How Beta Scaling Builds a Market-Neutral BAB Portfolio
Summary
The document explains the beta adjustment behind the betting-against-beta factor. It treats a risky asset's return above the risk-free rate as a zero-cost excess return, then scales that return by the inverse of its market beta. This changes the portfolio's market exposure to one: a high-beta portfolio is scaled down, while a low-beta portfolio is scaled up.
Subtracting the beta-adjusted low-beta return from the beta-adjusted high-beta return produces a portfolio with zero market beta under the stated model. The explanation gives the regression algebra behind this result, but does not provide implementation details such as estimating beta, rebalancing, financing costs, or trading constraints. Its account therefore clarifies the construction concept without establishing how the factor performs in practice.
Key ideas
- Scaling an excess return by the inverse of its beta makes its market beta equal to one under the stated model.
- A high-beta portfolio is scaled down to reach unit beta.
- A low-beta portfolio is scaled up to reach unit beta.
- Subtracting the two unit-beta excess returns creates a market-beta-neutral spread.
- The explanation does not address beta estimation, financing, or portfolio implementation.
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# In the "betting against beta" paper, what exactly is the "BAB factor"?
# In the "betting against beta" paper, what exactly is the "BAB factor"?
I refer here to the paper "Betting against beta" by Pedersen and Frazini.
In the model, they construct the following factor, on page 5.
I don't quite understand how this portfolio is being constructed. What do they mean by "leveraging the long side to a beta of 1"? Or deleveraging the short side to a beta of 1?
How exactly does that work in practice? What does leveraging have to do with beta?
As I understand leveraging, we just borrow to finance more investment, right? So what does that have to do with changing beta to become 1?
## Answer by Matthew Gunn (score 5)
https://quant.stackexchange.com/a/40169
- An excess return is the payoff of a zero cost portfolio. For example: $R_i - R_f$ is an excess return. $c \left( R_i - R_f \right) $ is an excess return for any $c \in \mathbb{R}$,. More generally, $R_i - R_j$ is an excess return for any returns $R_i$ and $R_j$.
Excess returns are nice to work with because you cans simply scale them up or scale them down and they're still excess returns. Let's imagine excess return $R_i - R_f$ has a market beta of $\beta_i$.
$$ R_i - R_f = \alpha_i + \beta_i \left( R_m - R_f \right) + \epsilon_i $$
Then excess return $\frac{1}{\beta_i} (R_i - R_f)$ has a market beta of $1$. $$\frac{1}{\beta_i} \left( R_i - R_f\right) = \frac{\alpha_i}{\beta_i} + \left( R_m - R_f \right) + \frac{\epsilon_i}{\beta_i} $$
Excess return $\frac{1}{\beta_i} (R_i - R_f) -\frac{1}{\beta_j} (R_j - R_f) $ will have a market beta of 0.
Since $\beta_H > 1$, multiplying by $\frac{1}{\beta_H}$ to obtain $\frac{1}{\beta_H} (R_H - R_f)$ is deleveraging the excess return $R_H - R_f$. Since $\beta_L < 1$, multiplying by $\frac{1}{\beta_L}$ to obtain $\frac{1}{\beta_L} (R_L - R_f)$ is leveraging the excess return $R_L - R_f$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.