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Finance questions: Calculate expected return on a portfolio, the weight of a stock, beta and more.

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A stock has a beta of 1.05 and an expected return of 19 percent. A risk-free asset currently earns 5.7 percent.

a. The expected return on a portfolio that is equally invested in the two assets is _______%. (Input answer as a percent rounded to 2 decimal places, without the percent sign.)

b. If a portfolio of the two assets has a beta of 0.75, the weight of the stock is _________% and the weight of the risk-free is _________% (Input answers as a percent rounded to 4 decimal places, without the percent sign).

c. If a portfolio of the two assets has an expected return of 7 percent, its beta is _________. (Round answer to 6 decimal places.)

d. If a portfolio of the two assets has a beta of 2.35, the weight of the stock is _________% and the weight of the risk-free is ________% (Input answers as a percent rounded to 2 decimal places, without the percent sign).

How do you interpret the weights for the two assets in this case? Explain

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Solution Preview

Before answering these questions, we need to know how to find the beta and the returns of a portfolio given the weights, betas and returns of its components. These are the formulas for the case of a two-security portfolio (in your case, there are two securities: the stock and the risk-free asset)

Beta of a portfolio = w1*B1 + w2*B2

where w1 and w2 are the weights in the portfolio of securities 1 and 2 respectively; and B1 and B2 are the betas of securities 1 and 2. Furthermore, since the sum of the weights of the securities must be equal to 1 (w1+w2=1), we can rewrite the above equation as:

Beta of a portfolio = w1*B1 + (1-w1)*B2

The expected return of a portfolio as a function of the weights and returns of tis components has a very similar formula:

Exp. return of portfolio = w1*R1 + (1-w1)*R2

where R1 and R2 are the expected returns ...

Solution Summary

The solution calculates expected return on a portfolio, weight of stock and beta.

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Can you please assist me with these questions -

1. Stock Betas - A stock has an expected return of 12.5%, the risk-free rate is 5%, and the market risk premium is 6%. What must the beta of this stock be?

8. Expected Returns - A stock has a beta of .7, the expected return on the market is 15%, and the risk-free rate is 6.5%. What must the expected return on this stock be?

10. Portfolio Weights A stock has a beta of .9 and expected return of 12%. A risk-free asset currently earns 6%.
a. What is the expected return on a portfolio that is equally invested in the two assets?
b. If a portfolio of the two assets has a beat of .5, what are the portfolio weights?
c. If a portfolio of the two assets has an expected return of 11%, what is its beta?
d. If a portfolio of the two assets has a beta of 1.80, what are the portfolio weights? How do you interpret the weights for the two assets in this case?

12. Relative Valuation - Stock Y has a beta of 1.45 and an expected return of 17%. Stock Z has a beta of .85 and an expected return of 12%. If the risk-free rate is 6% and the market risk premium is 7.5%, are these stocks correctly priced?

18. Analyzing a Portfolio - You have $100,000 to invest in a portfolio containing Stock X, Stock Y, and a risk-free asset. You must invest all of your money. Your goal is to create a portfolio that has an expected return of 16.5% and that has only 70% of the risk of the overall market. If X has an expected return of 28% and a beta of 1.7, Y has an expected return of 14% and a beta of 1.1, and the risk free rate is 7%, how much money will you invest in Stock Y? How do you interpret your answer?

21. CAPM - John Wilson, a portfolio manager, is evaluating the expected performance of two common stocks, Furhman Labs, Inc., and Garten Testing, Inc. The risk-free rate is 5%, the expected return on the market is 11.5%, and the betas of the two stocks are 1.5 and .8, respectively. Wilson's own forecasts of the returns on the two stocks are 13.25% for Furhman Labs and 11.25% for Garten. Calculate the required return for each stock. Is each stock undervalued, fairly valued, or overvalued?

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