A stock has a beta of 1.26 and an expected return of 12.4 percent. A risk-free a

Question

A stock has a beta of 1.26 and an expected return of 12.4 percent. A risk-free asset currently earns 4.1 percent.

What is the expected return on a portfolio that is equally invested in the two assets? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

If a portfolio of the two assets has a beta of 0.86, what are the portfolio weights? (Do not round intermediate calculations. Round your answers to 4 decimal places (e.g., 32.1616).)

If a portfolio of the two assets has an expected return of 11.6 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

If a portfolio of the two assets has a beta of 2.46, what are the portfolio weights? (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 4 decimal places (e.g., 32.1616).)

A stock has a beta of 1.26 and an expected return of 12.4 percent. A risk-free asset currently earns 4.1 percent.

Explanation / Answer

A portfolio has two type of securities. Stock and risk free securities.

Expected Return of stock = 12.4%

Beta of stock = 1.26

Return of risk free securities = 4.1%

a.

Expected return of on a portfolio that is equally invested in the two assets is calculated below:

Expected return of on a portfolio = 50% × 12.4% + 50% × 4.1%

                                                      = 6.2% +2.05%

                                                      = 8.25%

Hence, Expected return of on a portfolio that is equally invested in the two assets is 8.25%.

b.

Beta of the portfolio is 0.86 then weight of securities in portfolio is calculated below:

0.86 = X% × 1.26 + (100% - X %) ×0

X = 68.25%

Hence, Weight of stock in portfolio is 68.25. Then weight of risk free securities in portfolio is 31.75%.

c.

Expected return of portfolio is 11.6%. Then weight of securities in portfolio is calculated below:

11.6% = X% × 12.4% + (100% -X %) × 4.1%

11.6% = X % × 8.3% + 4.1%

X = 90.36%

That is weight of stock on portfolio is 90.36%. Then weight of risk free security in portfolio is 9.64%.

d.

Beta of the portfolio is 2.40 then weight of securities in portfolio is calculated below:

2.46 = X% × 1.26 + (100% - X %) ×0

X = 195.23%

Weight of stock in portfolio cannot be more than 100%. SO beta of 2.40 is not possible for portfolio of two assets.

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