# Risk and Return

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A portfolio has 75 shares of Stock A that sell for $72 per share and 105 shares of Stock B that sell for $42 per share. The weight of A is and the weight of B is .

ou own a portfolio that has $1,700 invested in Stock A and $1,400 invested in Stock B. If the expected returns on these stocks are 8 percent and 10 percent, respectively, the expected return on the portfolio is percent.

You own a portfolio that is 54 percent invested in Stock X, 32 percent in Stock Y, and 14 percent in Stock Z. The expected returns on these three stocks are 14 percent, 17 percent, and 11 percent, respectively. The expected return on the portfolio is percent

Based on the following information, calculate the expected return. (Input answer as a percent rounded to 2 decimal places, without the percent sign.)

State of Economy Probability of State of Economy Rate of Return

if State Occurs

Recession 0.45 -0.08

Boom 0.55 0.24

________________________________________

The expected return is percent.

You own a stock portfolio invested 10 percent in Stock Q, 10 percent in Stock R, 5 percent in Stock S, and 75 percent in Stock T. The betas for these four stocks are 1.52, 1.72, 0.62, and 1.64, respectively. The portfolio beta is

You own a portfolio equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 1.1 and the total portfolio is equally as risky as the market, the beta for the other stock in your portfolio is .

A stock has a beta of 0.95, the expected return on the market is 13 percent, and the risk-free rate is 7.15 percent. The expected return on this stock must be percent.

A stock has an expected return of 19 percent, the risk-free rate is 7.6 percent, and the market risk premium is 13 percent. The beta of this stock must be .

A stock has an expected return of 10 percent, its beta is 1.85, and the risk-free rate is 4.5 percent. The expected return on the market must be percent

A stock has an expected return of 9 percent and a beta of 0.85, and the expected return on the market is 10 percent. The risk-free rate must be percent.

You own a portfolio equally invested in a risk-free asset and two stocks.

Required:

If one of the stocks has a beta of 1 and the total portfolio is equally as risky as the market, what must the beta be for the other stock in your portfolio?

2.40

2.00

1.60

2.20

1.00

Using CAPM

A stock has an expected return of 13 percent, a beta of 1.25, and the expected return on the market is 11 percent.

Required:

What must the risk-free rate be?

2.40%

3.00%

94.55%

3.30%

3.60%

Consider the following information:

Rate of Return If State Occurs

State of Economy Probability of State of Economy Stock A Stock B Stock C

Boom 0.74 0.31 0.05 0.19

Bust 0.26 0.07 0.17 0.11

________________________________________

Required:

(a) What is the expected return on an equally weighted portfolio of these three stocks?

17.43%

15.00%

19.92%

18.26%

16.60%

(b) What is the variance of a portfolio invested 20 percent each in A and B and 60 percent in C?

0.00100

0.00850

0.00550

0.00600

0.00350

Returns and Standard Deviations

Consider the following information:

Rate of Return If State Occurs

State of Economy Probability of State of Economy Stock A Stock B Stock C

Boom 0.15 0.25 0.45 0.35

Good 0.25 0.14 0.23 0.12

Poor 0.25 0.09 0.18 0.07

Bust 0.35 0.01 0.08 0.04

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Requirement 1:

Your portfolio is invested 12 percent each in A and C and 76 percent in B. What is the expected return of the portfolio?

17.60%

19.36%

21.07%

14.08%

21.12%

Requirement 2:

(a) What is the variance of this portfolio?

0.02050

0.01300

0.01550

0.01800

0.00433

(b) The standard deviation of this portfolio?

14.32%

12.45%

6.58%

13.42%

11.40%

Based on the following information:

State of Economy Probability of State of Economy Rate of Return If State Occurs

Recession 0.10 -0.07

Normal 0.35 0.19

Boom 0.55 0.21

________________________________________

Required:

What is the expected return?

16.63%

17.50%

19.25%

11.00%

18.38%

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#### Solution Summary

The solution explains some questions relating to beta, CAPM, risk free rate, variance and standard deviation