<p>To be honest I don't quite understand the question, but it's here for a week so I'll give a short explanation of CAPM. The CAPM is an attempt to explain the risk and return on an asset i.e. it is a risk/return analysis. I don't understand why do we need to transform beta in first place.</p>

<p>The CAPM Formula is the following:</p>

<p>$E(R_i)=r_f+β_i[E(R_m)-r_f]$ $(1)$</p>

<p>or</p>

<p>$(R_{it}-R_{ft})=α_i+β_i(R_{mt}-R_{ft})+ε_i$ $(2)$</p>

<p>Where,</p>

<ol>
<li>$E(R_i)$ is an asset $i$ expected return,</li>
<li>$r_f$ is the rate on a risk-free asset,</li>
<li>$E(R_m)$ is the expected return on the market index (benchmark),</li>
<li>$β_i$ is the estimate of risk for asset $i$.</li>
</ol>

<p>As you may already know, we can either regress the $(2)$ if we are interested on both $α_i$ and $β_i$ or alternatively we just use the formula $β_i=Cov(R_i,R_m)/Var(R_m)$, because $α$ should be close to zero (transaction costs).</p>

CC BY-SA 3.0
2017-02-07T11:14:35.997Z
2017-02-07T11:14:35.997Z
Commissar Vasili Karlovic
<p>Usually for CAPM we have:</p>

<p>$$E(R_i)-\gamma=\frac{cov(R_i,R_m)}{var(R_m)}\times E(R_m-\gamma)$$</p>

<p>We know that</p>

<p>$$\beta=\frac{cov(R_i,R_m)}{var(R_m)}$$</p>

<p>When can we replace $\beta$ with $\left(\frac{E(R_iR_m)}{E(R_m)}\right)^2$ ?</p>

<asset-pricing>
Capital Asset Pricing Model Variation
SMK
# Capital Asset Pricing Model Variation

(Asked by: username_0 on 2017-01-31)

Usually for CAPM we have:

$$E(R\_i)-\gamma=\frac{cov(R\_i,R\_m)}{var(R\_m)}\times E(R\_m-\gamma)$$

We know that

$$\beta=\frac{cov(R\_i,R\_m)}{var(R\_m)}$$

When can we replace $\beta$ with $\left(\frac{E(R\_iR\_m)}{E(R\_m)}\right)^2$ ?

**Tags:** asset-pricing


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## 1 answers

### Answer by username_1 on 2017-02-07. Score: 2

To be honest I don't quite understand the question, but it's here for a week so I'll give a short explanation of CAPM. The CAPM is an attempt to explain the risk and return on an asset i.e. it is a risk/return analysis. I don't understand why do we need to transform beta in first place.

The CAPM Formula is the following:

$E(R\_i)=r\_f+β\_i[E(R\_m)-r\_f]$ $(1)$

or

$(R\_{it}-R\_{ft})=α\_i+β\_i(R\_{mt}-R\_{ft})+ε\_i$ $(2)$

Where,

1. $E(R\_i)$ is an asset $i$ expected return,
2. $r\_f$ is the rate on a risk-free asset,
3. $E(R\_m)$ is the expected return on the market index (benchmark),
4. $β\_i$ is the estimate of risk for asset $i$.

As you may already know, we can either regress the $(2)$ if we are interested on both $α\_i$ and $β\_i$ or alternatively we just use the formula $β\_i=Cov(R\_i,R\_m)/Var(R\_m)$, because $α$ should be close to zero (transaction costs).


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