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The regression beta uses the historical stock price for the company. Usually 5-year monthly data, and you run a regression to obtain beta. On the other hand, bottom-up beta uses publicly comparable firms then you obtain median or average leveraged beta. Also, estimate the average market value (D/E ratio). After that leverage it. use the following formula:
Beta unleveraged = Beta levered/ (1+(1-tax rate)*(D/E of comparable))
Beta firm = Beta unleveraged*(1+(1-tax rate)*(d/e of firm))
