Question

4. Portfolio beta and weights Rafael is an analyst at a wealth management firm. One of his clients holds a $10,000 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: Stock Investment Allocation Beta Standard Deviation Atteric Inc. (AI) 35% 0.600 38.00% Arthur Trust Inc. (AT) 20% 1.600 42.00% 45.00% Li Corp. (LC) Baque Co. (BC) 15% 30% 1.300 0.400 49.00% Rafael calculated the portfolio's beta as 0.845 and the portfolio's required return as 8.6475%. Rafael 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 Baque Co. The risk-free rate is 4%, and the market risk premium is 5.50%. According to Rafael's recommendation, assuming that the market is in equilibrium, how much will the portfolio's required return change? (Note: Do not round your intermediate calculations.) O 0.3850 percentage points O 0.4774 percentage points O 0.3003 percentage points O 0.4428 percentage points

Answer 1

step 1	Calculating the Revised Investment Allocation
	After Replacing Atteric Inc shares with Baque Co. , new Investment Allocation will be-
	Stock	Investment Allocation	Beta
	Atteric Inc	0%	0.600
	Arthur Trust Inc	20%	1.600
	Li Corp	15%	1.300
	Baque Co. (30% +35%)	65%	0.400
		100%
Step 2	Calculation of New Portfolio's Beta
	Portfolio Beta which is the weighted average of Beta of individual stock
	Hence,
	New Portfolio's Beta = (1.600x 20% + 1.300 x 15% + .400 x 60%)
	New Portfolio's Beta = .77500
Step 3	Calculating the New Portfolio's Required Return
	Expected Return = Risk free Rate + (Beta x Market Risk Premium )
	Given, Risk Free Rate = 4%
	Market Risk Premium = 5.5%
	Beta= .77500 (as calculated above)
	Expected Return = 4%+ (.77500 x 5.5%)
	Expected Return = 8.26250%
Step 4	Portfolio's Required Return Change
	New Portfolio's Return - Old Portfolio's Return
	=8.2625 % - 8.6475 %
	-0.3850%
Hence, correct Answer is Answer A i.e. 0.3850 percentage points

Second Part

Whenever required rate of return is more than the expected return, then stock is said to be overvalued.

Here, required rate of return is 8.26% whereas Expected rate is 6.76% , which is greater than the required rate of return, hence stock is said to be overvalued.

Correct Answer is C overvalued.

Third Part

If Rafael replaces Atteric Inc's with Company X which has higher beta than Atteic Inc's

Then overall Beta of the new portfolio will be higher, since beta of the portfolio is the weighted average beta of individual stock

If Beta is higher, then the Required Rate from the Portfolio will also be higher. Higher the Beta higher the Required Return and vice versa.

Therefore, required return from the portfolio would be higher.