expectedreturnoverafive-yearperiodandthatyouwanta
risk-freerate.Asix-monthTreasurybillrate,whiledefault
free,willnotberiskfree,becausethereisthereinvestment
riskofnotknowingwhattheTreasurybillratewillbeinsix
months.Evenafive-yearTreasurybondisnotriskfree,since
thecouponsonthebondwillbereinvestedatratesthatcannot
be predicted today.The risk-freerate for a five-year time
horizon has to be the expected return on a default-free
(government) five-year zero coupon bond.
Apurist’sviewofrisk-freerateswouldthenrequiredifferent
risk-free ratesfor cash flows in each period and different
expectedreturns.Asapracticalcompromise, however,itis
worthnotingthatthepresentvalueeffectofusingrisk-free
ratesthatvaryfromyeartoyeartendstobesmallformost
well-behaved
5 termstructures. Inthese cases, wecould use a duration
matching strategy, where the duration of the default-free
security used as the risk-free asset is matched up to the
duration of the cash flows in the analysis. The logical
consequenceforvaluations,wherecashflowsstretchoutover
longperiods (ortoinfinity), isthattherisk-freeratesused
shouldalmostalwaysbelong-termrates.Inmostcurrencies,
thereisusuallya10-yeargovernmentbondratethatoffersa
reasonable measure of the risk-free rate.
6
Cash Flows and Risk-Free Rates: The Consistency Principle
The risk-free rate used to come up with expected returns
shouldbemeasuredconsistentlywithhowthecashflowsare
measured.If thecash flowsarenominal, therisk-free rate
shouldbeinthesamecurrencyinwhichthecashflowsare