<p>I'm not sure I follow, but do the two portfolios mean the following? </p>

<p>For portfolio (1),
$$
r_i - r_f - b(r_m - r_f) = r_i + (b-1) r_f - b r_m
$$
and for portfolios (2)
$$
r_i - b r_m - (1-b) r_f = r_i + (b-1) r_f - b r_m.
$$
So, writing them out like this, they look the same.</p>

CC BY-SA 3.0
2015-03-07T23:50:10.143Z
2015-03-07T23:50:10.143Z
jmbejara
<p>I run the following regression: </p>

<p>$$r_i-r_f=a+b(r_m-r_f)+e
$$
Now I see that the alpha is not zero and I construct two different zero cost portfolios:</p>

<p>1) 100% long in ($r_i-r_f$) and -b short in ($r_m-r_f$)</p>

<p>2) 100% long in $r_i$ -b short in r_m and borrow/short (1-b) on$ r_f$</p>

<p>I have problems determining the expected returns of the two portfolios and determining if they are the same.</p>

<p>I would appreciate your help a lot!</p>

<finance><financial-economics>
Return on two different ways to construct a portfolio
Darumii
# Return on two different ways to construct a portfolio

(Asked by: username_0 on 2015-03-07)

I run the following regression:

$$r\_i-r\_f=a+b(r\_m-r\_f)+e
$$
Now I see that the alpha is not zero and I construct two different zero cost portfolios:

1) 100% long in ($r\_i-r\_f$) and -b short in ($r\_m-r\_f$)

2) 100% long in $r\_i$ -b short in r\_m and borrow/short (1-b) on$ r\_f$

I have problems determining the expected returns of the two portfolios and determining if they are the same.

I would appreciate your help a lot!

**Tags:** finance, financial-economics

---

## 1 answers

### Answer by username_1 on 2015-03-07. Score: 0 | Accepted answer

I'm not sure I follow, but do the two portfolios mean the following?

For portfolio (1),
$$
r\_i - r\_f - b(r\_m - r\_f) = r\_i + (b-1) r\_f - b r\_m
$$
and for portfolios (2)
$$
r\_i - b r\_m - (1-b) r\_f = r\_i + (b-1) r\_f - b r\_m.
$$
So, writing them out like this, they look the same.


---

