In this article the authors explain a theory/strategy called Betting Against Beta. My background is more in Math rather than finance so I have diffuculty understanding the idea/intuition in section 2 (the theory section). So, can someone provide an oral explaination of how portfolio construction in this strategy works and what the conection is to CAPM?
In the 1960's and 1970's it was believed that high Beta stocks offer higher returns and also higher risk; if so there is no reason to prefer or dislike high beta stocks, they offer the same Sharpe ratio as other stocks. Investors should be indifferent to Beta, it is neither good nor bad. This theory was called the CAPM.
Subsequently a man named Fischer Black (and others) found that High Beta stocks have had long term returns below what the CAPM theory suggests. The empirical findings contradict the theory. In some studies their returns are actually no higher than other stocks. If so then, with high risk and low returns, High Beta stocks are not attractive. If this were to continue to be true in the future (which no one knows) then investors should Bet Against Beta that is they should go short (or avoid) High Beta stocks and put the money into Low Beta stocks instead. Over the long run they would profit.
Mr. Frazzini and others have published extensive studies to expand on Black's idea and have started fund with millions of dollars in assets to try to make money from this. A lot of work has been put in to refine a very simple idea: high beta stocks have had disappointing returns compared to what the CAPM predicted, let's see if we can take advantage of that.
More specifically the strategy works by constructing a portfolio of high beta stocks which will be shorted (or "bet against") and a portfolio of low beta stocks which will be held long. Mr. Frazzini constructs these portfolios very carefully, with detailed rules, but presumably any similar strategy which considers Beta an undesirable chracteristic would work at least to some extent.
[Does this help? Feel free to ask a more specific question]