5. Portfolio beta and weights Gregory is an analyst at a wealth management firm.

Question

5. Portfolio beta and weights Gregory is an analyst at a wealth management firm. One of his clients holds a $7,500 portfolio that consists of four stocks. The investment allocation in the portfolio along with the contribution of risk from each stock is given in the following table: Investment Allocation 3590 20% 15% 30% Standard Deviation 38.00% 42.00% 45.00% 49.00% Stock Atteric Inc. (AI) Arthur Trust Inc. (AT) Li Corp. (LC) Transfer Fuels Co. (TF) Beta 0.900 1.500 1.100 0.500 Gregory calculated the portfolio's beta as 0.930 and the portfolio's expected return as 9.12% Gregory thinks it will be a good idea to reallocate the funds in his client's portfolio. He recommends replacing Atteric Inc.'s shares with the same amount in additional shares of Transfer Fuels Co. The risk-free rate is 4%, and the market risk premium is 5.50% According to Gregory's recommendation, assuming that the market is in equilibrium, how much will the portfolio's required return change? O 0.60 percentage points O 0.77 percentage points O 0.89 percentage points O 0.96 percentage points

Explanation / Answer

New weight of Atteric Inc (AI) = 0%

New weight of Arthur trust (AT) = 20%

New weight of Li Corp (LC) = 15%

New weight of Transfer fuels (TF) = 30% + 35% = 65%

New Portfolio Beta = Beta of AI x Weight of AI + Beta of AT x weight of AT + Beta of LC x weight of LC + Beta of TF x weight of TF

or, New Portfolio Beta = 0.900 x 0% + 1.500 x 20% + 1.100 x 15% + 0.500 x 65% = 0.790

New portfolio expected return = Risk free rate + New beta x market risk premium = 4% + 0.790 x 5.50% = 8.345% or 8.35%

Change in portfolio's return = 9.12% - 8.35% = 0.77% or 0.77 percentage points

Required return is now 8.35% against expected return of 6.85%, i.e., Required return > Expected return (Expectations are less than required). Therefore, the revised portfolio is overvalued.

Since the beta of Company X is higher than Atteric Inc's beta, the portfolio's beta would increase.

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