Chapter 11 HW Problems
If your portfolio beta is calculated to be 0.89 and the stock market has a maximum expected loss of -2.5 percent on a daily basis, what is the maximum daily loss to your portfolio?
0.89(-2.5%) = -2.225%
Why might investors derive an inaccurate valuation of a firm when using the price-earnings method?
A second reason for different valuations when using the PE method is that investors disagree on the proper measure of earnings. Some investors prefer to us operating earnings, or exclude some unusually high expenses that result from one-time events. A third reason is that investors may disagree on the firms that should represent the industry norm. Some investors use a narrow industry composite composed of firms that are very similar (in terms of size, lines of business, etc.) to the firm being valued; other investors prefer a broad industry composite. Consequently, even if investors agree on a firm's forecasted earnings, they may still derive different values for that firm as a result of applying different PE ratios. Furthermore, even if investors agree on the firms to include, they may disagree on how to weight each firm.
Identify the factors that affect a stock portfolio's volatility and explain their effects.
A stock portfolio has more volatility when its individual stock volatilities are high, other factors held constant. In addition, a stock portfolio has more volatility when its individual stock returns are highly correlated, other factors held constant. A stock portfolio containing some stocks with low or negative correlation will exhibit less volatility because the stocks will not experience peaks and troughs simultaneously. Some offsetting effects will occur, smoothing the returns of the portfolio over time.
A share of common stock currently sells for $110. Current dividends are $8 per share, and are expected to grow at 6 percent per year indefinitely. What is the rate of return required by investors in the stock?
D1 = D0(1 + g) = $8.00(1 + 0.06) = $8.48 k = (D1/PV of stock) + g = (8.48/110) + 0.06 = 0.137 = 13.7%
Suppose you know that a company just paid a dividend of $1.75 per share on its stock and that the dividend will continue to grow at a rate of 8 percent per year. If the required return on this stock is 10 percent, what is the current share price?
D1 = D0(1 + g) = 1.75(1 + 0.08) = 1.89 PV of stock = D1/(k - g) = 1.89/(0.10 - 0.08) = $94.5 per share
Assume Mess stock has a beta of 1.2. If the risk-free rate is 7 percent, and the market return is 10 percent, what is the expected return on Mess stock?
Expected return = 7% + 1.2(10% - 7%) = 10.6%
Impact of Interest Rates.
Given a choice of risk-free Treasury securities or stocks, stocks should be purchased only if they are appropriately priced to reflect a sufficiently high expected return above the risk-free rate.
Explain the meaning and use of implied volatility.
Investors can derive the stock's implied standard deviation (ISD) from the stock option pricing model. The premium on a call option for a stock is dependent on factors such as the relationship between the current stock price and the exercise (strike) price of the option, the number of days until the expiration date of the option, and the anticipated volatility of the stock price movements. There is a formula for estimating the call option premium based on various factors. The actual values of these factors are known, except for the anticipated volatility. However, by plugging in the actual option premium paid by investors for that specific stock, it is possible to derive the anticipated volatility level. Participants may use this measurement as their own forecast of that specific stock's volatility.
Price-Earnings Model. Explain the use of the price-earnings (PE) ratio for valuing a stock.
Investors can value a stock by applying the industry PE ratio to the firm's expected earnings for the next year. This method implicitly assumes that the growth in earnings in future years will be similar to that of the industry.
Suppose that you are interested in buying the stock of a company that has a policy of paying a $6 per share dividend every year. Assuming no changes in the firm's policies, what is the value of a share of stock if the required rate of return is 11 percent?
PV of stock = D/k = 6/0.11 = $54.5 per share
Micro, Inc. will pay a dividend of $2.30 per share next year. If the company plans to increase its dividend by 9 percent per year indefinitely, and you require a 12 percent return on your investment, what should you pay for the company's stock?
PV of stock = D1/(k - g) = 2.3/(0.12 - 0.09) = $76.67 per share
The next expected dividend for Sun, Inc., will be $1.20 per share and analysts expect the dividend to grow at a rate of 7 percent indefinitely. If Sun stock currently sells for $22 per share, what is the required rate of return?
PV of stock = D1/(k - g) k = (D1/PV of stock) + g k = (1.20/22) + 0.07 = 0.1245 = 12.45%
12. Measuring the Portfolio Beta. Assume the following information: Beta of IBM = 1.31 Beta of LUV = 0.85 Beta of ODP = 0.94 If you invest 40 percent of your money in IBM, 30 percent in LUV and 30 percent in ODP, what is your portfolio's beta? PART 2: Using the information from above, suppose that you instead decide to invest $20,000 in IBM, $30,000 in LUV and $50,000 in ODP. What is the beta of your portfolio now?
Portfolio Beta = 0.4(1.31) + 0.3(0.85) + 0.3(0.94) = 0.524 + 0.255 + 0.282 = 1.061 PART 2: Portfolio Beta = [(20 x 1.31) + (30 x 0.85) + (50 x 0.94)]/100 = (26.2 + 25.5 + 47)/100 = 0.987
Suppose you bought a stock at the beginning of the year for $76.50. During the year, the stock paid a dividend of $0.70 per share and had an ending share price of $99.25. What is the total percentage return from investing in that stock over the year?
R = ((SP - INV)+D) /INV = ((99.25 - 76.5) + .7)/76.5 = 30.6%
You are considering investing in a stock that has an expected return of 13 percent. If the risk-free rate is 5 percent and the market risk premium is 7 percent, what must the beta of this stock be?
Rj = Rf + Bj(Rm - Rf ) 0.13 = 0.05 + Bj (0.07) Bj = 1.142
A stock has a beta of 2.2, the risk-free rate is 6 percent, and the expected return on the market is 12 percent. Using the CAPM, what would you expect the required rate of return on this stock to be? What is the market risk premium?
Rj = Rf + Bj(Rm - Rf ) Rj = 6% + 2.2(12% - 6%) Rj = 19.2% The market risk premium is 6 percent.
1. Risk-Adjusted Return Measurements. Assume the following information over a five-year period. • Average risk-free rate = 6% • Average return for Crane stock = 11% • Average return for Load stock = 14% • Standard deviation stock returns = 2% • Standard deviation of Load stock returns = 4% • Beta of Crane stock = 0.8 • Beta of Load stock = 1.1 Determine which stock has higher risk-adjusted returns according to the Sharpe Index. Which stock has higher risk-adjusted returns according to the Treynor Index?
Sharpe Index = (R-Rf)/std dev Treynor Index = (R-Rf)/B Sharpe Index of Crane Stock: = (11%-6%)/2% = 2.5 Sharpe Index of Load Stock: = (11%-6%)/.8 = .0625 Treynor Index of Crane Stock: = (11%-6%)/.8 = .0625 Treynor Index of Load Stock: = (14%-6%)/1.1 = .0727 *Crane stock has a higher sharpe inxex while load stock has a higher treynor index
What are the risks of investing in stocks in emerging markets?
Stocks in emerging markets are more exposed to major government turnover and other forms of political risk. They also expose U.S. investors to a high degree of exchange rate risk because their local currencies are typically very volatile.
Explain how to estimate the beta of a stock. Explain why beta serves as a measure of the stock's risk.
The beta of a stock can be estimated by obtaining returns of the firm and the stock market over the last 12 quarters and applying regression analysis to derive the slope coefficient as in this model: Rjt= B0+ B1Rmt+ ut Where: Rjt = return of stock j in time t Rm = market return B0 = intercept B1 = regression coefficient that serves as an estimate of beta ut = error term Some investors or analysts prefer to use monthly returns rather than quarterly returns to estimate the beta. The choice is dependent on the holding period for which one wants to assess sensitivity. If the goal is to assess sensitivity to monthly returns, then monthly data would be more appropriate. The regression analysis estimates the intercept (B0) and the slope coefficient (B1), which serves as the estimate of beta. Beta serves as a measure of the stock's risk because it measures sensitivity to the market. The higher the sensitivity, the more likely that the stock will perform poorly under adverse market conditions.
Explain how the value of the dollar affects stock valuations.
The changing value of the dollar can also affect stock prices by affecting expectations of economic factors that influence the firm's performance. For example, if a weak dollar stimulates the U.S. economy, it may enhance the value of a U.S. firm whose sales are dependent on the U.S. economy. A strong dollar could adversely affect such a firm if it dampens U.S. economic growth. Because inflation affects some firms, a weak dollar value could indirectly affect a firm's stock by putting upward pressure on inflation. A strong dollar would have the opposite indirect impact
What are some limitations of the dividend discount model?
The dividend discount model may result in an inaccurate valuation of a firm because of potential errors in determining the dividend to be paid over the next year, or the growth rate, or the required rate of return by investors. The limitations of this model are more pronounced when valuing firms that retain most of their earnings rather than distribute them as dividends, because the model relies on the dividend as the base for applying the growth rate. For example, many Internet-related stocks retain any earnings to support growth and thus are not expected to pay any dividends.
Describe the dividend discount valuation model.
The dividend discount valuation model measures the value of a firm as the present value of future expected dividends to be received by the investor. The model can account for uncertainty by allowing dividends to be revised in response to revised expectations about a firm's cash flows, or by allowing the required rate of return to be revised in response to changes in the required rate of return by investors.
Explain how economic growth affects the valuation of a stock.
The firm's value should reflect the present value of its future cash flows. Because earnings are a primary component of corporate cash flows, many investors use forecasted earnings to determine whether a firm's stock is over- or undervalued.
Determine how the maximum expected loss on a stock would be affected by an increase in the expected return of the stock, based on a 95 percent confidence interval.
The maximum expected loss would now be less pronounced than before, because the expected outcome is higher and the deviation from that will result in a maximum loss that is not as bad.
How is the maximum expected loss on a stock affected by an increase in the volatility (standard deviation), based on a 95 percent confidence interval?
The maximum expected loss would now be more pronounced (worse) than before, because the larger standard deviation creates a greater deviation from (below) the expected outcome.
When computing the price of a stock using the constant-growth dividend discount model, determine how the price of a stock would be affected if the growth rate is reduced. Explain the logic of this relationship.
The price of the stock is reduced, because the expected future cash flows in distant periods are reduced if the growth rate is revised downward.
How are the interest rate, the required rate of return on a stock, and the valuation of a stock related?
The relation between interest rates and stock prices is not constant over time. However, most of the largest stock market declines have occurred in periods when interest rates increased substantially. Furthermore, the stock market's rise in the late 1990s is partially attributed to the low interest rates during that period, which encouraged investors to shift from debt securities (with low rates) to equity securities.
When using the CAPM, how would the required rate of return on a stock be affected if the beta were higher.
The required rate of return would be higher, because a given premium above the risk-free rate would now be higher.
When using the CAPM, how would the required rate of return on a stock be affected if the risk- free rate were lower.
The required rate of return would be lower, because it should reflect a premium above the risk-free rate (which is now lower).
When using the CAPM, how would the required rate of return on a stock be affected if the market return were lower.
The required rate of return would be lower, because the premium that is added to the risk-free rate would now be lower.
Describe the value-at-risk method for measuring risk.
The value at risk is also commonly used to measure the risk of a portfolio. Some stocks may be perceived to have high risk when assessed individually, but low risk when assessed as part of a portfolio. This is because the likelihood of a large loss in the portfolio is influenced by the probabilities of simultaneous losses in all of the component stocks for the period of concern.
Impact of Exchange Rates.
The value of the dollar can affect U.S. stock prices for a variety of reasons. First, foreign investors tend to purchase U.S. stocks when the dollar is weak and sell them when it is near its peak. Thus, the foreign demand for any given U.S. stock may be higher when the dollar is expected to strengthen, other things being equal. Also, stock prices are affected by the impact of the dollar's changing value on cash flows. Stock prices of U.S. firms primarily involved in exporting could be favorably affected by a weak dollar and adversely affected by a strong dollar. U.S. importing firms could be affected in the opposite manner. Stock prices of U.S. companies may also be affected by exchange rates if stock market participants measure performance by reported earnings. A multinational corporation's consolidated reported earnings will be affected by exchange rate fluctuations even if the company's cash flows are not affected. A weaker dollar tends to inflate the reported earnings of a U.S.-based company's foreign subsidiaries. Some analysts argue that any effect of exchange rate movements on financial statements is irrelevant unless cash flows are also affected.
Explain the difference between weak-form, semistrong-form, and strong-form efficiency
The weak form suggests that security prices reflect recent price movements and trading information. The semistrong form suggests that security prices reflect all publicly traded information. The strong form suggests that security prices reflect public and private information.
Why might investors derive different valuations for a stock when using the price-earnings method?
This method has several variations, which can result in different valuations. For example, investors may use different forecasts for the firm's earnings or the mean industry earnings over the next year. The previous year's earnings are often used as a base for forecasting future earnings, but the recent year's earnings do not always provide an accurate forecast of the future.
You found that Verto Stock is expected to generate earnings of $4.38 per share this year, and that the mean PE ratio for its industry is 27.195. Use the PE valuation method to determine the value of Verto shares.
Value = (Expected earnings of IBM per share) × (Mean industry P/E ratio) Value = $4.38 X 27.195 Value = $119.114
Value at Risk.
Value at risk is a risk measurement that estimates the largest expected loss to a particular investment position for a specified confidence level. It is intended to warn investors about the potential maximum loss that could occur. If the investors are uncomfortable with the potential loss that could occur in a day or a week, they can revise their investment portfolio to make it less risky.
Which of these forms of efficiency is most difficult to test? Which is most likely to be refuted? Explain how to test weak-form efficiency in the stock market.
Weak-form efficiency can be tested by searching for a nonrandom pattern in stock prices. If future price movements can be predicted by assessing the past movements, a market inefficiency is detected.
Assume that Quitar Co. has a beta of 1.31. a. If you assume that the stock market has a maximum expected loss of -3.2 percent on a daily basis (based on a 95 percent confidence level), what is the maximum daily loss for the Quitar Co. stock? b. If you have $19,000 invested in Quitar Co. stock, what is your maximum daily dollar loss?
a. 1.31(-3.2%) = -4.192% b. (-4.192%)(19,000) = -$796.48
When computing the price of the stock with the dividend discount model, how would the price of a stock be affected if the required rate of return is increased. Explain the logic of this relationship.
the price of the stock is reduced, because the cash flows would be discounted at a higher rate.