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You can find the estimated expected return of a stock today just by using the closing values but how far back do you go to find the expected return? Do you use all of the closing values since the stock when public or do you just go back a certain number of years?

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I don't know to which specific method you're referring to but when estimating expected return with CAPM for instance, it is generally advised to have at least a full market cycle, or two. Your concern is justified because if you go back too far in the past you may end up with data not representative of the future growth prospect of a company. For instance, it is not likely that the excess return of companies involved in producing photographic film will the same in the coming years as it was in the 70s. There is no quick and easy way to figure this out. Share price return in the past is just a component of the analysis.

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