Let's say that I have a universe of stocks from a certain sector. I want to compute the market portfolio of this sector. Beta is the covariance between each stock and the market. But how do you compute the market portfolio?

I read in several papers that a proxy for the market portfolio of a universe of securities is the portfolio with weights equal to the first principal component of the correlation matrix.

1. Why PCA? My concern is that PCA is maximizing the variance and I am not sure this is exactly what we want.

2. Are there other ways to choose the weights of this portfolio (apart from equally weighted or value weighted)? I am thinking, for instance, of minimizing the portfolio that is long a stock and short all others. Or I could use ANOVA.

Once I have separated systematic and idiosyncratic risk, I intend to apply specific trading strategies on each part. The idiosyncratic returns can, for instance, be obtained using APT. The problem is for the systematic part. You will tell me that the remainder of the idiosyncratic is the systematic. But then each stock has its own systematic component. What I want is ONE index that contains the beta of the universe. How do I define that? For instance if one component is less correlated with the rest, maybe we need to decrease its contribution.

Let's say that I have a universe of stocks from a certain sector. I want to compute the market portfolio of this sector. Beta is the covariance between each stock and the market. But how do you compute the market portfolio?

I read in several papers that a proxy for the market portfolio of a universe of securities is the portfolio with weights equal to the first principal component of the correlation matrix.

1. Why PCA? My concern is that PCA is maximizing the variance and I am not sure this is exactly what we want.

2. Are there other ways to choose the weights of this portfolio (apart from equally weighted or value weighted)? I am thinking, for instance, of minimizing the portfolio that is long a stock and short all others. Or I could use ANOVA.

I read in several papers that a proxy for the beta of a universe of underlyings is to use the first eiggenportfolio of the PCA approach (The portfolio that corresponds to the biggest eiggenvalue of the correlation matrix)

My purpose here is to create a basket that contains the beta of the universe, eg. the non idiosyncratic risk.

1/ Why PCA? My concern is that PCA is maximizing the variance and I am not sure this is exactly what we want to have.

2/ Is there other ways to choose the weights of this basket (appart for equally weighted :) I am thinking for instance of minimizing the portfolio that is long a stock and short all others? or ANOVA?

Thanks

Let's say that I have a universe of stocks from a certain sector. I want to compute the market portfolio of this sector. Beta is the covariance between each stock and the market. But how do you compute the market portfolio?

I read in several papers that a proxy for the market portfolio of a universe of securities is the portfolio with weights equal to the first principal component of the correlation matrix.

1. Why PCA? My concern is that PCA is maximizing the variance and I am not sure this is exactly what we want.

2. Are there other ways to choose the weights of this portfolio (apart from equally weighted or value weighted)? I am thinking, for instance, of minimizing the portfolio that is long a stock and short all others. Or I could use ANOVA.

Once I have separated systematic and idiosyncratic risk, I intend to apply specific trading strategies on each part. The idiosyncratic returns can, for instance, be obtained using APT. The problem is for the systematic part. You will tell me that the remainder of the idiosyncratic is the systematic. But then each stock has its own systematic component. What I want is ONE index that contains the beta of the universe. How do I define that? For instance if one component is less correlated with the rest, maybe we need to decrease its contribution.

I read in several papers that a proxy for the beta of a universe of underlyings is to use the first eiggenportfolio of the PCA approach (The portfolio that corresponds to the biggest eiggenvalue of the correlation matrix)

My purpose here is to create a basket that contains the beta of the universe, eg. the non idiosyncratic risk.

1/ Why PCA? My concern is that PCA is maximizing the variance and I am not sure this is exactly what we want to have.

2/ Is there other ways to choose the weights of this basket (appart for equally weighted :) I am thinking for instance of minimizing the portfolio that is long a stock and short all others?

Thanks

I read in several papers that a proxy for the beta of a universe of underlyings is to use the first eiggenportfolio of the PCA approach (The portfolio that corresponds to the biggest eiggenvalue of the correlation matrix)

My purpose here is to create a basket that contains the beta of the universe, eg. the non idiosyncratic risk.

1/ Why PCA? My concern is that PCA is maximizing the variance and I am not sure this is exactly what we want to have.

2/ Is there other ways to choose the weights of this basket (appart for equally weighted :) I am thinking for instance of minimizing the portfolio that is long a stock and short all others? or ANOVA?

Thanks