If $30,000 was invested in the following four stocks:

Security            Amount Invested                  Beta
Stock A             $5,000                            0.75
Stock B              10,000                           1.10
Stock C               8,000                           1.36
Stock D               7,000                           1.88

The risk free rate is 4 percent and the expected rate of return on the
market portfolio is 15 percent.  Based on the CAPM, what is the
expected rate of return?

Hi again!!


First of all we need to determine the beta of the portfolio:

Total Amount Invested 	= $5,000 + $10,000 + $8,000 + $7,000 =
			= $30,000

Weight of Stock A = $5,000 / $30,000 = 1/6
Weight of Stock B = $10,000 / $30,000 = 1/3
Weight of Stock C = $8,000 / $30,000 = 4/15
Weight of Stock D = $7,000 / $30,000 = 7/30

The beta of a portfolio is the weighted average of the betas of its
individual securities, then:
Beta = (1/6)(0.75) + (1/3)(1.1) + (4/15)(1.36) + (7/30)(1.88) =     
     = 1.293


Now we can determine the expected rate of return of the portfolio;
according to the CAPM we have that:
E = rf + Beta * [E_m ? rf]

where
E = the expected return on the portfolio
rf = the risk-free rate
E_m = the expected return on the market portfolio

In this problem:			 
rf = 0.04
Beta_Port = 1.293
E_m = 0.15

Then:
E = 0.04 + 1.293*(0.15 ? 0.04) =
  = 0.1822

The expected rate of return on the portfolio is 18.22%.

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I hope that this helps you. As always, if you find something unclear
or incomplete do not hesitate to request for a clarification.

Regards.
livioflores-ga