Why a Low Market Beta Does Not Mean Low Portfolio Volatility
Summary
The discussion explains why a governance portfolio’s estimated market beta can be below one without implying that its total volatility is proportionately lower than the market’s. Beta measures the portfolio’s covariance with the market relative to market variance; it is also related to correlation and the ratio of volatilities. A sufficiently low correlation can therefore produce a low beta even when comparing volatility alone might suggest otherwise.
The responses also distinguish the market-related component of returns from idiosyncratic risk. In a one-factor regression, the residual captures movements not explained by the market factor, so portfolio volatility cannot be inferred from beta alone. The suggested diagnostic is to compare sample portfolio and market variances directly. The exchange gives conceptual guidance rather than an empirical assessment of the governance portfolios, and it does not address possible data, specification, or estimation issues in the Fama–French regression.
Key ideas
- Market beta measures covariance with the market scaled by market variance, rather than total portfolio volatility.
- A low correlation with the market can result in a beta below one even when the portfolio is not less volatile.
- Regression residuals represent idiosyncratic return variation that beta does not capture.
- Compare portfolio and market sample variances directly to assess their relative volatility.
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# Fama French model-small market beta (weird)
# Fama French model-small market beta (weird)
I am analyzing if good governance portfolios outperform bad governance portfolios. After dividing firms with good governance into one pf and bad ones into another for European companies I tried to run the regression of excess monthly returns on the Fama an French factors (from the official library). I have 3 portfolios and I obtain for each a market beta smaller than 0.5 which tells me that my sample is much less volatile than the market, which makes no sense. Any suggestions ? Please
## Answer by fni (score 3)
https://quant.stackexchange.com/a/18337
Market beta just tells your portfolio has low covariance, scaled by variance, with the market. Remember that $$ \beta= \frac{Cov(x,y)}{Var(x)} = \rho\frac{\sigma_x \sigma_y}{\sigma_x^2}=\rho\frac{\sigma_y}{\sigma_x} $$ You can see that it well may be that $\sigma_x<\sigma_y$ but $\rho$ is small enough to have a beta of 0.5. By the way, you can directly check whether the sample variance of your portfolios is smaller than the sample variance of the market.
What in general happens with Fama-French factors, to be fair with many other factor models, is that market betas tend to be close to one. But i don't see any problem with the fact you have a beta of 0.5
## Answer by lehalle (score 1)
https://quant.stackexchange.com/a/19370
I am afraid you are missing something (as a lot of people) about beta computation and meaning:
The model you are fitting links the returns of a market factor $r_m$ with your returns $r_g$ thanks to a linear relationship:
$$r_g = \beta \;r_m + \epsilon_{m,g}.$$
As you can see, it does not say the volatility of $r_g$ can be deduced from the one of $r_m$ using $\beta$: you forgot the volatility of $\epsilon_{m,g}$, which is the idiosyncratic part of $r_g$ seen from your market factor $r_m$.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.