Question

Annie is curious to know whether the following five stocks are appropriately valued in the market. Accordingly, she creates a table (shown below) listing the betas of each stock along with their ex-ante expected return values that have been calculated using a probability distribution. She also lists the current risk-free rate and the expected rate of return on the broad market index. Help her out and state your steps. Stock Expected Return Beta 1 26.00% 1.8 2 16.00% 0.9 3 14.00% 1.2 4 16.15% 1.1 5 20.00% 1.4 Rf 3.50% ---- Rm 15.00% 1.0 b. If Annie wants to form a two-stock portfolio of the most undervalued stocks with a beta of 1.3, how much will she have to weight each of the stocks by?

Answer 1

Step1: First Find the Expected Return using CAPM Model & then find the position of each stock –

Annie:
Stock	Expected Return	Beta	ER using CAPM	Position
1	26%	1.8	24.20%	Highly Undervalued
2	16%	0.9	13.85%	Highly Undervalued
3	14%	1.2	17.30%	Overvalued
4	16.5%	1.1	16.15%	Appropriate
5	20%	1.4	19.60%	Moderately Undervalued

Step2: Calculate the weights of the undervalued stock –

Since Stocks 1 & 2 is highly undervalued, Annie will choose these stocks to form her two-stock portfolio with Beta of 1.3

Let Stock 1’s Weight be = X%

Then, Stock 2’s Weight be = (1 – X)%

Using Beta-adjusted Weights;

or; (1.8 × X%) + [0.9 × (1 – X)%] = 1.3

or; 1.8X + 0.9 – 0.9X = 1.3

or; 0.9X = 0.4

or; X = 0.444444444 = 44.44%

& (1 – X)% = (1 – 0.444444444) = 0.555555555 = 55%

∴ Weight of Stock 1 = 44.44%

∴ Weight of Stock 2 = 55.55%

DO UPVOTE !