Your client has $80,000 invested in stock A. She would like to build a two-stock portfolio by investing another $80,000 in either stock B or C. She wants a portfolio with an expected return of at least 15% and as low a risk as possible, the standard deviation must be no more than 25%. Expected Return Standard Deviation Correlation With A A 18% 30% 1.0 B 17% 25% 0.3 C 15% 15% 0.4_____

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.

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