投资学讲义12

2005-11-111122005-11-11212.1OverviewofTermStructureofInterestRates„Therelationshipbetweenyieldtomaturityandmaturity.„Informationonexpectedfutureshorttermratescanbeimpliedfromyieldcurve.„Theyieldcurveisagraphthatdisplaystherelationshipbetweenyieldandmaturity.„Threemajortheoriesareproposedtoexplaintheobservedyieldcurve.2005-11-113„Yieldtomaturitythetermtomaturity„——„()()010112111CC,...,1(1)(1)(1)ntntniiCFPyyyCFPrrrr===+⇒+++=++++++∑∏2005-11-11412.1.11.51Shortinterestrate1n162839%49.5%59.5%1n2005-11-1152.100121100/(1+6)=94.3402100/[(1+8)(1+6%)]=87.3523100/[(1+9%)(1+8)(1+6%)]=80.1394100/[(1+9.5%)(1+9%)(1+8)(1+6%)]=73.1865100/[(1+9.5%)2(1+9%)(1+8)(1+6%)]=66.83722005-11-1161y1=(100/94.340)-1=6%2y2=(100/87.352)1/2-1=6.7%3y3=(100/80.139)1/3-1=7.66%4y4=(100/73.186)1/4-1=8.12%5y5=(100/66.837)1/5-1=8.39%3.200/1(1)nnFpyFpy=⇒=−+3123456%9.5%9%8%9.5%6%6.7%7.66%8.12%8.39%2005-11-11912.1.2„E(ri)„„„„2005-11-1110„Forwardrate„n“”1n2n11„2005-11-11113232005-11-111233223323323131.87100(1):118.87100(1)1,1(1)/(1)131.87/118.87111%yyffyyf=+=++=++=−=11(1)(1)nnnnnyfy−−+=+n112312.1.32005-11-111512.2„themarketexpectationstheory„„theliquidityperferencetheory)„liquiditypremium„themarketsegentationtheory)„2005-11-111612.2.11.ƒ2.3.2005-11-1117„11221222(1)(1)(1)()yyfErf+=++=2212(1)(1)(1())yyEr+=++122005-11-111832232323332212331233312312(1)(1)(1)(1)(1())()(1)(1)(1)(1)(1)(1)(1)(1)(1)(1)1()2,3,....,(1)(1),....,(1)1,2,3,....,ttnntyyfyErfEryyfyyffyyfffErtnyyfftn+=++=++=+=+++=+++=+++−===+++−=12005-11-11191.f2,f3,….,fnyn„„02.„roll-over)12(1)(1),....,(1)12,3,....,nntyyfftn=+++−=()ttfEr=2005-11-1120nynnynnynnyn2005-11-1121„Long-termbondsaremorerisky.„Investorswilldemandapremiumfortheriskassociatedwithlong-termbonds.„Theyieldcurvehasanupwardbiasbuiltintotheforwardratesbecauseoftheriskpremium.„Forwardratescontainaliquiditypremiumandaremorethanexpectedfutureshort-termrates.12.2.22005-11-1122()2,3,...,ltttlfErtn=−=1112212(1)(1)(1())lyyEr+++221222(1)(1)(1),()(),2,3,...,llllttyyffErfErtn+=++=2005-11-1123112323238%,()9%,()10%,1%,10%,11%llyrErErllff========222222(1.08)(1.1)18.9%(1.08)(1.09)18.5%llyyyy⎫=−=⎪⎬=−=⎪⎭233323(1.08)(1.1)(1.11)19.66%(1.08)(1.09)(1.11)18.90%llyyyy⎫=−=⎪⎬=−=⎪⎭2005-11-1124„121223312()()2,3,....,(1)(1),....,(1)1(1)(1())(1()),....,(1())1(1)(1()),....,(1())1lttttlnntnttntnfErlErtnyyffyErlErlErlyErEry=+==+++−+++++++−+++−=122005-11-11251.l1=l2=,…ln)YieldsMaturity2005-11-1126YieldsMaturity2.l1=l2=,…ln)2005-11-11273.l1l2,…ln)YieldsMaturity2005-11-11284.l1l2,…ln)YieldsMaturity2005-11-11295.YieldsMaturity2005-11-1130„„„2005-11-113112.2.3„„„„2005-11-1132„2005-11-1133„„„„„“”preferredhabittheory)„2005-11-11341828.539.049.5123212