1	2	3	1*2*3
0.05	0.05	120	0.3
0.05	0.05	-98	-0.245
0.05	0.9	260	11.7
0.05	0.05	-98	-0.245
0.05	0.05	286	0.715
0.05	0.9	-40	-1.8
0.9	0.05	260	11.7
0.9	0.05	-40	-1.8
0.9	0.9	125	101.25
portfolio variance	121.575

standard deviation = square root of variance =  square root of 121.575 = 11.03 (rounded with 2 decimal points)