Ct 8. You form a portfolio that invests 65% of total funds in stock X and 35% in

Question

Ct 8. You form a portfolio that invests 65% of total funds in stock X and 35% in stock Z. Two possible outcomes exist. The probability is 30% that the first outcome occurs, in which case the rates ofreturn equal 32% for X and 30% for Z. The probability is 70% that the second outcome occurs, in which case the rates of return equal 40% for X and 22% for Z. Find the diversification benefit, measured as the standard deviation reduction in basis points (BP), that the portfolio provides a. 634 BP b. 516 BP c. 481 BP d. 328 BP e. 257 BP

Explanation / Answer

Expected Returns of X =0.3x32 + 0.7x40 =37.6%

Expected Returns of Z =0.3x30 + 0.7x22 =24.4%

Expected Return of Portfolio in first state =0.65x32 + 0.35x30 =31.3%

Expected Return of Portfolio in second state =0.65x40 + 0.35x22 =33.7%

Expected Returns of Portfolio =0.30x31.30 + 0.70x33.70 = 32.98%

Standard Deviation of X ={0.30x(32-37.6)2 + 0.70x(40-37.6)2}1/2 =(0.001344)1/2 =3.66%

Standard Deviation of Z ={0.30x(30-24.4)2 + 0.70x(22-24.4)2}1/2 =(0.001344)1/2 =3.66%

Standard Deviation of Portfolio ={0.30x(31.3-32.98)2 + 0.70x(33.7-32.98)2}1/2 =(0.000121)1/2 =1.10%

Diversification Benefit = 3.66 - 1.10 = 2.57% or 257 BP

Hence, Option-e is the right answer

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