Valuing stocks and assesing risk ch.7 (uts)

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Chapter 11

Stock Valuation and Risk

Financial Markets and Institutions, 7e, Jeff MaduraCopyright ©2006 by South-Western, a division of Thomson Learning. All rights reserved.

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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

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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

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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

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Valuing A Stock Using the PE MethodA 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?

$2814$2

ratio) PEindustry (Meanshare) per firm of earnings Expected(share per Valuation

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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

1 )1(Price

tt

t

k

Dk

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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:

k

D

k

D

tt

t

1 )1(Price

gk

D

k

D

tt

t

1

1 )1(Price

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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?

14$%15

10.2$

)1(Price

1

k

D

k

D

tt

t

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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?

50.17$%3%15

10.2$

)1(Price 1

1

gk

D

k

D

tt

t

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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

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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

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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

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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?

26.11$)03.1(10$

)1( yearsn in earnings Forecasted4

nGE

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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?

82.78$726.11$

industry) of ratio (PE years)4 in Earnings( years4 in price Stock

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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?

29.54$

)13.1(

82.78$

)13.1(

2$

)13.1(

2$

)13.1(

2$

)13.1(

2$44321

PV

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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

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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:

)( fmjfj RRBRR

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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

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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?

%5.13

%)5%10(7.1%5

)(

fmjfj RRBRR

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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

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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:

m

iiiFBBRE

10)(

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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

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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

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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

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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

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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

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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

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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

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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

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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

INV

DINVSPR

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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

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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

ijjijijjiip CORRwwww 22222

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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:

tmtjt uRBBR 10

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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

iip BwB

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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

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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

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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

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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?

%55.1%)1(65.1%1.

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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?

%73.2%)1.2(3.1

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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

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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

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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

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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

fRR

index Sharpe

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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?

54.0%13

%8%15

index Sharpe

fRR

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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

B

RR findex Treynor

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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?

04.08.1

%8%15

index Treynor

B

RR f

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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

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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)

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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

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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

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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

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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

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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

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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