estimated.Thisalsoimpliesthatitisnotwhereanasset or
firmis domiciledthat determinesthechoice of a risk-free
rate,butthecurrencyinwhichthecashflowsontheproject
orfirmareestimated.Thus,wecanvalueaMexicancompany
indollars,usingadollardiscountrate,orinpesos,usinga
pesodiscountrate. Fortheformer,we wouldusetheU.S.
Treasurybondrateastherisk-freerate,butforthelatterwe
would need a peso risk-free rate.
Underconditionsofhighandunstableinflation,valuationis
oftendone in real terms.Effectively, this means thatcash
flows are estimated using real growth rates and without
allowingforthegrowththatcomesfrompriceinflation.Tobe
consistent,thediscountratesusedinthesecaseshavetobe
realdiscountrates.Togetarealexpectedrateofreturn,we
needtostartwitharealrisk-freerate.Whilegovernmentbills
andbondsofferreturnsthatareriskfreein nominalterms,
theyarenotriskfreeinrealterms,sinceexpectedinflation
can be volatile. The standard approach of subtracting an
expectedinflationratefromthenominalinterestratetoarrive
atarealrisk-freerateprovidesatbestanestimateofthereal
risk-free rate. Until recently, there were few traded
default-free securities that could be used to estimate real
risk-free rates; but the introduction of inflation-indexed
Treasurieshasfilledthisvoid.Aninflation-indexedTreasury
securitydoesnotofferaguaranteednominalreturntobuyers,
butinsteadprovidesaguaranteedrealreturn.Inearly2005,
for example, the inflation-indexed U.S. 10-year Treasury
bondratewasonly2.1percent,muchlowerthanthenominal
10-year bond rate of 4.3 percent.
Risk-Free Rates When There Is No Default-Free Entity