1. Stock Valuation and Risk
Chapter 11
Stock Valuation and Risk
Financial Markets and Institutions, 7e, Jeff Madura
Copyright ©2006 by South-Western, a division of Thomson Learning. All rights reserved.

2. Chapter Outline Stock valuation methods
Determining the required rate of return to value stocks
Factors that affect stock prices
Role of analysts in valuing stocks
Stock risk
Applying value at risk
Forecasting stock price volatility and beta
Stock performance measurement
Stock market efficiency
Foreign stock valuation, performance, and efficiency

3. Stock Valuation Methods
The price-earnings (PE) method assigns the mean PE ratio based on expected earnings of all traded competitors to the firm’s expected earnings for the next year
Assumes future earnings are an important determinant of a firm’s value
Assumes that the growth in earnings in future years will be similar to that of the industry

4. Stock Valuation Methods (cont’d)
Price-earnings (PE) method (cont’d)
Reasons for different valuations
Investors may use different forecasts for the firm’s earnings or the mean industry earnings
Investors disagree on the proper measure of earnings
Limitations of the PE method
May result in inaccurate valuation for a firm if errors are made in forecasting future earnings or in choosing the industry composite
Some question whether an investor should trust a PE ratio

5. Valuing A Stock Using the PE Method
A firm is expected to generate earnings of $2 per share next year. The mean ratio of share price to expected earnings of competitors in the same industry is 14. What is the valuation of the firm’s shares according to the PE method?

6. Stock Valuation Methods (cont’d)
Dividend discount model
John Williams (1931) stated that the price of a stock should reflect the present value of the stock’s future dividends:
D can be revised in response to uncertainty about the firm’s cash flows
k can be revised in response to changes in the required rate of return by investors

7. Stock Valuation Methods (cont’d)
Dividend discount model (cont’d)
For a constant dividend, the cash flow is a perpetuity:
For a constantly growing dividend, the cash flow is a growing perpetuity:

8. Valuing A Stock Using the Dividend Discount Model
Example 1: A firm is expected to pay a dividend of $2.10 per share every year in the foreseeable future. Investors require a return of 15% on the firm’s stock. According to the dividend discount model, what is a fair price for the firm’s stock?

9. Valuing A Stock Using the Dividend Discount Model
Example 2: A firm is expected to pay a dividend of $2.10 per share in one year. In every subsequent year, the dividend is expected to grow by 3 percent annually. Investors require a return of 15% on the firm’s stock. According to the dividend discount model, what is a fair price for the firm’s stock?

10. Stock Valuation Methods (cont’d)
Dividend discount model (cont’d)
Relationship between dividend discount model and PE ratio
The PE multiple is influenced by the required rate of return and the expected growth rate of competitors
The inverse relationship between required rate of return and value exists in both models
The positive relationship between a firm’s growth rate and its value exists in both models

11. Stock Valuation Methods (cont’d)
Dividend discount model (cont’d)
Limitations of the dividend discount model
Errors can be made in determining the:
Dividend to be paid
Growth rate
Required rate of return
Errors are more pronounced for firms that retain most of their earnings

12. Stock Valuation Methods (cont’d)
Adjusting the dividend discount model
The value of the stock is:
The PV of the future dividends over the investment horizon
The PV of the forecasted price at which the stock will be sold
Must estimate the firm’s EPS in the year they plan to sell the stock by applying an annual growth rate to the prevailing EPS

13. Using the Adjusted Dividend Discount Model
Parker Corp. currently has earnings of $10 per share. Investors expect that the EPS will growth by 3 percent per year and expect to sell the stock in four years. What is the EPS in four years?

14. Using the Adjusted Dividend Discount Model (cont’d)
Other firms in Parker’s industry have a mean PE ratio of 7. What is the estimated stock price in four years?

15. Using the Adjusted Dividend Discount Model (cont’d)
Parker is expected to pay a dividend of $2 per share over the next four years. Investors require a return of 13% on their investment. Based on this information, what is a fair value of the stock according to the adjusted dividend discount model?

16. Stock Valuation Methods (cont’d)
Adjusting the dividend discount model (cont’d)
Limitations of the adjusted dividend discount model
Errors can be made in deriving the PV of dividends over the investment horizon or the forecasted price at which the stock can be sold
Errors can be made if an improper required rate of return is used

17. Determining the Required Rate of Return to Value Stocks
The capital asset pricing model:
Assumes that the only important risk is systematic risk
Is not concerned with unsystematic risk
Suggests that the return on an asset is influenced by the prevailing risk-free rate, the market return, and the covariance between a stock’s return and the market’s return:

18. Determining the Required Rate of Return to Value Stocks (cont’d)
The capital asset pricing model (cont’d)
Estimating the risk-free rate and the market risk premium
The yield on newly issued T-bonds is commonly used as a proxy for the risk-free rate
The terms within the parentheses measure the market risk premium
Historical data over 30 or more years can be used to determine the average market risk premium over time
Estimating the firm’s beta
Beta reflects the sensitivity of the stock’s return to the market’s overall return
Beta is typically measured with monthly or quarterly data over the last four years or so

19. Using the CAPM
Fantasia Corp. has a beta of 1.7. The prevailing risk-free rate is 5% and the market risk premium is 5%. What is the required rate of return of Fantasia Corp. according to the CAPM?

20. Determining the Required Rate of Return to Value Stocks (cont’d)
The capital asset pricing model (cont’d)
Limitations of the CAPM
A study by Fama and French found that beta is unrelated to the return on stock over the 1963–1990 period
Chan and Lakonishok:
Found that the relation between stock returns and beta varied with the time period used
Concluded that it is appropriate to question whether beta is the driving force behind stock returns
Found that firms with the highest betas performed much worse than firms with low betas
Found that high-beta firms outperformed low-beta firms during market upswings

21. Determining the Required Rate of Return to Value Stocks (cont’d)
Arbitrage pricing model
Suggests that a stock’s price can be influenced by a set of factors in addition to the market
e.g., economic growth, inflation
In equilibrium, expected returns on assets are linearly related to the covariance between assets returns and the factors:

22. Factors That Affect Stock Prices
Economic factors
Impact of economic growth
An increase in economic growth increases expected cash flows and value
Indicators such as employment, GDP, retail sales, and personal income are monitored by market participants
Impact of interest rates
Given a choice of risk-free Treasury securities or stocks, stocks should only be purchased if they offer a sufficiently high expected return

23. Factors That Affect Stock Prices (cont’d)
Economic factors (cont’d)
Impact of the dollar’s exchange rate value
The value of the dollar affects U.S. stocks because:
Foreign investors purchase U.S. stocks when the dollar is weak
Stock prices are affected by the impact of the dollar’s changing value on cash flows
Some U.S. firms are involved in exporting
U.S.-based MNCs have some earnings in foreign currencies
Exchange rates may affect expectations of other economic factors

24. Factors That Affect Stock Prices (cont’d)
Market-related factors
Investor sentiment
In some periods, stock market performance is not highly correlated with existing economic conditions
Stocks can exhibit excessive volatility because their prices are partially driven by fads and fashions
A study by Roll found that only one-third of the variation in stocks returns can be explained by systematic economic forces
January effect
Many portfolio managers invest in riskier small stocks at the beginning of the year and shift to larger companies near the end of the year
Places upward pressure on small stocks in January

25. Factors That Affect Stock Prices (cont’d)
Firm-specific factors
Some firms are more exposed to conditions within their own industry than to general economic conditions, so participants monitor:
Industry sales forecasts
Entry into the industry by new competitors
Price movements of the industry’s products
Market participants focus on announcements that signal information about a firm’s sales growth, earnings, or characteristics that cause a revision in the expected cash flows

26. Factors That Affect Stock Prices (cont’d)
Firm-specific factors (cont’d)
Dividend policy changes
An increase in dividends may reflect the firm’s expectation that it can more easily afford to pay dividends
Earnings surprises
When a firm’s announced earnings are higher than expected, investors may raise their estimates of the firm’s future cash flows
Acquisitions and divestitures
Expected acquisitions typically result in an increased demand for the target’s stock and raise the stock price
The effect on the acquiring firm is less clear
Expectations
Investors attempt to anticipate new policies so they can make their move before other investors

27. Factors That Affect Stock Prices (cont’d)
Integration of factors affecting stock prices
Whenever economic indicators signal the expectation of higher interest rates, there is upward pressure on the required rate of return
Firms’ expected future cash flows are influenced by economic conditions, industry conditions, and firm-specific conditions

28. Role of Analysts in Valuing Stocks
Many investors rely on opinions of stock analysts employed by securities firms or other financial firms
Many analysts are assigned to specific stocks and issue ratings that can indicate whether investors should buy or sell the stock
A 2001 study by Thomson Financial determined that analysts at the largest brokerage firms typically recommended “sell” for less than 1 percent of all the stocks for which they provided ratings

29. Role of Analysts in Valuing Stocks (cont’d)
Conflicts of interest
Many analysts are employed by securities firms that have other investment banking relationships with rated firms
Some analysts may own the stock of some of the firms they rate
Impact of disclosure regulations
In October 2000, the SEC enacted Regulation FD, which requires firms to disclose any significant information simultaneously to all market participants
Unbiased analyst rating services
Popular rating services include Morningstar, Value Line, and Investor’s Business Daily
Analyst rating services typically charge subscribers between $100 and $600 per year

30. Stock Risk
Risk reflects the uncertainty about future returns such that the actual return may be less than expected
The holding period return is measured as:
The main source of uncertainty is the price at which the stock can be sold
Dividends tend to be much more stable than stock price

31. Stock Risk (cont’d) Measures of risk The volatility of a stock:
May indicate the degree of uncertainty surrounding the stock’s future returns
Reflects total risk because it reflects movements in stock prices for any reason

32. Stock Risk (cont’d) Measures of risk (cont’d)
The volatility of a stock portfolio depends on:
The volatility of the individual stocks in the portfolio
The correlations between returns of the stocks in the portfolio
The proportion of total funds invested in each stock
A portfolio containing some stocks with low or negative correlation will exhibit less volatility

33. Stock Risk (cont’d) Measures of risk (cont’d) The beta of a stock:
Measures the sensitivity of its returns to market returns
Is used by many investors who have a diversified portfolio of stocks
Can be estimated by obtaining returns of the firm and the stock market and applying regression analysis to derive the slope coefficient:

34. Stock Risk (cont’d) Measures of risk (cont’d)
The beta of a stock portfolio:
Is useful for investors holding more than one stock
Can be measured as a weighted average of the betas of stocks in the portfolio, with the weights reflecting the proportion of funds invested in each stock:
The risk of a high-beta portfolio can be reduced by replacing some of the high-beta stocks with low-beta stocks

35. Stock Risk (cont’d) Measures of risk (cont’d) Value at risk:
Is a risk measurement the estimates the largest expected loss to a particular investment position for a specified confidence level
Became very popular in the late 1990s after some mutual funds and pension funds experienced abrupt large losses
Is intended to warn investors about the potential maximum loss that could occur
Focuses on the pessimistic portion of the probability distribution of returns
Is commonly used to measure the risk of a portfolio

36. Applying Value at Risk
Methods of determining the maximum expected loss
Use of historical returns to derive the maximum expected loss
e.g., an investor may determine that out of the last 100 trading days, a stock experienced a decline of greater than 7 percent on 5 different days
The investor could infer a maximum daily loss of no more than 7 percent for that stock based on a 95 percent confidence level

37. Applying Value at Risk (cont’d)
Methods of determining the maximum expected loss (cont’d)
Use of standard deviation to derive the maximum expected loss
The standard deviation of daily returns over the previous period can be used and applied to derive boundaries for a specific confidence level
Use of beta to derive the maximum expected loss

38. Using the Standard Deviation to Derive the Maximum Expected Loss
The standard deviation of daily returns for a stock in a recent period is 1%. The 95% confidence level is desired for the maximum loss. The stock has an expected daily return of .1%. What is the lower boundary of expected returns?

39. Using Beta to Derive the Maximum Expected Loss
A stock’s beta over the last 100 days is 1.3. The stock market is expected to perform no worse than –2.1% on a daily basis based on a 95% confidence level. What is the maximum loss to the stock over a given day based on this information?

40. Applying Value at Risk (cont’d)
Deriving the maximum dollar loss
The maximum percentage loss for a given confidence level can be applied to derive the maximum dollar loss of a particular investment
Value at risk is commonly applied to assess the maximum possible loss for an entire portfolio
Common adjustments to value at risk applications
Investment horizon desired
Length of historical period used
Time-varying risk
Restructuring the investment portfolio

41. Forecasting Stock Price Volatility and Beta
Methods of forecasting stock price volatility
The historical method uses a historical period to derive a stock’s standard deviation of returns and uses that estimate as the forecast for the future
The time-series method uses volatility patterns in previous periods
Places more weight on the most recent data
Normally uses the weights and number of periods that were the most accurate in previous periods
The implied standard deviation derives the estimate from the stock option pricing model
Represents the anticipated volatility of the stock over a future period by investors trading the stock

42. Forecasting Stock Price Volatility and Beta (cont’d)
Forecasting a stock portfolio’s volatility
Portfolio volatility can be forecast by first deriving forecasts of individual volatility levels
Next, the correlation coefficient for each pair of stock in the portfolio is forecast by estimating the correlation in recent periods
Forecasting a stock portfolio’s beta
First forecast the betas of the individual stocks and then take a weighted average

43. Stock Performance Measurement
The Sharpe index is appropriate when total variability is thought to be the appropriate measure of risk:
The higher the stocks’ mean return relative to the mean risk-free rate and the lower the standard deviation, the higher the Sharpe index
Measures the excess return above the risk-free rate per period

44. Using the Sharpe Index
Patrick stock has an average return of 15% and an average standard deviation of 13%. The average risk-free rate is 8%. What is the Sharpe index for Patrick stock?

45. Stock Performance Measurement (cont’d)
The Treynor index is appropriate when beta is thought to be the most appropriate type of risk:
The higher the Treynor index, the higher the return relative to the risk-free rate, per unit of risk

46. Using the Treynor Index
Patrick stock has an average return of 15% and a beta of 1.8. The average risk-free rate is 8%. What is the Sharpe index for Patrick stock?

47. Stock Market Efficiency
Forms of efficiency
Weak-form efficiency suggests that security prices reflect all trade-related information
Semistrong-form efficiency suggests that security prices fully reflect all public information
Includes announcements by firms, economic news or events, and political news or events
If semistrong-form efficiency holds, weak-form efficiency holds as well
Strong-form efficiency suggests that security prices fully reflect all information, including private or insider information

48. Stock Market Efficiency (cont’d)
Tests of the efficient market hypothesis
Test of weak-form efficiency
Tested by searching for a nonrandom pattern in security prices
Studies have generally found that historical price changes are independent over time
There is some evidence that stocks:
Have performed better in January (January effect)
Have performed better on Fridays than on Mondays (weekend effect)
Have performed well on the trading days just before holidays (holiday effect)

49. Stock Market Efficiency (cont’d)
Tests of the efficient market hypothesis
Test of semistrong-form efficiency
Tested by assessing how security returns adjust to particular announcements
Generally, security prices immediately reflect the information from announcements
There is evidence of unusual profits from investing in IPOs
Test of strong-form efficiency
Difficult to test
There is evidence that share prices of target firms rise substantially when the acquisition is announced
Insiders are discouraged from using inside information because it is illegal

50. Foreign Stock Valuation, Performance, and Efficiency
Valuation of foreign stocks
PE method
The expected EPS of the foreign firm are multiplied by the appropriate PE ratio based on the firm’s risk and local industry
The PE ratio for a given industry may change continuously in some foreign markets
The PE ratio for a particular industry may need to be adjusted for the firm’s country
Dividend discount model
An adjustment for expected exchange rate movements is required
The value of foreign stocks from a U.S. perspective is subject to more uncertainty than the value of the stock from a local investor’s perspective

51. Foreign Stock Valuation, Performance, and Efficiency (cont’d)
Measuring performance from investing in foreign stocks
The performance measurement should control for general market movements and exchange rate movements in the region where the portfolio managers has been assigned to invest funds

52. Foreign Stock Valuation, Performance, and Efficiency (cont’d)
Performance from global diversification
Stock investors can benefit by diversifying internationally
Economies do not move in tandem
Stock markets across countries may respond to some of the same expectations
In general, correlations between stock indexes have been higher in recent years than they were several years ago

53. Foreign Stock Valuation, Performance, and Efficiency (cont’d)
Performance from global diversification (cont’d)
Integration of markets during the 1987 crash
There was a high correlation among country stock markets during the crash
This suggests that the underlying cause of the crash systematically affected all markets
Integration of markets during mini-crashes
On August 27, 1998 (“Bloody Thursday”) most stock markets around the world experienced losses
Illustrates that even a well-diversified international portfolio is not insulated from some events
Diversification among emerging stock markets
These markets have lower correlations with developed countries, but also higher risk

54. Foreign Stock Valuation, Performance, and Efficiency (cont’d)
International market efficiency
Some foreign markets are inefficient because of the small number of analysts and portfolio managers
Market inefficiencies are more common in small foreign stock markets
Insider trading is more prevalent in many foreign markets
Political and exchange rate risk may be high in some foreign markets