Practice Question
A portfolio has ten (10) stocks, and it has beta of 1.7. Security X represents 16% of the portfolio’s wealth and security Y represents 18% of the portfolio’s wealth. Security X has a beta of 0.7 and stock B has a beta of -0.7. What will be your new portfolio beta if you sell all of your investment in security X and Y in order to invest the proceeds in the risk-free asset?
Step 1: Calculate the contribution of X and Y to the portfolio beta
βX × wX = 0.7 × 0.16 = 0.112
βY × wY = -0.7 × 0.18 = -0.126
Step 2: Subtract their contribution from the total portfolio beta
Total = 1.7 - (-0.014) = 1.714
Step 3: Remaining weight of portfolio (after selling X & Y)
1 - 0.16 - 0.18 = 0.66
Step 4: Estimate beta of remaining portfolio
βremaining = 1.714 / 0.66 ≈ 2.59697
Step 5: New portfolio beta (investing X & Y in risk-free asset)
New beta = 2.59697 × 0.66 ≈ 1.714
Conclusion:
The new portfolio beta is 1.714, since the risk-free asset has beta 0 and only the 66% invested in the remaining stocks contributes to beta.