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Portfolio risk and risk of constituent stocks

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You own a portfolio of two stocks (X and Y), with 40% of the portfolio invested in Stock X. You have observed over many years that the variance of your portfolio value is 0.0144 and that the correlation between the stock X and stock Y is 0.7. If the standard deviation of Stock X is 0.20, what is the standard deviation of the stock Y?

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Portfolio variance = (Weight of Stock X in portfolio*standard deviation of stock X in portfolio)^2+(Weight of Stock Y in ...

Solution Summary

Illustrates how to calculate the standard deviation of a stock given the standard deviation for the portfolio of two stocks and standard deviation of one stock.

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Valuation, Interest rates, Constant growth, Preferred stock value

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(5-2) "Short-term interest rates are more volatile than long-term interest rates, so short-term bond prices are more sensitive to interest rate changes than are long-term bond prices." Is this statement true or false? Explain.

(5-3) The rate of return you would get if you bought a bond and held it to its maturity date is called the bond's yield to maturity. If interest rates in the economy rise after a bond has been issued, what will happen to the bond's price and to its YTM? Does the length of time to maturity affect the extent to which a giving change in interest rates will affect the bond's price?

(5-5) A sinking fund can be set up in one of two ways. Discuss the advantages and disadvantages of each procedure from the viewpoint of both the firm and its bondholders.


Bond Valuation with
Annual Payments
Jackson Corporation's bonds have 12 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 8%. The bonds have a yield to maturity of 9%. What is the current market price of these bonds?

Determinant of
Interest Rates
The real risk-free rate of interest is 4%. Inflation is expected to be 2% this year and 4% during the next 2 years. Assume that the maturity risk premium is zero. What is the yield on 2-years Treasure securities? What is the yield on 3-years Treasure securities?

(1) Discuss the value of foreign (non-United States) stocks in an investment portfolio. Do you want them? If so, which ones? Do you diversify the classes as you would domestic stock? If so, what classes would you select? Any countries you'd avoid? What about a stock index for foreign stocks...is this a good or bad idea?

(7-2) Two investors are evaluating General Electric's stock for possible purchase. They agree on the expected value of D1 and also on the expected future dividend growth rate. Further, they agree on the risk of the stock. However, one investor normally holds stocks for 2 years and the other normally holds stocks for 10 years. On the basis of the type of analysis done in this chapter, they should both be willing to pay the same price for General Electric's stock. True or false? Explain.

(7-3) A bond that pays interest forever and has no maturity date is a perpetual bond, also called a perpetuity or a consol. In what respect is a perpetual bond similar to (1) a no-growth common stock and (2) a share of preferred stock?

(7-4) People have argued that a stock's market price can deviate from its intrinsic value. Discuss the following question: If all investors attempt to behave in an entirely rational manner, could these differences still exist? In answering this question, think about information that's available to insiders versus outsiders, the fact that historical probabilities of financial events are "fuzzier" than probabilities related to physical items, and the validity of the concepts of animal spirits, herding, and anchoring.
Constant Growth
Boehm Incorporated is expected to pay a $1.50 per share dividend at the end of this year (i.e., D1 = $1.50). The dividend is expected to grow at a constant rate of 7% a year. The required rate of return on the stock, rs, is 15%. What is the value per share of Boehm's stock?

Preferred Stock
Nick's Enchiladas Incorporated has preferred stock outstanding that pays a dividend of $5 at the end of each year. The preferred sells for $50 a share. What is the stock's required rate of return?

Constant Growth
Rate, g
A stock is trading at $80 per share. The stock is expected to have a year-end dividend of $4 per share (D1 = $4), and it is expected to grow at some constant rate g through-out time. The stock's required rate of return is 14%. If markets are efficient, what is your forecast of g?


(1) From the reading you discovered that most firms rely on a mix of debt, preferred stock, and common equity. Since debt tends to be less risky to bondholders than equity is to stockholders, the cost of debt to the firm (r(d)) is lower than the cost of equity (r(s)). That said, since debt is less expensive than equity, briefly explain why firms tend not to rely upon all (100%) debt to fund their capital needs.

(9-2) How can the WACC be both an average cost and a marginal cost?

(9-3) How would each of the factors in the following table affect a firm's cost of debt, rd (1 - T); its cost of equity, rs; and its weighted average cost of capital, WACC? Indicate by a plus (+), a minus (-), or a zero (0) if the factor would raise, lower, or have an indeterminate effect on the item in question. Assume that all other factors are held constant. Justify your answer, but recognized that several of the parts probably have no single correct answer.

rd (1 - T) rs WACC
a. The corporate tax rate is lowered.
b. The Federal Reserved tightens credit.
c. The firm uses more debt.
d. The firm doubles the amount of capital
it raises during the year.
e. The firm expands into a risky new area.
f. investors become more risk averse.

(9-4) Distinguish between beta (or market) risk, within-firm (or corporate) risk, and stand-alone risk for a potential project. Of the three measures, which is theoretically the most relevant, and why?

(9-5) Suppose a firm estimates its overall cost of capital for the coming year to be 10 %. What might be reasonable cost of capital for average-risk, high risk, and low-risk projects?

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