The riskless interest rate is 1%. You hold a portfolio consisting of short-term

Question

The riskless interest rate is 1%. You hold a portfolio consisting of short-term safe assets and the market portfolio of risky assets, which has a mean return of 9% and a standard deviation of 20%. You are considering the stock of COMPANY X that you believe to have a beta of 1.2 with the market portfolio, and a standard deviation of return of 30%. What is the standard deviation of the idiosyncratic component of COMPANY X return (the residual in the market model regression)? What is the correlation of COMPANY X return with the market's return? If the CAPM holds, what must be the mean excess return on COMPANY X over the riskfree rate? What must be COMPANY X alpha? What must be its Sharpe ratio? Is the Sharpe ratio on COMPANY X higher or lower than the Sharpe ratio on the market? Explain, and generalize to other stocks. Suppose that COMPANY X stock has a higher alpha than the CAPM implies. Explain how to change its weight in your portfolio in such a way as to increase the mean return on your portfolio without changing its variance. (Do this in words, or write down a relevant equation if you can.) Now suppose COMPANY X has a lower alpha than the CAPM implies. How does your answer to part c) change?)

Explanation / Answer

a)

While computing the cost of equity, it is important for an analyst to calculate the beta of the company’s stock.

Beta of a publicly traded company can be calculated using the Market Model Regression (Slope).

Where,

ri is the stock’s return

represents the intercept

is the stock’s beta

rm is the market returns

Thus,

Now, substituting the formulae:

1%=+1.2*9

1%= +10.8%

= 10.8-1

=9.8%

Thus, the standard deviation of the component is 9.8%

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.