Suppose we had the following investments: Security Amount Invested Expected Return Beta Stock A $1,000 8% .80 Stock B 2.000 12 .95 Stock C 3.000 15 1.10 Stock D 4.000 18 1.40 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?

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: [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, β[latex]_{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 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: What is the expect...

Fundamentals of Corporate Finance

Suppose we had the following investments:

Security	Amount Invested	Expected Return	Beta
Stock A	$1,000	8%	.80
Stock B	2.000	12	.95
Stock C	3.000	15	1.10
Stock D	4.000	18	1.40

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?

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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, $E(R_{P}),$ is:

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

= .10 × 8% + .20 × 12% + .30 × 15% + .40 × 18%

= 14.9%

Similarly, the portfolio beta, β $_{P}$ , is:

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

= .10 × .80 + .20 × .95 + .30 × 1.10 + .40 × 1.40

= 1.16

This portfolio 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.