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# CH11 - .384.15 =.0576 Good.12.3.10.4.17.3 =.127.127.45...

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7. State of Economy Probability A Expected Return A B Expected Return Recession .2 .01 .002 -.25 -.05 Normal .55 .09 .0495 .15 .0825 Boom .25 .14 .035 .38 .095 .0865 or 8.65% .1275 or 12.75% Squared Standard Deviation A = .2*(.01-.0865)^2+.55*(.09-.0865)^2+.25*(.14-.0865)^2 Squared Standard Deviation A = .00189 Standard Deviation A = .04351 or 4.35% Squared Standard Deviation B = .2*(-.25-.1275)^2+.55*(.15-.1275)^2+.25*(.38-.1275)^2 Squared Standard Deviation B = .04472 Standard Deviation B = .2115 or 21.15% 9. a. Boom = (.08*1/3+.02*1/3+.23*1/3) .11 * .65 = .0715 or 7.15% Bust = (.12*1/3+.18*1/3+-.03*1/3) .09 * .35 = .0315 or 3.15% Expected Return of portfolio = .0315 + .0715 Expected Return of portfolio = .103 or 10.3% b. Portfolio Return Boom Boom = (.08*.2+.02*.2+.23*.6) = .158 .158 * .65 = .1027 Portfolio Return Bust Bust = (.12*.2+.18*.2+-.03*.6) = .042 .042*.35 =.0147 Expected Portfolio Return = .1027 + .0147 = .1174 or 11.74% Variance = .65*(.158-.1174)^2 + .35*(.042-.1174)^2 = .00306 10.a. Boom (.35*.3+.45*.4+.33*.3) = .384

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Unformatted text preview: .384 * .15 = .0576 Good (.12*.3+.10*.4+.17*.3) = .127 .127*.45 = .05715 Poor (.01*.3+.02*.4+-.05*.3) = -.004-.004 * .35 = -.0014 Bust (-.11*-.3+-.25*.4+-.09*.3) = -.16-.16 * .05 = -.008 Portfolio return = .0576 + .05715 + -.0014 + -.008 = .1054 or 10.54% b. Variance = .15*(.384-.1054)^2 + .45*(.127-.1054)^2 + .35*(-.004-.1054)^2 + .05*(-.16-.1054)^2 = .0196 Standard Deviation = Square root of variance = .1399 or 13.99% 17.a. .5 *.118 + .5*.038 = .078 or 7.8% b. .8 = X * 1.2 + (1-X)*0 .8 = X*1.2 X = .8/1.2 X = .6667 Stock weight = .6667 or 2/3 Risk free asset =.3333 or 1/3 c. Weights .11 = .118 *X + .038*(1-X) .11 = .118x+.038-.038x .11 = .08x + .038 .072 = .08x X = .9 Beta b= .9*1.2+(1-.9)*0 b = .9*1.2 b = 1.08 d. Weights 2.4 = X*1.2 + (1-X)*0 2.4 = X*1.2 X = 2 Give the stock weight of 2, the risk free weight is -1 (1-2). This means that the investor is borrowing 100% extra at the risk-free rate for the stock....
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CH11 - .384.15 =.0576 Good.12.3.10.4.17.3 =.127.127.45...

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