ABSTRACT
AlreadyIrvingFisher,aswesaw,viewedthelong-termrateasanaverage oftheshort-termrateswhichareexpectedtoprevailduringtheperiodfor whichalong-termloanisgranted.Hewasthefirsttodevelopwhatwe herecallthe"expectationtheory"ofthetermstructureofinterestrates.4 Inexpoundingthistheory,letusfirstassumeperfectforesightandneglect thecostswhichariseifaninvestorshiftsfromshortmaturitiestolonger onesorviceversa.Inthiscasecompetitionwillequalizetheyieldonall investmentsundertakenforequalperiods,regardlessofwhatformthey take-i.e.,whetherwearedealingwithashort-terminvestmentrepeated severaltimes,orwithasinglelong-terminvestment,orwithseveralshortterminvestmentssucceededbyalonger-termone,andsoon.Iftheconditionofequalyieldsonallpossibleconfigurationsofinvestmentsover thesametimespanisnotfulfilled,profitablearbitrageoperationscanand willbecarriedoutwiththeresultthatyieldswillbeequalized.Thesum intowhichadollargrowsifinvestedfornyearsatthelong-termrate R , mustthenbeequaltothesumintowhichitwouldgrowifitwere investedseveraltimesinsuccessionattheshort-termratesr l > r 2..•r , , or:
Fromthiswecanobtaintheformulaeforthelongerrates(whichwere
already known to Irving Fisher)li:
It is through the variation in the price of the bonds outstanding that yields calculated for the same period will be equalized for bonds with different terms to maturity. If, for instance, the short-term rates are r 1=5-%, r2 =6%, r3 = 8%, the price of a five per cent bond redeemable after three years with a nominal value of 100 will be 96.6, so that the capital gain of 3.4 plus the annual interest payments of 5 will together constitute a yield equal to the return from the three successive short rates.
