Analysis of Asset Allocation

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Asset Allocation & Portfolio Management:
Stock Sensibility (alpha and beta)
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The asset allocation and portfolio management techniques we will describe mainly use statistical indicators you should be familiar with. If you are not, first visit our statistics tutorial.

To estimate the stock/market sensibility, we will use the notion of regression on historical data of both market and stock prices.

The regression line will be built around the stock return and the market return:

Where:

Rit = (Pit - Pit-1 + Dit) / Pit-1
Rmt = (Pmt - Pmt-1) / Pmt-1
m = market index
i = stock i
t = time t
t-1 = time t minus 1
D = dividend

This regression line will give you what is usually called alpha and beta. Of course to use these coefficient, the model must follow the assumptions of the linear regression and a stability analysis must be performed.

The model can be interpreted as follows:

  • Alpha (intercept of the regression line) measures the systematic return of the stock (independent of the market.

  • Beta (slope of the regression line) measures the sensibility of the stock to the market.

  • R square of the model shows the proportion of the total variance of the stock price changes that can be explained by market movements. This R square is the market risk and 1 - R square is the unique risk (see diversification).

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