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4

Let us ignore the riskless rate for simplicity of the presentation. If you have (historical or simulated) return series $r_i$ for the portfolio and $r_i^M$ for the market, then the beta is the OLS regression beta: $$\beta = cov(r_i,r_i^M)/var(r_i^M).$$ Then if you write $r_i = \alpha + \beta r_i^M + \epsilon_i$ on the other hand  \epsilon_i = r_i - ( ...

5

Active return: $R-R_m$ i.e. your security (or portfolio) compared to the market portfolio. Used to judge performance before the CAPM was invented Excess return: $R-R_f$ the security compared to the risk free rate, appears on the left hand side of the CAPM equation. Excess return on the market: $R_m-R_f$, appears on the right hand side In words the CAPM ...

0

If you want a portfolio to accurately describe an industry you should not perform any kind of optimization on it. You have 2 options: equal weighted portfolio market cap weighted portfolio Search for S&P Index Methodology for an example and yes, you have a small sample bias issue. i am guessing you want to make factor portfolios sorted on size , ...

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