Suppose we had the following investments:

Question

Beta	Expected Return	Amount Invested	Security
.80	8%	$1,000	Stock A
.95	12	2,000	Stock B
1.10	15	3,000	Stock C
1.40	18	4,000	Stock D

What is the expected return on this portfolio? What is the beta of this portfolio? Does this portfolio have more or less systematic risk than an average asset?

Accepted Answer

To answer, we first have to calculate the portfolio weights. Notice that the total amount invested is $10,000. Of this, $1,000/10,000 =10% is invested in Stock A.
Similarly, 20 percent is invested in Stock B, 30 percent is invested in Stock C, and 40 percent is invested in Stock D. The expected return, [latex]E(R_{P}) [/latex], is thus:

[latex]E(R_{P} )=.10×E(R_{A})+.20×E(R_{B} )+.30×E(R_{C} )+.40 ×E(R_{D}) [/latex]

=.10×8%+.20×12%+.30×15%+ .40×18%

=14.9%

Similarly, the portfolio beta, [latex]β_{P} [/latex], is:

[latex]β_{P}=.10×β_{A}+.20×β_{B}+.30×β_{C}+.40×β_{D} [/latex]

=.10×.80+.20×.95+.30×1.10+.40×1.40

=1.16

This portfolio thus has an expected return of 14.9 percent and a beta of 1.16. Because the beta is larger than 1, this portfolio has greater systematic risk than an average asset.

Question 13.6: Suppose we had the following investments:

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