Otimização de Portfolios e CAPM
Zvi Bodie, Alex Kane and Alan Marcus, "Investments", 11th Edition, McGraw-Hill, 2017.
Uma Explicação Sucinta sobre o Sharpe Ratio
CAPM Theory
Therefore, we begin by supposing that all investors optimize their portfolios á la Markowitz. That is, each investor uses an input list (expected returns and covariance matrix) to draw an efficient frontier employing all available risky assets and identifies an efficient risky portfolio, P, by drawing the tangent CAL (capital allocation line) to the frontier as in Figure 9.1, Panel A.
As a result, each investor holds securities in the investable universe with weights arrived at by the Markowitz optimization process.
The CAPM asks what would happen if all investors shared an identical investable universe and used the same input list to draw their efficient frontiers.
Not surprisingly in light of these assumptions [CAPM Theory assumptions], investors would calculate identical efficient frontiers of risky assets.
they would then draw an identical tangent CAL and naturally all would arrive at the same risky portfolio, P. All investors therefore would choose the same set of weights for each risky asset.
Therefore, if all investors choose the same risky portfolio, it must be the market portfolio, that is, the value-weighted portfolio of all assets in the investable universe.
We conclude that the capital allocation line based on each investor’s optimal risky portfolio will in fact also be the capital market line, as depicted in Figure 9.1, Panel B.
Zvi Bodie, Alex Kane and Alan Marcus, "Investments", 11th Edition, McGraw-Hill, 2017.
Capital Market Line Equation
Yves Hilpisch, “Python for Finance: Mastering Data-Driven Finance”, O'Reilly Media, 2nd Edition, January 8, 2019.
Aplicação Prática de Portfolio
Comparação entre o Fundo de Investimento Multimercado (FIM) High Vol da Kadima com os 5 FIM´s que mais haviam captado dinheiro na janela de abril/2017 a março/2019.
Observar que o “High Vol” não tem um Valor Esperado de Retorno negativo nos meses que apresentaram menor volatilidade, mas em compensação apresentou um Valor Esperado de Retorno bem maior nos meses de maior volatilidade.
E o que é o melhor de tudo. Se você for fazer um Portfolio de FIM´s com os 5 FIM´s mais o da “High Vol”, então a sua carteira de 30% no “High Vol” e 70% nos outros cincos vai apresentar um Risco menor e um Retorno maior.
“Entrevista com Rodrigo Maranhão, da Kadima Asset”
https://www.youtube.com/watch?v=n6XTYnvqxPY
Borrowing and Lending
Of course, large investment funds can choose from thousands of stocks and thereby achieve a wider choice of risk and return. This choice is represented in Figure 8.5 by the shaded, broken-egg-shaped area. The set of efficient portfolios is again marked by the red curved line.
obs: Os Portfolios que são marcados com a linha curva preta (na Figura 8.5), são os Potfolios dominados conforme Teria de Markowitz !
In Figure 8.6 we have plotted the risk and expected return from Treasury bills and the market portfolio. You can see that Treasury bills have a beta of 0 and a risk premium of 0. The market portfolio has a beta of 1 and a risk premium of Rm – Rf. This gives us two benchmarks for an investment’s expected risk premium. But what is the expected risk premium when beta is not 0 or 1?
Brealey, Myers and Allen,"Principles of Corporate Finance", 12th Ed., McGraw-Hill Education, 2017.
Zvi Bodie, Alex Kane and Alan Marcus, "Investments", 11th Edition, McGraw-Hill, 2017.
Systematic Risk
When common sources of risk affect all firms, however, even extensive diversification cannot eliminate risk.
[]…portfolio standard deviation falls as the number of securities increases, but it cannot be reduced to zero.
The risk that remains even after extensive diversification is called market risk, risk that is attributable to marketwide risk sources. Such risk is also called systematic risk, or nondiversifiable risk. In contrast, the risk that can be eliminated by diversification is called unique risk, firm-specific risk, nonsystematic risk, or diversifiable risk.