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I asked this question on Personal Finance and Money but was asked to ask it here.

On the Coursera course Portfolio and Risk Management, on Week 2, I am having trouble finding the link between the following 2 formulas from the following 2 slides:

From the slides above my conclusion would be the following equation:

$$ \beta_i = \frac{cov(R_i,R_M)}{var(R_M)} = \frac{\sigma_i}{\sigma_M} $$

So I have the following doubts:

  1. Is this right?
  2. How do you get from one expression to the other?
  3. In Formula 2, the expression for $\beta$ includes a relation between the asset and the market. But in Formula 1 the relation $\frac{\sigma_i}{\sigma_M}$ suggest there is no relation between the market and the asset.
    Why is this?
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