Susan's investment portfolio currently contains three stocks that have a total value equal to $100,000. The beta of this portfolio is 1.5. Susan is considering investing an additional $50,000 in a stock that has a beta equal to 3. After she adds this stock, what will be the portfolio's new beta?

Question

blacksteel · Answer

A stock portfolio's overall beta is found by multiplying each stock's beta times the percentage of the overall portfolio it makes up and adding these terms together. Since the current portfolio's beta is known, we can treat all the stocks in the portfolio as a single stock for calculating its weight in the new portfolio. Thus, our new portfolio will have a value of $150,000, $100,000, or 2/3, of which has a beta of 1.5 and $50,000, or 1/3, of which has a beta of 3. Then the beta of the new portfolio will be 1.5*(2/3) + 3*(1/3) = 2.

anonymous · Answer

You can use the WACC equation to do this (which will need to be known later on if you do finance). it's fairly simple. it's just the percentage of the asset, times by the unit you're measuring.
so like above, it would be 
1.5(the unit) * 66.66% + 3 * 33.33% = beta of 3
          1.0                    +       2          =    3 
This will also work with multiple shares being added. Just as long as you get the percentages right.

anonymous · Answer

Black Steel is correct. JDN while doing your calculation of 33.33% * 3 you calculated 2 when the value should have been 1. That was your only error.