Chapter 2 Hw
portfolio beta= w1b1+w2b2 w1 = 20,000/55,000= .3636 w2= 35,000/55,000= .6364 portfolio bet= .3636*.7 + .6364*1.3 = 1.082 Required rate of return AA industries = risk free rate + market risk premium*beta AA industries ri = rRF + (rM - rRF)b
4% + (12%-4%)*.8 = 10.4% required return= risk free rate+ market risk premium*beta ri = rRF + RPM* b
Market- required return= 5%+7%= 12%
Beta of 1- required return= 5%+ 7%*1= 12%
Beta of 1.7- required return= 5%+ 7%*1.7 = 16.9% = P1r1+P2r2+P3r3+ etc.
= (0.1)(-50%) + (0.2)(-5%) + (0.4)(16%) + (0.2)(25%) + (0.1)(60%) = 11.40% σ2=( r1- )2*P1+( r2- )2*P2+( r3- )2*P3+ etc then square rooted
(-50% - 11.40%)2(0.1) + (-5% - 11.40%)2(0.2) + (16% - 11.40%)2(0.4) + (25% - 11.40%)2(0.2) + (60% - 11.40%)2(0.1) = 712.44 standard deviation = square root of 712.44 = 26.69%
coefficient of variation= CV= σ/ = 26.69%/11.40% = 2.34 expected return = = P1r1+P2r2+P3r3 expected return market= .3*15%+.4*9%+.3*18%= 13.5% expected return stock j= .3*20%+.4*5%+.3*12%=11.6%
standard deviation =( r1- )2*P1+( r2- )2*P2+( r3- )2*P3 then square rooted standard deviation of market = ((15% - 13.5%)2*.3 + (9% - 13.5%)2*.4 + (18% -13.5%)2*.3) then square rooted = 3.85% standard deviation of stock j = ((20% - 11.6%)2*.3 + (5% - 11.6%)2*.4 + (12% -11.6%)2*.3) then square rooted = 6.22% coefficient of variation= CV= σ/ =
CV of market = 3.85%/13.5% = .29
CV of stock J = 6.22%/11.6% = .54
ri = rRF + (rM - rRF)b
12% = 5%+ (10%-5%)*b
7% = 5%b b= 1.4 r= 5% + (10%-5%)*2 = 15% ri = rRF + (rM - rRF)b r = 5% + (12%-5%)*1.4 = 14.8% if the risk free rate increases by 1 percentage point to 6% then the market rate also would increase by 1 percent from 12 to 13% because of a constant slope ri = rRF + RPM* b = 6%+ 5%*1.4 = 15.8% if the risk free rate decreases by 1 percentage point to 4% then the market rate would also decrease by 1 percent from 12 to 11% because of a constant slope ri = rRF
4% + (12%-4%)*.8 = 10.4% required return= risk free rate+ market risk premium*beta ri = rRF + RPM* b
Market- required return= 5%+7%= 12%
Beta of 1- required return= 5%+ 7%*1= 12%
Beta of 1.7- required return= 5%+ 7%*1.7 = 16.9% = P1r1+P2r2+P3r3+ etc.
= (0.1)(-50%) + (0.2)(-5%) + (0.4)(16%) + (0.2)(25%) + (0.1)(60%) = 11.40% σ2=( r1- )2*P1+( r2- )2*P2+( r3- )2*P3+ etc then square rooted
(-50% - 11.40%)2(0.1) + (-5% - 11.40%)2(0.2) + (16% - 11.40%)2(0.4) + (25% - 11.40%)2(0.2) + (60% - 11.40%)2(0.1) = 712.44 standard deviation = square root of 712.44 = 26.69%
coefficient of variation= CV= σ/ = 26.69%/11.40% = 2.34 expected return = = P1r1+P2r2+P3r3 expected return market= .3*15%+.4*9%+.3*18%= 13.5% expected return stock j= .3*20%+.4*5%+.3*12%=11.6%
standard deviation =( r1- )2*P1+( r2- )2*P2+( r3- )2*P3 then square rooted standard deviation of market = ((15% - 13.5%)2*.3 + (9% - 13.5%)2*.4 + (18% -13.5%)2*.3) then square rooted = 3.85% standard deviation of stock j = ((20% - 11.6%)2*.3 + (5% - 11.6%)2*.4 + (12% -11.6%)2*.3) then square rooted = 6.22% coefficient of variation= CV= σ/ =
CV of market = 3.85%/13.5% = .29
CV of stock J = 6.22%/11.6% = .54
ri = rRF + (rM - rRF)b
12% = 5%+ (10%-5%)*b
7% = 5%b b= 1.4 r= 5% + (10%-5%)*2 = 15% ri = rRF + (rM - rRF)b r = 5% + (12%-5%)*1.4 = 14.8% if the risk free rate increases by 1 percentage point to 6% then the market rate also would increase by 1 percent from 12 to 13% because of a constant slope ri = rRF + RPM* b = 6%+ 5%*1.4 = 15.8% if the risk free rate decreases by 1 percentage point to 4% then the market rate would also decrease by 1 percent from 12 to 11% because of a constant slope ri = rRF