Question

1. 1. calculate the correlation between the returns of Stock A and Stock B.
2. 2. If you invest 30% in Stock A and 70% in Stock B, what would the expected return and standard deviation of your portfolio be?

States of the Economy	Probability	Return of Stock A	Return of Stock B
Recession	0.15	-0.10	-0.25
Low Growth	0.25	-0.05	-0.15
Normal	0.35	0.08	0.20
Boom	0.25	0.35	0.40

Answer 1

Correlation (r) between A & B = Covariance (A,B) / [ ]

Covariance (A,B)

=

=

dA = Given return (A) - Expected return (A)

dB = Given return (B) - Expected return (B)

Standard deviation () =

Stock A

Expected return (A) =

= 0.15*(-0.10) + 0.25(-0.05) +0.35(0.08) + 0.25(0.35) = 0.088

Given return	Expected return	dA(Given return - Expected return)	(Given return - Expected return)2	Prob *(Given return - Expected return)2
-0.1	0.088	-0.188	0.035344	0.0053016
-0.05	0.088	-0.138	0.019044	0.004761
0.08	0.088	-0.008	0.000064	0.0000224
0.35	0.088	0.262	0.068644	0.017161
Total		-0.072	0.123096	0.027246

Standard deviation of A = = 0.1651 = 16.51%

Stock B

Expected return (B) =

= 0.15*(-0.25) + 0.25(-0.15) +0.35(0.20) + 0.25(0.40) = 0.095

Given return	Expected return	dB(Given return - Expected return)	(Given return - Expected return)2	Prob *(Given return - Expected return)2
-0.25	0.095	-0.345	0.119025	0.01785375
-0.15	0.095	-0.245	0.060025	0.01500625
0.20	0.095	0.105	0.011025	0.00385875
0.40	0.095	0.305	0.093025	0.02325625
Total		-0.18	0.2831	0.059975

Standard deviation of B = = 0.2449 = 24.49%

Probability	dA	dB	Prob*dA*dB
0.15	-0.188	-0.345	0.009729
0.25	-0.138	-0.245	0.0084525
0.35	-0.008	0.105	-0.000294
0.25	0.262	0.305	0.0199775
Covariance			0.037865

Correlation between A & B = 0.037865 / 0.1651*0.2449 = 0.9365 = 0.937 = 0.94 Approx (rAB)

30% invested in A and 70% invested in B

Weight of A (WA) = 0.3 ; Weight of B (WB​​​​​​) = 0.7

Return of portfolio = A expected return * weight of A + B expected return * weight of B

= 0.088 * 0.3 + 0.095* 0.7 = 0.0929 = 9.29%

Standard deviation of the portfolio

=

=

= 0.2186 = 21.86%

(in case any doubt please comment, I wil get back to you immdiately)