Estimating Industry Cost of Equity with Fama–French Factors
Summary
The note clarifies how a three-factor Fama–French regression can inform an expected return, interpreted as a cost of equity. It recommends estimating exposure coefficients from excess stock returns against the market, SMB, and HML factors, while including a residual term in the regression. To form an expected return, the estimated coefficients are combined with expected factor returns rather than each date’s realized factor values, and the risk-free rate is added back.
For an industry-level estimate, the response suggests fitting the regression within each sector and using sector-specific factor exposures and expected returns. It also notes that a historical average return is a simpler possible estimate. The approach depends on the reliability of the factor model and the chosen sample and frequency; the short answer provides no estimation diagnostics, uncertainty measures, or evidence comparing these alternatives.
Key ideas
- Cost of equity is treated as an estimate of expected equity return.
- A Fama–French regression relates excess returns to market, size, and value factors while retaining a residual.
- Expected factor returns, rather than date-by-date realized values, are combined with estimated exposures.
- Industry estimates can be formed by estimating factor exposures within each industry.
- The response offers a historical average as a simpler alternative and gives no diagnostics.
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Full text
# Fama and French 1997 Cost of Equity
# Fama and French 1997 Cost of Equity
Dear Quantitative Finance Members,
I was wondering if you can clarify me the following issue. I am trying to estimate the cost of equity following "Industry costs of equity" (Fama and French, 1997). I am not sure if I correctly understood the steps that I need to follow. Here they are:
- Obtain firm returns (from CRSP database) and SMB, HML, Rm-rf from Fama and French website.
- Run $$R_i -r_f = \beta_0 + \beta_1(R_m-r_f) + \beta_2 SMB + \beta_3 HML$$ over each out of 48 industries, whole sample.
- Save estimated coefficients of $\beta_0, \beta_1, \beta_2, \beta_3$
- Estimate fitted Cost of Equity ($CE$) as $$CE = \beta_0 + \beta_1 \times (R_m-r_f) + \beta_2 \times (SMB) + \beta_3 \times (HML)$$
Please, correct me if I am wrong
## Answer by lehalle (score 1)
https://quant.stackexchange.com/a/40458
First of all, the cost of equity is the expected returns on equity of a stock. This means that you could take any estimate of $\mathbb{E}(R_i)$ as cost of equity.
- a first version would be the empirical average ${1\over D} \sum_{d=1}^D R_i(d)$ where $d$ are available days in your database.
- to obtain a more robust version of the cost of equity you can rely on proxies of stable sources of returns.
- if you believe in reliability of FF factors, you can do it this way: estimate the beta to the factors (like you propose in your question; you forgot the epsilon --i.e. residuals--): $$R_i -r_f = \beta_0 + \beta_1(R_m-r_f) + \beta_2 SMB + \beta_3 HML+\epsilon$$ plug the empirical averages in place of the daily (or weekly) version of the data you used to estimate your beta (no more epsilon if you used any non-biased version of regression to obtain the betas): $$CE := \mathbb{E}(R_i) = r_f + \beta_0 + \beta_1(\mathbb{E}(R_m)-r_f) + \beta_2 \mathbb{E}(SMB) + \beta_3 \mathbb{E}(HML)$$
- [EDIT] If you want to have one cost of equity by industry / sector, you can simply perform a regression within each sector, thus you will obtain $\mathbb{E}(\beta_i\vert Sector)$ in place of $\beta_i$ (for $i\in\{0,\ldots, 3\}$). As a consequence, you will replace $\mathbb{E}(R_i)$ by $\mathbb{E}(R_i\vert Sector)$. And it is what you want.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.