1、1ObjectiveExplain market mechanisms for implementing hedges and insurance2345678910111213141516171819202122232425Value of 30-Year Mortgage 5-Years Out (6%)02,000,0004,000,0006,000,0008,000,00010,000,00012,000,00014,000,00016,000,0001%3%5%7%9%11%Market Interest RateMarket Value of MortgageMarket Valu

2、e of MortgagesBook Value of MortgagesniipmtPV111*262728obligation to purchase)2930Hedging v. Insuring05000010000015000020000025000030000035000040000045000000.511.522.533.54Price of WheatRevenue from WheatHedgedInsured313233343536373839Hedging with a Put-2000020004000600080001000012000140001600050607

3、08090100110120130140150Share PriceShare HoldingValue PutsFV PremiumTotal Wealth4041424344454647State of the World ProbabilityPayoffMeanDeviationDev SQR- * ProbOne Failure0.50200000-2000004E+102E+10One Success0.54000002000002000004E+102E+10Sum =4E+10Sqrt |200000The Standard Deviation is $200,00048Sta

4、te of the World ProbabilityPayoffMeanDeviationDev SQR- * ProbOne Failure0.250200000-2000004E+101E+10One Success0.5200000200000000Two Successes0.254000002000002000004E+101E+10Sum =2E+10Sqrt |141421.356The Standard Deviation is about $141,000 (c.f. $200,000)49502 , 121212222212122wwwwp5152Standard Dev

5、iations of Portfolios, rho = 0.2, sig = 0.2 0.000.020.040.060.0005101520253035404550Portfolio Size Standare Deviation 53Standard Deviations of Portfolios, rho = 0.5, sig = 0.2 0.000.020.040.060.0005101520253035404550Portfolio Size Standare Deviation 54

6、Standard Deviations of Portfolios, rho = 0.8, sig = 0.2 0.000.020.040.060.0005101520253035404550Portfolio Size Standare Deviation 55Standard Deviations of Portfolios, rho = 0.2, sig = 0.2 0.000.020.040.060.0005101520253035404550Portfolio Size Standare

7、Deviation Diversifiable Security Risk Nondiversifiable Security Risk56Standard Deviations of Portfolios, rho = 0.0, sig = 0.2 0.000.020.040.060.0005101520253035404550Portfolio Size Standare Deviation All risk is diversifiable All risk is diversifiable 5758Standard Deviations of Portfolios, rho = 1/(1-50) = -0.0204, sig = 0