Answer: Please see below for answer
Explanation:
Expected Return Standard Deviation Correlation With A
A 18% 30% 1.0
B 17% 25% 0.3
C 15% 15% 0.4_____
Expected return of A (RA) = 18%
Expected return of B (RB) = 17%
Standard Deviation of A (σA) = 30%
Standard Deviation of B (σB) = 25%
Weight of A (WA) = 50% (Since equal amount of $80,000 is being invested)
Weight of B (WB) = 50%
Correlation = 0.3
Portfolio Returns = WARA + WBRB = (18%*50%) + (17%*50%) = 17.5%
Portfolio Standard Deviation = (WA2 * σA2 + WB2 * σB2 + 2*(WA)*(WB)*CorrelationAB* σA* σB)(1/2)
= [(50%2 X 30%2) + (50%2 X 25%2) + (2 X 50% X 50%X 0.3 X 30% X 25%)](1/2)
=0.0025 +0.015625+SQR 0.01125
=0.0025+0.015625+0.1061=0.1241= 12.4%
If Invested in Stock C
Expected return of A (RA) = 18%
Expected return of C (RC) = 15%
Standard Deviation of A (σA) = 30%
Standard Deviation of C (σC) = 15%
Weight of A (WA) = 50% (Since equal amount of $80,000 is Being invested)
Weight of C (WC) = 50%
Correlation = 0.4
Portfolio Returns = WARA + WCRC = (18%*50%) + (15%*50%) = 16.5%
Portfolio Standard Deviation = (WA2 * σA2 + WC2 * σC2 + 2*(WA)*(WC)*CorrelationAC* σA* σC)(1/2)
= [(50%²X 30%²) + (50%² X 15%²) + (2 X 50% X 50%X 0.4 X 30% X 15%)]^1/2
= 0.0025+0.005625+ SQR 0.009= 0.1029= 10.29%= 10.3%
The expected return and standard deviation if invested in Stock B is 17.5% and 12.4% while that of STOCK C is 16.5% and 10.2 % but the client wants expected return of at least 15% and at low risk as possible with standard deviation not more than 25%, it is advised that the client invest in stock C as the values obtained are more towards her choice.
