returnsonstocksandaveragereturnsonrisk-freesecurities
over an extended period of history.
Estimation Issues
Whileusersofriskandreturnmodelsmayhavedevelopeda
consensusthathistoricalpremiumis,infact,thebestestimate
oftheriskpremiumlookingforward,therearesurprisingly
largedifferences in theactualpremiums weobserve being
usedinpractice.Forinstance,theriskpremiumsestimatedin
theU.S.marketsbydifferentinvestmentbanks,consultants,
andcorporationsrangefrom 4 percentatthelowerendto 12
percentattheupperend.Giventhattheyalmostallusethe
same database of historical returns, provided by Ibbotson
Associates,
10 summarizingdatafrom1926,thesedifferencesmayseem
surprising. There are, however, three reasons for the
divergence in risk premiums.
1.Timeperiodused.While therearemanywhouseallthe
datagoingbackto1926,therearealmostasmanyusingdata
overshortertimeperiods,suchas50,20,oreven 10 years,to
come up with historical risk premiums. The rationale
presentedbythose whouseshorter periodsisthat therisk
aversionoftheaverageinvestorislikelytochangeovertime
andthatusingashorterandmorerecenttimeperiodprovides
amoreupdatedestimate.Thishastobeoffsetagainstacost
associated with using shorter time periods, which is the
greatererrorintheriskpremiumestimate.Infact,giventhe
annual standard deviation in stock prices
11 of 20 percent, the standard error
12 associated with the risk premium estimate can be
estimated for different estimation periods as inTable 2.1.