Question

The investment portfolio currently contains 3 stocks that have a total value equal to $100,000. The beta is 1.5. The investor is considering investing an additional $50000 in a stock that has a beta of 3. After this is done, what will be the portfolio's new beta

Answer 1

see beta of portfolio is wt avg beta hence,
beta of new portfolio = (1.5 * 1 lacs) + (0.5 lacs * 3) whole divided by 1.50 lacs
so the ans is 2

Answer 2

Logic to support why wt. avg. beta:
Beta is systematic risk in relative terms hence formula will be simply the weighted average, in a diversified portfolio no further diversification possible.
Just tried, if wrong please correct.

Answer 3

Beta of a portfolio is calculated by using this formula
\[\beta_{P} = \sum_{i=1}^{n}\beta_{i}weight_{i}\]
Now in your case \[\beta_{Security_{1}}=1.5\] and total investment in first security =
$ 100000
While second security has a beta of 3 and investment of $ 50000
so what proportion of amout you have invested into first security and second security
total investment is $ 150000
First security weight = 0.667
Second Security weight = 0.337
\[\beta_{p} = 0.667 \times1.5 + 0.337 \times 3\]
\[\beta_{p} = 1.0005 + 1.011\]
\[\beta_{p} = 2.0115\]