Estimating CAPM Cost of Equity with Rolling Beta and Market Premium
Summary
The document asks how to implement a firm-specific CAPM cost-of-equity estimate. The proposed procedure estimates each firm’s beta from a trailing window of monthly stock and market returns, with a shorter minimum window when history is limited. It also proposes estimating the market risk premium as a rolling historical average of the CRSP value-weighted index’s excess return over the risk-free rate, and using monthly risk-free data from the Fama-French source.
The reply confirms that beta is estimated from an individual stock’s returns relative to a market benchmark, while emphasizing that there is no universally required observation window. It points to external references for provider-specific beta conventions and surveys of risk-free rates and premia, but does not resolve the precise annualization, timing, or rolling-window choices in the question. The exchange therefore offers implementation context rather than a complete, validated estimation recipe; results depend on the benchmark and assumptions selected.
Key ideas
- CAPM beta is estimated for an individual stock by relating its returns to a market index.
- A rolling historical window can be used to estimate firm-specific beta through time.
- The choice of beta estimation period is a convention rather than a universal rule.
- Risk-free rates and market risk premia require explicit sources and consistent return frequency and annualization.
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Full text
# Cost of equity proper way of calculation # Cost of equity proper way of calculation Dear Community members, I need to calculate cost of equity following the following description: (Please, correct me if I misinterpret the meaning) "The annualized cost of equity, re(t), is determined as a firm-specific rate using the CAPM, where the time-t beta is estimated using the trailing five years (or, if there is not enough data, at least two years) of monthly return data. The market risk premium assumed in the CAPM is the average annual premium over the risk-free rate for the CRSP value-weighted index over the preceding 30 years" - CAPM calculation is done by each firm (not whole sample) using 5 years rolling window. I.e. for firm A you estimate CAPM Beta for month 12 using 5 years of data before month 12. - Market risk premium assumed in CAPM is calculated as 30 years rolling means for each month and then multiplied by 12. - The risk-free rate is a monthly risk-free rate from Fama and French website. Please, correct me if I am wrong. ## Answer by Magic is in the chain (score 1) https://quant.stackexchange.com/a/41855 Yes Beta is computed using the individual stock return against the market returns (say S&P 500 or FTSE). See the link below: https://www.fool.com/knowledge-center/how-to-calculate-the-beta-coefficient-for-a-single.aspx There are no hard and fast rules regarding the length of observations/holding period but you might want to see Reuters parameters here: https://reuters.zendesk.com/hc/en-us/articles/215714003-What-method-does-Reuters-use-to-calculate-the-beta-displayed-on-your-website- For risk premia and risk free rate, this guy does very regular surveys: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3155709
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