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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 OutlineStock valuation methodsDetermining the required rate of return to value stocksFactors that affect stock pricesRole of analysts in valuing stocksStock risk

Applying value at riskForecasting stock price volatility and beta

Stock performance measurementStock market efficiencyForeign stock valuation, performance, and efficiency

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Stock Valuation Methods

The price-earnings (PE) method assigns themean PE ratio based on expected earnings of

all traded competitors to the firm’s expectedearnings for the next year Assumes future earnings are an importantdeterminant of a firm’s value

Assumes that the growth in earnings in future yearswill 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 earningsor the mean industry earningsInvestors disagree on the proper measure of earnings

Limitations of the PE methodMay result in inaccurate valuation for a firm if errors aremade in forecasting future earnings or in choosing theindustry compositeSome question whether an investor should trust a PE ratio

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Valuing A Stock Using the PEMethod

A firm is expected to generate earnings of $2 pershare next year. The mean ratio of share priceto expected earnings of competitors in thesame industry is 14. What is the valuation ofthe firm’s shares according to the PE method?

$2814$2

ratio)PEindustry(Meanshare)per firmof earningsExpected(shareper Valuation

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Dividend discount modelJohn Williams (1931) stated that the price of a stockshould reflect the present value of the stock’s futuredividends:

D can be revised in response to uncertainty about thefirm’s cash flows k can be revised in response to changes in the requiredrate of return by investors

1 )1(Price

t t

t

k D

k

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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

t t

t

1 )1(Price

g k D

k D

t t

t 1

1 )1(Price

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Valuing A Stock Using the

Dividend Discount Model: A firm is expected to pay a dividend1Example

of $2.10 per share every year in theforeseeable future. Investors require a returnof 15 % on the firm’s stock. According to thedividend discount model, what is a fair price

for the firm’s stock? 14$

%1510.2$

)1(Price

1 k D

k D

t t

t

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Valuing A Stock Using the

Dividend Discount Model: A firm is expected to pay a dividend2Example

of $2.10 per share in one year. In everysubsequent year, the dividend is expected togrow by 3 percent annually. Investorsrequire 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 g k D

k D

t t

t

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Dividend discount model (cont’d) Relationship between dividend discount model

and PE ratioThe PE multiple is influenced by the required rate ofreturn and the expected growth rate of competitorsThe inverse relationship between required rate of returnand value exists in both models

The positive relationship between a firm’s growth rateand its value exists in both models

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Adjusting the dividend discount modelThe value of the stock is:

The PV of the future dividends over the investmenthorizonThe PV of the forecasted price at which the stock will besold

Must estimate the firm’s EPS in the year they plan to sellthe stock by applying an annual growth rate to theprevailing EPS

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Using the Adjusted Dividend

Discount ModelParker Corp. currently has earnings of $10 pershare. Investors expect that the EPS willgrowth by 3 percent per year and expect tosell the stock in four years. What is the EPSin four years?

26.11$)03.1(10$

)1(yearsninearningsForecasted4

nGE

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Discount Model (cont’d) Other firms in Parker’s industry have a mean PEratio of 7. What is the estimated stock price infour years?

82.78$726.11$industry)of ratio(PEyears)4inEarnings(years4inpriceStock

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Discount Model (cont’d) Parker is expected to pay a dividend of $2 pershare over the next four years. Investorsrequire a return of 13% on their investment.Based on this information, what is a fair valueof 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$44321PV

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Adjusting the dividend discount model(cont’d)

Limitations of the adjusted dividend discountmodelErrors can be made in deriving the PV of dividends overthe investment horizon or the forecasted price at whichthe stock can be sold

Errors can be made if an improper required rate ofreturn is used

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Determining the Required Rate of

Return to Value StocksThe capital asset pricing model:

Assumes that the only important risk is systematic

riskIs not concerned with unsystematic riskSuggests that the return on an asset is influencedby the prevailing risk-free rate, the market return,

and the covariance between a stock’s return and themarket’s return:

)( f m j f j R R BR R

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Return to Value Stocks (cont’d) The capital asset pricing model (cont’d)

Estimating the risk-free rate and the market risk premiumThe yield on newly issued T-bonds is commonly used as a proxyfor the risk-free rateThe terms within the parentheses measure the market riskpremiumHistorical data over 30 or more years can be used to determinethe average market risk premium over time

Estimating the firm’s beta Beta reflects the sensitivity of the stock’s return to the market’soverall returnBeta is typically measured with monthly or quarterly data over thelast four years or so

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Using the CAPM

Fantasia Corp. has a beta of 1.7. The prevailingrisk-free rate is 5% and the market riskpremium is 5%. What is the required rate ofreturn of Fantasia Corp. according to theCAPM?

%5.13%)5%10(7.1%5

)( f m j f j R R BR R

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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 unrelatedto the return on stock over the 1963 – 1990 periodChan and Lakonishok:

Found that the relation between stock returns and betavaried with the time period usedConcluded that it is appropriate to question whether beta isthe driving force behind stock returnsFound that firms with the highest betas performed muchworse than firms with low betasFound that high-beta firms outperformed low-beta firmsduring market upswings

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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 markete.g., economic growth, inflation

In equilibrium, expected returns on assets arelinearly related to the covariance between assetsreturns and the factors:

m

i i i F BBR E

10)(

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Factors That Affect Stock Prices

Economic factorsImpact of economic growth

An increase in economic growth increases expected cashflows and valueIndicators such as employment, GDP, retail sales, andpersonal income are monitored by market participants

Impact of interest ratesGiven a choice of risk-free Treasury securities or stocks,stocks should only be purchased if they offer a sufficientlyhigh expected return

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(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 isweakStock prices are affected by the impact of the dollar’schanging value on cash flowsSome U.S. firms are involved in exportingU.S.-based MNCs have some earnings in foreign currenciesExchange rates may affect expectations of other economicfactors

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(cont’d) Market-related factors

Investor sentimentIn some periods, stock market performance is not highlycorrelated with existing economic conditionsStocks can exhibit excessive volatility because their prices arepartially driven by fads and fashions

A study by Roll found that only one-third of the variation in stocksreturns can be explained by systematic economic forces

January effect

Many portfolio managers invest in riskier small stocks at thebeginning of the year and shift to larger companies near the endof the yearPlaces upward pressure on small stocks in January

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(cont’d) Firm-specific factors

Some firms are more exposed to conditions within their ownindustry than to general economic conditions, so participants

monitor:Industry sales forecastsEntry into the industry by new competitorsPrice movements of the industry’s products

Market participants focus on announcements that signalinformation about a firm’s sales growth, earnings, orcharacteristics that cause a revision in the expected cash flows

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(cont’d) Firm-specific factors (cont’d) Dividend policy changes

An increase in dividends may reflect the firm’s expectation that itcan more easily afford to pay dividends

Earnings surprisesWhen a firm’s announced earnings are higher than expected,investors may raise their estimates of the firm’s future cash flows

Acquisitions and divestituresExpected acquisitions typically result in an increased demand forthe target’s stock and raise the stock price

The effect on the acquiring firm is less clearExpectations

Investors attempt to anticipate new policies so they can maketheir move before other investors

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(cont’d) Integration of factors affecting stock prices

Whenever economic indicators signal theexpectation of higher interest rates, there is upwardpressure on the required rate of returnFirms’ expected future cash flows are influenced byeconomic conditions, industry conditions, and firm-specific conditions

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Role of Analysts in Valuing Stocks

Many investors rely on opinions of stock analystsemployed by securities firms or other financial firmsMany analysts are assigned to specific stocks andissue ratings that can indicate whether investorsshould buy or sell the stock

A 2001 study by Thomson Financial determined thatanalysts at the largest brokerage firms typicallyrecommended “sell” for less than 1 percent of all thestocks 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 otherinvestment banking relationships with rated firmsSome analysts may own the stock of some of the firms they rate

Impact of disclosure regulationsIn October 2000, the SEC enacted Regulation FD, which requiresfirms to disclose any significant information simultaneously to allmarket participants

Unbiased analyst rating services

Popular rating services include Morningstar, Value Line , andInvestor’s Business Daily Analyst rating services typically charge subscribers between $100and $600 per year

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Stock Risk

Risk reflects the uncertainty about future returns suchthat the actual return may be less than expectedThe holding period return is measured as:

The main source of uncertainty is the price at which the stockcan be soldDividends tend to be much more stable than stock price

INV DINV SP

R )(

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Stock Risk (cont’d)

Measures of riskThe volatility of a stock:

May indicate the degree of uncertainty surrounding thestock’s future returns Reflects total risk because it reflects movements in stockprices 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 portfolioThe correlations between returns of the stocks in theportfolioThe proportion of total funds invested in each stock

A portfolio containing some stocks with low or negative

correlation will exhibit less volatility

ij j i j i j j i i p CORR w w w w 22222

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Measures of risk (cont’d) The beta of a stock:

Measures the sensitivity of its returns to market returnsIs used by many investors who have a diversified portfolioof stocksCan be estimated by obtaining returns of the firm and thestock market and applying regression analysis to derive the

slope coefficient:t mt jt uR BBR 10

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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 levelBecame very popular in the late 1990s after some mutual fundsand pension funds experienced abrupt large lossesIs intended to warn investors about the potential maximum lossthat could occur

Focuses on the pessimistic portion of the probability distribution ofreturnsIs commonly used to measure the risk of a portfolio

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Applying Value at Risk

Methods of determining the maximumexpected loss

Use of historical returns to derive the maximumexpected losse.g., an investor may determine that out of the last 100trading days, a stock experienced a decline of greater than7 percent on 5 different days

The investor could infer a maximum daily loss of no morethan 7 percent for that stock based on a 95 percentconfidence level

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Applying Value at Risk (cont’d)

Methods of determining the maximumexpected loss (cont’d)

Use of standard deviation to derive the maximumexpected lossThe standard deviation of daily returns over the previousperiod can be used and applied to derive boundaries for aspecific confidence level

Use of beta to derive the maximum expected loss

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Using the Standard Deviation to

Derive the Maximum Expected LossThe standard deviation of daily returns for astock in a recent period is 1%. The 95%confidence level is desired for the maximumloss. The stock has an expected daily returnof .1%. What is the lower boundary ofexpected 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. Thestock market is expected to perform no worsethan – 2.1% on a daily basis based on a 95%confidence level. What is the maximum lossto the stock over a given day based on thisinformation?

%73.2%)1.2(3.1

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Applying Value at Risk (cont’d)

Deriving the maximum dollar lossThe maximum percentage loss for a given confidence levelcan be applied to derive the maximum dollar loss of aparticular investmentValue at risk is commonly applied to assess the maximumpossible loss for an entire portfolio

Common adjustments to value at risk applicationsInvestment horizon desired

Length of historical period usedTime-varying riskRestructuring the investment portfolio

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Forecasting Stock Price Volatility

and BetaMethods of forecasting stock price volatilityThe historical method uses a historical period to derive astock’s standard deviation of returns and uses that estimate asthe forecast for the future

The time-series method uses volatility patterns in previousperiodsPlaces more weight on the most recent dataNormally uses the weights and number of periods that were themost accurate in previous periods

The implied standard deviation derives the estimate from the

stock option pricing modelRepresents the anticipated volatility of the stock over a futureperiod 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 derivingforecasts of individual volatility levelsNext, the correlation coefficient for each pair ofstock in the portfolio is forecast by estimating thecorrelation in recent periods

Forecasting a stock portfolio’s beta First forecast the betas of the individual stocks andthen take a weighted average

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Stock Performance Measurement

The Sharpe index is appropriate when total variabilityis 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 theSharpe index

Measures the excess return above the risk-free rate per period

f R R indexSharpe

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Using the Sharpe Index

Patrick stock has an average return of 15% andan average standard deviation of 13%. Theaverage risk-free rate is 8%. What is theSharpe index for Patrick stock?

54.0%13

%8%15

indexSharpe

f R R

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Stock Performance Measurement

(cont’d) The Treynor index is appropriate when beta isthought 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

BR R f indexTreynor

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Using the Treynor Index

Patrick stock has an average return of 15% anda beta of 1.8. The average risk-free rate is8%. What is the Sharpe index for Patrickstock?

04.08.1

%8%15

indexTreynor B

R R f

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Stock Market Efficiency

Forms of efficiencyWeak-form efficiency suggests that security prices reflect alltrade-related information

Semistrong-form efficiency suggests that security prices fullyreflect all public information

Includes announcements by firms, economic news or events, andpolitical news or eventsIf semistrong-form efficiency holds, weak-form efficiency holds as

wellStrong-form efficiency suggests that security prices fully reflectall information, including private or insider information

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Stock Market Efficiency (cont’d)

Tests of the efficient market hypothesisTest of weak-form efficiency

Tested by searching for a nonrandom pattern in security

pricesStudies have generally found that historical price changesare independent over timeThere 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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Foreign Stock Valuation,

Performance, and EfficiencyValuation of foreign stocksPE method

The expected EPS of the foreign firm are multiplied by theappropriate PE ratio based on the firm’s risk and local industry The PE ratio for a given industry may change continuously insome foreign marketsThe PE ratio for a particular industry may need to be adjusted forthe firm’s country

Dividend discount model

An adjustment for expected exchange rate movements is requiredThe value of foreign stocks from a U.S. perspective is subject tomore uncertainty than the value of the stock from a localinvestor’s perspective

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Foreign Stock Valuation, Performance,and Efficiency (cont’d)

Measuring performance from investing inforeign stocks

The performance measurement should control forgeneral market movements and exchange ratemovements in the region where the portfoliomanagers has been assigned to invest funds

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Performance from global diversificationStock investors can benefit by diversifyinginternationally

Economies do not move in tandemStock markets across countries may respond to some ofthe same expectationsIn general, correlations between stock indexes have been

higher in recent years than they were several years ago

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Performance from global diversification (cont’d) Integration of markets during the 1987 crash

There was a high correlation among country stock markets duringthe crash

This suggests that the underlying cause of the crashsystematically affected all marketsIntegration of markets during mini-crashes

On August 27, 1998 (“Bloody Thursday”) most stock marketsaround the world experienced lossesIllustrates that even a well-diversified international portfolio is notinsulated from some events

Diversification among emerging stock marketsThese markets have lower correlations with developed countries,but also higher risk

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International market efficiencySome foreign markets are inefficient because of thesmall number of analysts and portfolio managersMarket inefficiencies are more common in smallforeign stock marketsInsider trading is more prevalent in many foreignmarketsPolitical and exchange rate risk may be high insome foreign markets

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