YearBustNormalBoom 1--170.190.8 0.01 Black Portfolio Price 639 White Portfolio Price 2235 Yield rate=8%

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YearBustNormalBoom Black Portfolio Price 639 White Portfolio Price 2235 Yield rate=8%

YearBustNormalBoom Yield rate=8% Black Portfolio Expected annual return = 0.19* * *(-20000) = 70 White Portfolio Expected annual return = 0.19*(-500)+0.8*300+0,01*10000 = 245 NPV of Black Portfolio = *PVIFA(8%, 17)= 0 NPV of White Portfolio = *PVIFA(8%, 17) = 0 State of EconomyBlack PortfolioWhite Portfolio Boom Normal Bust

State of Economy Black PortfolioWhite Portfolio Boom Normal Bust YearBustNormalBoom Black Portfolio Expected annual return = 0.5* *100 = 550 White Portfolio Expected annual return = 0.5*(-500)+0.5*300 = -100 Year 1—17 NPV of Black Portfolio = 550*PVIFA(8%, 17)= 5017 NPV of White Portfolio = -100*PVIFA(8%, 17) = -912 Normal 50% Bust 50%

YearBustNormalBoom State of EconomyBlack PortfolioWhite Portfolio Boom Normal Bust Black Portfolio Year 1—13 Expected annual return = 0.2* *100 = 280 Year 14—17 Expected annual return = 0.8* *(-20000) = White Portfolio Year 1—13 Expected annual return = 0.2*(-500)+0.8*300 = 140 Year 14—17 Expected annual return = 0.8*(-500)+0.2*10000 = 1600 Year 1—17 NPV of Black Portfolio = 280*PVIFA(8%, 13)+(-3200)*PVIFA(8%, 4)/ = NPV of White Portfolio = 140*PVIFA(8%, 13)+1600*PVIFA(8%, 4)/ = 3055

Real Market Situation YearBustNormalBoom √ √ 17 √ State of EconomyBlack PortfolioWhite Portfolio Boom Normal Bust Black Portfolio Price=638.5 Year 1—13 Annual return=100 Year 14—16 Annual return=1000 Year 17 Annual return= NPV = *PVIFA(8%, 13)+1000*PVIFA(8%, 3)/ / =-4306 White Portfolio Price= Year 1—13 Annual return=300 Year 14—16 Annual return=-500 Year 17 Annual return=10000 NPV = *PVIFA(8%, 13)-500*PVIFA(8%, 3)/ / =2365