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.

Please show all work.

Answer 1

Part A

As per CAPM return from security is Risk free Rate+Beta(Return from market-Risk free Rate) ie Rf+B(Rm-Rf)

	Security X	Security Y	Security Z
Formula	2+0.7(8-2)	2+1.3(8-2)	2+2.5(8-2)
Actual Return	6.2%	9.8%	17%
Expected Return	8%	8%	17%
Under/Over Priced	Overpriced	Under priced	Correctly Priced

Part B

As per CAPM, Abnormal Return is Actual Return- Expected/Normal Return

	Security X	Security Y	Security Z
Position	Long by $35,000	Short by $ 15,000	Long by $ 5,000
Actual Return	6.2%	9.8%	17%
Normal Return	8%	8%	17%
Abnormal Return	35000(6.2-8)%= -630	15000(9.8-8)%= - 270	5000(17-17)%=0