Question

1. Use the information for securities X, Y and Z in the table below to answer parts a and b.

	Security X	Security Y	Security Z
Expected return	8%	8%	17%
Beta	0.7	1.3	2.5

The risk-free rate is 2% and the expected return of the market portfolio is 8%.

1. According to the CAPM, are these securities overpriced, fairly priced or underpriced?
2. Using the CAPM, calculate the abnormal return of a portfolio that takes a long position in security X by $35,000, a short position in security Y by $15,000, and a long position in security Z by $5,000.
3. You have $100,000 and you want to set up a portfolio of security X and security Y with an abnormal return of 2.7% based on the CAPM. Specify the position to be taken (long or short) and the dollar amount to be invested in each security.

Answer 1

a. CAPM gives us expected return for stock

Expected Return Re = Rf + Beta x (Rm - Rf)

where Beta = stock beta

Re = Expected Return

Rf = Risk free rate

Rm = Market portfolio Return

If the required rate of return (expected return as per CAPM) is greater than the estimated return, then the stock is overvalued or vice versa

Computing this we get,

	Security X	Security Y	Security Z
Expected return	8%	8%	17%
Beta	0.7	1.3	2.5
Risk Free Rate	2%	2%	2%
Exp Market Portfolio Return	8%	8%	8%
Expected Return according to CAPM	6.20%	9.80%	17.00%
	Undervalued	Overvalued	Fair

B.  

The portfolio has a long position in security X by $35,000, a short position in security Y by $15,000, and a long position in security Z by $5,000.

	Security X	Security Y	Security Z
Expected Return according to CAPM (A)	6.20%	9.80%	17.00%
Positions (B)	$35,000	($15,000)	$5,000
Stock Returns C = A X B	$2,170.00	($1,470.00)	$850.00
Total Returns (Sum of C for X, Y & Z)	$1,550.00

C.

Let us assume investment in X = x

& Investment in Y = y

Thus total investment = x + y = $100000 or y = 100000 - x

Return on this investment is 2.7% = 2.7% x $100,000 = $2700 ........ (1)

Now return on x = 6.2% & return on y = 9.8%

Return on total investnment = 6.2% * x + 8% * y = 6.2%x + 9.8%(100000 - x) = 9800 - 3.6% x.... (2)

Equating equation 1 & 2

$9800 - 3.6%x = $2700

x = -7100/ 0.036 = $197222

Thus, Y = $100000 - x = $100000 - $ 197222 = -$ 97222 (Short)

Thus, $197222 should be long in X and $97222 short in Y