Chapter 2 Hw

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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 + RPM* b
= 4%+ 5%*1.4 = 13.8%

if the market rate increased to 14% which will make the SML steeper and the risk free remains constant
ri = rRF + (rM - rRF)bi
4% + (12% - 5%)1.4 = 13.8%.
if the market rate decrease to 11% it would make the SML slope less steep and the risk free rate would remain constant
ri = rRF + (rM - rRF)bi
5% + (11% - 5%)1.4 = 13.4%.

total dollars invested in portfolio = 15*5,000= 75,000
original portfolio beta 1.2 = 70,000/75,000 (stocks still in portfolio) * b + 5,000/75,000 (stock sold) *.8
1.2= .9333b + .06667 * .8
1.2= .9333b+.0533
1.1467= .9333b
b = 1.229 for the 14 stocks not sold
New portfolio beta = 70,000/75,000 * 1.229 + 5,000/75,000 * 1.6
= .9333*1.229 + .06667*1.6
= 1.147 + .106667
= 1.254
total funds in portfolio = 400,000 + 600,000+ 1,000,000+2,000,000 = 4,000,000 portfolio beta = 400,000/4,000,000*1.50 + 600,000/4,000,000 * -.50 + 1,000,000/4,000,000*1.25 + 2,000,000/4,000,000*.75 =.1*1.5 + .15*-.5 + .25*1.25 + .5*.75

= .15 - .075 + .3125 + .375 = .7625 (beta)
rp= rRF + (rM - rRF)(bp)
rp = ?
rRF = 6%
rM = 14%
bp = .7625
rp = 6% + (14% - 6%)(0.7625) = 12.1%.
The fund's required rate of return is 12.1%
total dollars invested in portfolio = 2,000,000
original portfolio beta 1.1 = 1,900,000/2,000,000 (stocks still in portfolio) * b + 100,000/2,000,000 (stock sold) *.9
1.1= .95b + .05* .9
1.1= .95b+.045
1.055= .95b
b = 1.111 for the stocks not sold
new portfolio beta = 1,900,000/2,000,000 * 1.111 + 100,000/2,000,00 *1.4
=.95*1.111 + .05 * 1.4
=1.125
rp= rRF + (rM - rRF)(bp
beta of R = 1.50
beta of S = .75
market rate = 13%
risk free rate = 7%
7% + 13%-7% * beta
required rate for R = 7% + (13%-7%) * 1.50 = 16%
required rate for S = 7% + (13%-7%) * .75 = 11.5%
The required rate of return for Stock R exceeds Stock S by 4.5%

average rate of return stock A =...
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