Portfolio Theory and Betting Against Beta

The main goal of this thesis is the study of the   paper "Betting Against Beta" (2014). In the first chapter we define   the financial market and basic definitions we are going to work with the rest   of the paper. During Chaper 1, we introduce the Mean/Variance analysis   (Markowitz model), and this will be the support of all our research, since to   choose a portfolio we only focus on mean and variance. Taking into account   this Markowitz model, and with the aim to minimize the portfolio's variance   for a fixed expected return, we calculate the efficient frontier for two   financial situations: the case where we deal with $n$ risky assets and the   situation with $n+1$ assets (composed of $n$ risky assets and a risk-free   asset). Later, in Chapter 2, we talk about the economic equilibrium model   CAPM and the statistical Single-Index model. Firstly we define them and set   the assumptions they need to fulfil. Afterwards, we claim the relation   between these two models and build 4 efficient statistical tests in order to   test this relation. In Chapter 3 we try to get empirical evidence of what we   theoretically claimed in previous chapters, taking the financial data from   Keneth R. French homepage and S\&P 500 as market index for robustness   tests from "Open knowledge" homepage. Finally, holding all this   previous theory as setup, we talk about "Betting Against Beta"   (2014). Andrea Frazzini and Lasse H. Pedersen build a constrained model where   some investors can use leverage, others can use it but keeping some   constraints and others cannot use it at all. Since many investors face   leverage constraints and want to maximize their expected wealth, they prefer   to invest their money in high-beta stocks even if they provide lower returns,   because less risky assets require the use of leverage. Therefore, to get a   profit from this market situation, authors create the "Betting Against   Beta"-factor. This strategy consists in buying low-beta (less risky)   stocks and sell high-beta (more risky) stocks, creating a low-beta portfolio   and a high-beta portfolio. That is, BAB factor is a portfolio that is long   low-beta portfolio and shorts high-beta portfolio. Authors gather all their   findings in 5 propositions giving empirical evidence. We are going through   these 5 propositions and use our financial datasets to test Proposition 1 and   Proposition 2, comparing the BAB-factor results we come out with and the   BAB-factor from Lasse H. Pedersen's homepage \cite{Lasse_data}. Testing   Proposition 1 we conclude that it does not fulfil with our industry   portfolios dataset. In order to build our BAB-factors we research among many   methods to split our stocks into low-portfolio or high-portfolio. The first   method we use is the "median" method. In this case, the low-beta   portfolio will be comprised of all stocks with a beta below the stocks' beta   median and the high-beta portfolio will be comprised of all stocks with the   beta above or equal to the stocks' beta median. As a robustness test for   Proposition 2, we will use four different ways to split our stocks into these   two portfolios. The first method will be to take the low-beta portfolio as the   stock that holds the minimum beta and the high-beta portfolio as the stock   that holds the maximum beta. The second will be taking the two minimum and   maximum beta values and the third method taking the three minimum and maximum   beta values. The last method consist in choosing the low-beta portfolio as   all the stocks whose beta is lower than one and choosing the high-beta   portfolio as all the stocks whose beta is larger than one. We claim that for   all our BAB-factors (depending on the method) Proposition 2 holds. To   conclude, we mention some other works that are related and have developed   another researchs basing on this betting against beta strategy.