Question

You have been provided the following data on the securities of three firms and the market:

Security	E[Rj]	sj	rjM	bj
Firm A	0.13	.12	?	.90
Firm B	0.16	?	0.40	1.10
Firm C	0.25	0.24	0.75	?
Market	0.15	0.10	1	1
Risk-free	0.05	0	0	0

Assume the CAPM holds true.

Fill in the missing values in the table.

0.9 = (r_jM)(0.12) / 0.10

r_i,_m= .75

b_j     = (r_jM)(s_j) / s_m

= .4 (s_j) / .10

s_j) = .275

b_j= (r_jM)(s_j) / s_m

= (0.75)(0.24) / 0.10= 1.8

What is your investment recommendation on each asset? Buy or sell?

E(r)    = fr + b[EMR – rf]

Firm A:  0.05 + 0.9(0.15 – 0.05) = 0.14

Firm B: 0.05 + 1.1(0.15 – 0.05)= .16

Firm C: 0.05 + 1.8(0.15 – 0.05) = 0.23

Firm A is the only underpriced stock so I would buy firm A.

Suppose that you are currently holding a portfolio consisting of Firm B only. If you increase your portfolio weight on Firm B by 0.2 (or 20%) and borrow the needed money at the risk-free rate, what will be the new standard deviation of your portfolio?

Answer 1

Beta = Corr(Security, Market) * STDEV(Security) / STDEV(Market)

Firm A: Corr = 0.90*0.10/0.12 = 0.75

Firm B: STDEV(Security) = 1.10*0.10/0.4 = 0.275

Firm C: Beta = 0.75*0.24/0.10 = 1.80

Compute required return using CAPM

Firm A: 0.05 + 0.9*(0.15 - 0.05) = 0.14

Higher required return makes price low.

Based on risk involved, price of firm-A is lower but speculator expects higher price.

Rule: buy low, sell high.

As A is underpriced, buy security of firm-A.

Secirity	E(R)	STDEV	Corr	Beta	Required Return
Firm A	0.130	0.120	0.750	0.900	0.140	Underprice; Buy
Firm B	0.160	0.275	0.400	1.100	0.160	Fairly Priced
Firm C	0.250	0.240	0.750	1.800	0.230	Overprice; Sell
Market	0.150	0.100	1.000	1.000
Risk-Free	0.050	0.000	0.000	0.000

When you leverage your portfolio, both risk and return will increase.

Weight of portfolio B = 1.2, weight on risk-free asset = -0.2

Standard Deviation of risk-free asset = 0

Standard Deviation of portfolio = 0.275*1.2 = 0.33

Return on portfolio = 1.2*0.16 + (-0.2)*0.05 = 0.182