# Compute the beta of portfolios constructed from the Betting Against Beta strategy [on hold]

http://pages.stern.nyu.edu/~lpederse/papers/BettingAgainstBeta.pdf

I am trying to understand how to apply the Betting Against Beta strategy. Let's for instance consider two stocks A and B with $\beta_A<1$ and $\beta_B>1$ and current prices $P_A$ and $P_B$. With inspiration from Equation 9 I will construct these two portfolios:

In my Low-beta portfolio I will buy $\beta_A^{-1}/P_A$ shares of A and maybe borrow/store some money at the riskfree rate $r$.

In my high-beta portfolio I will short sell $\beta_B^{-1}/P_B$ shares of B and maybe borrow/store some money at the riskfree rate $r$.

Now ... according to the theory from the paper, both of my portfolios should have a beta of $1$. How can I make sure that this is satisfied?

In otherwords the following must hold: $$\beta_L = Cov(r^L,r^m)/var(r^m)=1$$$$r^m:=r^{\text{market}}$$ Does it?

## put on hold as unclear what you're asking by Alex C, Helin, LocalVolatility, Attack68, amdopt15 hours ago

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• I do not understand your question. As you yourself said, the way to make each of the portfolio betas equal to 1 is to "borrow or lend some money at the risk free rate r" until this is so. – Alex C Aug 11 at 2:34