what is the new portfolio beta calculation for the following:

5,000 investment in each of 10 stocks, portfolio beta = 1.12. Sold one
5,000 stock with a beta of 1.0, used proceeds to buy another stock
with beta of 1.5.

Kitty4400 --

As Campbell Harvey points out in the article linked, "The beta of the
portfolio is the weighted average of the individual asset betas where
the weights are the portfolio weights."

Duke University
"Asset Pricing and Risk Management," (Harvey, Nov. 27, 1995)
http://www.duke.edu/~charvey/Classes/ba350/riskman/riskman.htm


So, 
Portfolio ? = 0.90 * (Other stocks ?) + .10 * (Stock 1 ?)

Or,
1.12 = 0.90 * OS? + .10 * 1.0 ==> OS? = 1.1333


Now we can figure the new portfolio ?: 
New portfolio ? = 0.90 * 1.1333 + 0.10 * 1.50 = 1.17

Google search strategy:
?change in portfolio? beta calculation


Best regards,

Omnivorous-GA

---

Request for Answer Clarification by kitty4400-ga on 25 Sep 2005 11:28 PDT

I have my dumb hat on...

what is the .90 and .10 in your calculation?

---

Clarification of Answer by omnivorous-ga on 25 Sep 2005 12:26 PDT

Kitty4400 --

You've replaced 1 stock of 10 or 10% of the portfolio.  The other
stocks are 90% of the portfolio.  Of course, they're represented in
decimals as 0.10 and 0.90, so we have --

Portfolio ? = 0.90 * (Other stocks ?) + .10 * (Stock 1 ?)

Does that explain it?

Best regards,

Omnivorous-GA

Excellent. Thanks! I had a brain cramp. It is very clear now.