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Unformatted text preview: Journal of Fmanclal Economtcs 5 (1977) 309-327 P North-Holland Publlshmg Company ESTlhlATINC BETAS FROhI NON!3 NCHRONOUS DATA hiyron SCHOLES and Joseph WILLlAhIS* LSlirersrrr of Chcugo Chcugn IL 60637, Lf S 4 Recened Noiember 1976 Ic\lsed \erslon reccl\ed October 1977 Nons)nchronous trading of securmcb Introduces Into the market model a porentiallv serious econometric problem of ct rors In \arrahles In thlb paper propertles of the obberved market model and a>soclated oldlnar\ least squares estimators are developed tn detail In addltlon. compulatlonally cometvent, consrqtent estimators tor parameers of the marhet model are calculated and then applied to dad} returns of securltleb Il,ted In the NYSE and ASE 1. Iohoductioo Central to contemporary theory In finance IS the fundamental concept of systematic rrsl\ or beta for a security Not surprlslngly, much current empu-ical \\ork rn finance focuses on the associated problem of estlmatlng this systematic risk or beta Although to date almost all estimates have used monthly returns on common stochs, recently daily returns hake become a\allable With this new data more pobierful empirical tests are now possible Unfortunately, the use of daily data introduces Into the market model a potentially serious econometric problem In particular, manq securities hsted on organized exchanges are traded only infrequently, with fei! securities so actively traded that prxes are recorded almost continuously Because prices for most securltres are reported onI> at dlbtinct random intervals, completely accurate calculation of returns o\er any lived sequence of periods IS wrtually rmposslble In turn this Introduces Into the market model the econometric problem of errors in \nrlables With daily dat.1 thib problem appears partlcu- larly severe *Ue thanh hlrchxl Jensen and the reieree, G WIllram Schitert, for comment> on a pre\wus draft, MarbIn Llpson for programmmg assl,tdnce and the Center for Rewarch In Security Prices, Utwersit> of ChIcago for iindnclal support Da~l) dota for total returns on approwmatelq WOO AecuIt~cs Insted on the Ne\\ \ orb and -2mericnn \rock Exchange5 betiteen Julk 2 1961 and December 31, 1975 hale been collected at thecenter for Research rn Securrlr Prices Graduate School of Bwnesh Unt\erslr\ 01 Chicago 2Fama (1965) and rl>her (19661 first reco_enlzed the nonfradlng ofsecurrucs a> I potentlJllj serious empirical problem Some of the results In this paper appear In a xt 01 unpuhll\hed notes bv Oldrrch Laslchch, Graduate School of hlanagcmenr. Unl\ersrt) of Rochebrsr R&l4 results appear m Cohen, hlaler, Schwarlz, and Whltcomb f 1977) 310 M Scholes and J Wdhams, Estrmatrng betas In sectlon 2 of this paper, properties ofthe market model wth nonsynchronous data are developed In detail Assuming that true Instantaneous returns on securities are normally distributed, It IS shoi\ n that variances and co\ wances of reported returns differ from corresponding variances and co\arrances of true returns...
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This note was uploaded on 04/28/2010 for the course ECON FINC3017 taught by Professor Xelloss during the Spring '10 term at University of St Andrews.
- Spring '10