Bba 2204 fin mgt week 8 risk and return

Risk and ReturnRisk and ReturnRisk and ReturnRisk and Return

BBA 2204 FINANCIAL MANAGEMENTBBA 2204 FINANCIAL MANAGEMENT

bybyStephen OngStephen Ong

Visiting Fellow, Birmingham City Visiting Fellow, Birmingham City University Business School, UKUniversity Business School, UK

Visiting Professor, Shenzhen UniversityVisiting Professor, Shenzhen University

Today’s Overview Today’s Overview

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Learning GoalsLearning Goals1.1. Understand the meaning and fundamentals of risk, return, and Understand the meaning and fundamentals of risk, return, and

risk preferences.risk preferences.

2.2. Describe procedures for assessing and measuring the risk of a Describe procedures for assessing and measuring the risk of a single asset.single asset.

3.3. Discuss the measurement of return and standard deviation for Discuss the measurement of return and standard deviation for a portfolio and the concept of correlation.a portfolio and the concept of correlation.

4.4. Understand the risk and return characteristics of a portfolio in Understand the risk and return characteristics of a portfolio in terms of correlation and diversification, and the impact of terms of correlation and diversification, and the impact of international assets on a portfolio.international assets on a portfolio.

5.5. Review the two types of risk and the derivation and role of Review the two types of risk and the derivation and role of beta in measuring the relevant risk of both a security and a beta in measuring the relevant risk of both a security and a portfolio.portfolio.

6.6. Explain the capital asset pricing model (CAPM), its Explain the capital asset pricing model (CAPM), its relationship to the security market line (SML), and the major relationship to the security market line (SML), and the major forces causing shifts in the SML.forces causing shifts in the SML.

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Risk and Return Risk and Return FundamentalsFundamentals

In most important business decisions there are two key financial considerations: risk and return.

Each financial decision presents certain risk and return characteristics, and the combination of these characteristics can increase or decrease a firm’s share price.

Analysts use different methods to quantify risk depending on whether they are looking at a single asset or a portfolio—a collection, or group, of assets.

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Risk and Return Risk and Return Fundamentals:Fundamentals:Risk DefinedRisk Defined Risk is a measure of the uncertainty

surrounding the return that an investment will earn or, more formally, the variability of returns associated with a given asset.

Return is the total gain or loss experienced on an investment over a given period of time; calculated by dividing the asset’s cash distributions during the period, plus change in value, by its beginning-of-period investment value.

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Focus on EthicsFocus on EthicsIf It Sounds Too Good To Be True...If It Sounds Too Good To Be True...

For many years, investors around the world For many years, investors around the world clamoured to invest with Bernard Madoff. clamoured to invest with Bernard Madoff.

Madoff generated high returns year after year, Madoff generated high returns year after year, seemingly with very little risk. seemingly with very little risk.

On December 11, 2008, the U.S. Securities and On December 11, 2008, the U.S. Securities and Exchange Commission (SEC) charged Madoff with Exchange Commission (SEC) charged Madoff with securities fraud. Madoffsecurities fraud. Madoff’’s hedge fund, Ascot s hedge fund, Ascot Partners, turned out to be a giant Ponzi scheme.Partners, turned out to be a giant Ponzi scheme.

What are some hazards of allowing investors to What are some hazards of allowing investors to pursue claims based their most recent accounts pursue claims based their most recent accounts statements?statements?

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Risk and Return Risk and Return Fundamentals:Fundamentals:

Risk Defined (cont.)Risk Defined (cont.)The expression for calculating the total rate of return earned The expression for calculating the total rate of return earned on any asset over period on any asset over period t, rt, rtt,, is commonly defined as is commonly defined as

wherewhererrtt == actual, expected, or required rate of return during period actual, expected, or required rate of return during period

ttCCtt == cash (flow) received from the asset investment in the time cash (flow) received from the asset investment in the time

period period tt –– 1 to 1 to ttPPtt == price (value) of asset at time price (value) of asset at time tt

PPtt –– 1 1 == price (value) of asset at time price (value) of asset at time tt –– 1 1

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Risk Defined (cont.)Risk Defined (cont.)At the beginning of the year, Apple stock traded for At the beginning of the year, Apple stock traded for $90.75 per share, and Wal-Mart was valued at $55.33. $90.75 per share, and Wal-Mart was valued at $55.33. During the year, Apple paid no dividends, but Wal-Mart During the year, Apple paid no dividends, but Wal-Mart shareholders received dividends of $1.09 per share. At shareholders received dividends of $1.09 per share. At the end of the year, Apple stock was worth $210.73 and the end of the year, Apple stock was worth $210.73 and Wal-Mart sold for $52.84. Wal-Mart sold for $52.84.

We can calculate the annual rate of return, We can calculate the annual rate of return, r,r, for each for each stock.stock.

Apple: ($0 + $210.73 Apple: ($0 + $210.73 –– $90.75) $90.75) ÷÷ $90.75 = 132.2% $90.75 = 132.2%

Wal-Mart: ($1.09 + $52.84 Wal-Mart: ($1.09 + $52.84 –– $55.33) $55.33) ÷÷ $55.33 = $55.33 = ––2.5% 2.5%

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Table 8.1 Historical Table 8.1 Historical Returns on Selected Returns on Selected

Investments (1900–2009)Investments (1900–2009)

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Risk PreferencesRisk PreferencesEconomists use three categories to describe how investors respond to risk.

Risk averse is the attitude toward risk in which investors would require an increased return as compensation for an increase in risk.

Risk-neutral is the attitude toward risk in which investors choose the investment with the higher return regardless of its risk.

Risk-seeking is the attitude toward risk in which investors prefer investments with greater risk even if they have lower expected returns.

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Risk of a Single Asset: Risk of a Single Asset:

Risk AssessmentRisk Assessment Scenario analysis is an approach for assessing risk that uses several possible alternative outcomes (scenarios) to obtain a sense of the variability among returns. One common method involves considering pessimistic

(worst), most likely (expected), and optimistic (best) outcomes and the returns associated with them for a given asset.

Range is a measure of an asset’s risk, which is found by subtracting the return associated with the pessimistic (worst) outcome from the return associated with the optimistic (best) outcome.

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Risk of a Single Asset: Risk of a Single Asset: Risk Assessment (cont.)Risk Assessment (cont.)

Norman Company wants to choose the better of two investments, A Norman Company wants to choose the better of two investments, A and B. Each requires an initial outlay of $10,000 and each has a most and B. Each requires an initial outlay of $10,000 and each has a most likely annual rate of return of 15%. Management has estimated the likely annual rate of return of 15%. Management has estimated the returns associated with each investment. Asset A appears to be less returns associated with each investment. Asset A appears to be less risky than asset B. The risk averse decision maker would prefer asset risky than asset B. The risk averse decision maker would prefer asset A over asset B, because A offers the same most likely return with a A over asset B, because A offers the same most likely return with a lower range (risk).lower range (risk).

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Risk of a Single Asset: Risk of a Single Asset: Risk AssessmentRisk Assessment

Probability is the chance that a given outcome will occur.

A probability distribution is a model that relates probabilities to the associated outcomes.

A bar chart is the simplest type of probability distribution; shows only a limited number of outcomes and associated probabilities for a given event.

A continuous probability distribution is a probability distribution showing all the possible outcomes and associated probabilities for a given event.

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Risk of a Single Risk of a Single Asset: Asset:

Risk Assessment Risk Assessment (cont.)(cont.)Norman CompanyNorman Company’’s past estimates s past estimates

indicate that the probabilities of the indicate that the probabilities of the pessimistic, most likely, and optimistic pessimistic, most likely, and optimistic outcomes are outcomes are 25%, 50%, 25%, 50%, andand 25%, 25%, respectively. Note that the sum of these respectively. Note that the sum of these probabilities must equal 100%; that is, probabilities must equal 100%; that is, they must be based on all the they must be based on all the alternatives considered.alternatives considered.

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Figure 8.1 Bar charts for Figure 8.1 Bar charts for asset A’s and asset B’s asset A’s and asset B’s

returnsreturns

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Figure 8.2 Figure 8.2 Continuous Continuous Probability Probability

DistributionsDistributions

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Matter of FactMatter of FactBeware of the Black SwanBeware of the Black Swan

Is it ever possible to know for sure that a particular outcome can Is it ever possible to know for sure that a particular outcome can never happen, that the chance of it occurring is 0%?never happen, that the chance of it occurring is 0%?

In the 2007 best seller, In the 2007 best seller, The Black Swan: The Impact of the The Black Swan: The Impact of the Highly ImprobableHighly Improbable, Nassim Nicholas Taleb argues that , Nassim Nicholas Taleb argues that seemingly improbable or even impossible events are more likely seemingly improbable or even impossible events are more likely to occur than most people believe, especially in the area of to occur than most people believe, especially in the area of finance.finance.

The bookThe book’’s title refers to the fact that for many years, people s title refers to the fact that for many years, people believed that all swans were white until a black variety was believed that all swans were white until a black variety was discovered in Australia. discovered in Australia.

Taleb reportedly earned a large fortune during the 2007Taleb reportedly earned a large fortune during the 2007––2008 2008 financial crisis by betting that financial markets would plummet.financial crisis by betting that financial markets would plummet.

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Risk of a Single Asset:Risk of a Single Asset:Risk MeasurementRisk Measurement

Standard deviation (Standard deviation (rr)) is the most common statistical is the most common statistical

indicator of an assetindicator of an asset’’s risk; it measures the dispersion s risk; it measures the dispersion around the around the expected value.expected value.

Expected value of a return (Expected value of a return (rr) ) is the average return is the average return that an investment is expected to produce over time.that an investment is expected to produce over time.

wherewhererj = return for the jth outcome

Prt = probability of occurrence of the jth outcomen = number of outcomes considered

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Table 8.3 Expected Values Table 8.3 Expected Values of Returns for Assets A and of Returns for Assets A and

BB

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Risk of a Single Asset: Risk of a Single Asset: Standard DeviationStandard Deviation

The expression for the standard deviation of The expression for the standard deviation of returns, returns, rr, is, is

In general, the higher the standard deviation, In general, the higher the standard deviation, the greater the risk.the greater the risk.

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Table 8.4a The Calculation of the Table 8.4a The Calculation of the Standard Deviation of the Standard Deviation of the Returns for Assets A and BReturns for Assets A and B

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Table 8.4b The Calculation of the Table 8.4b The Calculation of the Standard Deviation of the Standard Deviation of the Returns for Assets A and BReturns for Assets A and B

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Table 8.5 Historical Returns and Table 8.5 Historical Returns and Standard Deviations on Selected Standard Deviations on Selected

Investments (1900–2009)Investments (1900–2009)

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Matter of FactMatter of FactAll Stocks Are Not Created EqualAll Stocks Are Not Created Equal

Stocks are riskier than bonds, but are some stocks riskier Stocks are riskier than bonds, but are some stocks riskier than others? than others?

A recent study examined the historical returns of large A recent study examined the historical returns of large stocks and small stocks and found that the average stocks and small stocks and found that the average annual return on large stocks from 1926-2009 was annual return on large stocks from 1926-2009 was 11.8%11.8%, while small stocks earned , while small stocks earned 16.7%16.7% per year on per year on average. average.

The higher returns on small stocks came with a cost, The higher returns on small stocks came with a cost, however. however.

The standard deviation of small stock returns was a The standard deviation of small stock returns was a whopping whopping 32.8%32.8%, whereas the standard deviation on , whereas the standard deviation on large stocks was just large stocks was just 20.5%20.5%..

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Figure 8.3 Figure 8.3 Bell-Shaped CurveBell-Shaped Curve

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Risk of a Single Asset: Risk of a Single Asset: Standard Deviation Standard Deviation

(cont.)(cont.)Using the data in Table 8.2 and assuming that the Using the data in Table 8.2 and assuming that the probability distributions of returns for common probability distributions of returns for common stocks and bonds are normal, we can surmise that: stocks and bonds are normal, we can surmise that:

68% of the possible outcomes would have a return 68% of the possible outcomes would have a return ranging between 11.1% and 29.7% for stocks and ranging between 11.1% and 29.7% for stocks and between between ––5.2% and 15.2% for bonds5.2% and 15.2% for bonds

95% of the possible return outcomes would range 95% of the possible return outcomes would range between between ––31.5% and 50.1% for stocks and between 31.5% and 50.1% for stocks and between ––15.4% and 25.4% for bonds15.4% and 25.4% for bonds

The greater risk of stocks is clearly reflected in their The greater risk of stocks is clearly reflected in their much wider range of possible returns for each level of much wider range of possible returns for each level of confidence (68% or 95%).confidence (68% or 95%).

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Risk of a Single Risk of a Single Asset: Asset:

Coefficient of Coefficient of VariationVariation The coefficient of variation, CV, is a measure of

relative dispersion that is useful in comparing the risks of assets with differing expected returns.

A higher coefficient of variation means that an investment has more volatility relative to its expected return.

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Risk of a Single Asset: Risk of a Single Asset: Coefficient of Variation Coefficient of Variation

(cont.)(cont.)Using the standard deviations (from Using the standard deviations (from Table 8.4) and the expected returns (from Table 8.4) and the expected returns (from Table 8.3) for assets A and B to calculate Table 8.3) for assets A and B to calculate the coefficients of variation yields the the coefficients of variation yields the following:following:

CVCVAA = 1.41% ÷ 15% = 0.094 = 1.41% ÷ 15% = 0.094

CVCVBB = 5.66% ÷ 15% = 0.377 = 5.66% ÷ 15% = 0.377

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Personal Finance Personal Finance ExampleExample

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Personal Finance Personal Finance Example (cont.)Example (cont.)

Assuming that the returns are equally Assuming that the returns are equally probable:probable:

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Risk of a Risk of a PortfolioPortfolio In real-world situations, the risk of any In real-world situations, the risk of any

single investment would not be viewed single investment would not be viewed independently of other assets. independently of other assets.

New investments must be considered in New investments must be considered in light of their impact on the risk and return light of their impact on the risk and return of an investorof an investor’’s portfolio of assets. s portfolio of assets.

The financial managerThe financial manager’’s goal is to create s goal is to create an an efficient portfolio,efficient portfolio, a portfolio that a portfolio that maximum return for a given level of risk. maximum return for a given level of risk.

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Risk of a Portfolio: Risk of a Portfolio: Portfolio Return and Portfolio Return and Standard DeviationStandard DeviationThe return on a portfolio is a weighted average The return on a portfolio is a weighted average

of the returns on the individual assets from of the returns on the individual assets from which it is formed.which it is formed.

wherewherewwjj == proportion of the portfolioproportion of the portfolio ’’s total s total

dollar value represented by asset dollar value represented by asset jjrrjj == return on asset return on asset jj

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Risk of a Portfolio: Risk of a Portfolio: Portfolio Return and Portfolio Return and Standard DeviationStandard DeviationJames purchases 100 shares of Wal-Mart at a price of James purchases 100 shares of Wal-Mart at a price of

$55 per share, so his total investment in Wal-Mart is $55 per share, so his total investment in Wal-Mart is $5,500. He also buys 100 shares of Cisco Systems at $5,500. He also buys 100 shares of Cisco Systems at $25 per share, so the total investment in Cisco stock $25 per share, so the total investment in Cisco stock is $2,500. is $2,500.

Combining these two holdings, JamesCombining these two holdings, James ’’ total portfolio is total portfolio is worth $8,000. worth $8,000.

Of the total, 68.75% is invested in Wal-Mart Of the total, 68.75% is invested in Wal-Mart ($5,500/$8,000) and 31.25% is invested in Cisco ($5,500/$8,000) and 31.25% is invested in Cisco Systems ($2,500/$8,000). Systems ($2,500/$8,000).

Thus, Thus, ww11 = 0.6875, = 0.6875, ww22 = 0.3125, and = 0.3125, and ww11 + + ww22 = 1.0. = 1.0.

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Table 8.6a Expected Return, Table 8.6a Expected Return, Expected Value, and Standard Expected Value, and Standard

Deviation of Returns for Deviation of Returns for Portfolio XYPortfolio XY

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Table 8.6b Expected Return, Expected Table 8.6b Expected Return, Expected Value, and Standard Deviation of Value, and Standard Deviation of

Returns for Returns for Portfolio XYPortfolio XY

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Risk of a Portfolio: Risk of a Portfolio: CorrelationCorrelation

Correlation is a statistical measure of the relationship between any two series of numbers. Positively correlated describes two series that move in the

same direction. Negatively correlated describes two series that move in

opposite directions.

The correlation coefficient is a measure of the degree of correlation between two series. Perfectly positively correlated describes two positively

correlated series that have a correlation coefficient of +1. Perfectly negatively correlated describes two negatively

correlated series that have a correlation coefficient of –1.

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Figure 8.4 Figure 8.4 CorrelationsCorrelations

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Risk of a Portfolio: Risk of a Portfolio: DiversificationDiversification

To reduce overall risk, it is best to diversify by combining, or adding to the portfolio, assets that have the lowest possible correlation.

Combining assets that have a low correlation with each other can reduce the overall variability of a portfolio’s returns.

Uncorrelated describes two series that lack any interaction and therefore have a correlation coefficient close to zero.

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Figure 8.5 Figure 8.5 DiversificationDiversification

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Table 8.7 Forecasted Returns, Table 8.7 Forecasted Returns, Expected Values, and Standard Expected Values, and Standard

Deviations for Assets X, Y, and Z and Deviations for Assets X, Y, and Z and Portfolios XY and XZPortfolios XY and XZ

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Risk of a Portfolio: Risk of a Portfolio: Correlation, Diversification, Correlation, Diversification,

Risk, and ReturnRisk, and ReturnConsider two assetsConsider two assets——Lo and HiLo and Hi——with the with the characteristics described in the table below:characteristics described in the table below:

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Figure 8.6 Possible Figure 8.6 Possible CorrelationsCorrelations

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Risk of a Portfolio: Risk of a Portfolio: International International

DiversificationDiversification The inclusion of assets from countries with business cycles The inclusion of assets from countries with business cycles that are not highly correlated with the U.S. business cycle that are not highly correlated with the U.S. business cycle reduces the portfolioreduces the portfolio’’s responsiveness to market movements.s responsiveness to market movements.

Over long periods, internationally diversified portfolios tend Over long periods, internationally diversified portfolios tend to perform better (meaning that they earn higher returns to perform better (meaning that they earn higher returns relative to the risks taken) than purely domestic portfolios. relative to the risks taken) than purely domestic portfolios.

However, over shorter periods such as a year or two, However, over shorter periods such as a year or two, internationally diversified portfolios may perform better or internationally diversified portfolios may perform better or worse than domestic portfolios.worse than domestic portfolios.

Currency risk and political risk Currency risk and political risk are unique to international are unique to international investing.investing.

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Global FocusGlobal FocusAn International Flavour to Risk ReductionAn International Flavour to Risk Reduction

Elroy Dimson, Paul Marsh, and Mike Staunton Elroy Dimson, Paul Marsh, and Mike Staunton calculated the historical returns on a portfolio that calculated the historical returns on a portfolio that included U.S. stocks as well as stocks from 18 other included U.S. stocks as well as stocks from 18 other countries. countries.

This diversified portfolio produced returns that were not This diversified portfolio produced returns that were not quite as high as the U.S. average, just quite as high as the U.S. average, just 8.6%8.6% per year. per year.

However, the globally diversified portfolio was also less However, the globally diversified portfolio was also less volatile, with an annual standard deviation of volatile, with an annual standard deviation of 17.8%. 17.8%.

Dividing the standard deviation by the annual return Dividing the standard deviation by the annual return produces a coefficient of variation for the globally produces a coefficient of variation for the globally diversified portfolio of 2.07, slightly lower than the 2.10 diversified portfolio of 2.07, slightly lower than the 2.10 coefficient of variation reported for U.S. stocks in Table coefficient of variation reported for U.S. stocks in Table 8.5.8.5.

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Risk and Return: The Risk and Return: The Capital Asset Pricing Capital Asset Pricing

Model (CAPM)Model (CAPM)The capital asset pricing model (CAPM) is the basic theory that links risk and return for all assets.

The CAPM quantifies the relationship between risk and return.

In other words, it measures how much additional return an investor should expect from taking a little extra risk.

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Risk and Return: The Risk and Return: The CAPM:CAPM:

Types of RiskTypes of Risk Total riskTotal risk is the combination of a security is the combination of a security’’s nondiversifiable s nondiversifiable risk and diversifiable risk.risk and diversifiable risk.

Diversifiable risk Diversifiable risk is the portion of an assetis the portion of an asset’’s risk that is s risk that is attributable to firm-specific, random causes; can be eliminated attributable to firm-specific, random causes; can be eliminated through diversification. Also called unsystematic risk.through diversification. Also called unsystematic risk.

Nondiversifiable risk Nondiversifiable risk is the relevant portion of an assetis the relevant portion of an asset’’s risk s risk attributable to market factors that affect all firms; cannot be attributable to market factors that affect all firms; cannot be eliminated through diversification. Also called systematic risk.eliminated through diversification. Also called systematic risk.

Because any investor can create a portfolio of assets that will Because any investor can create a portfolio of assets that will eliminate virtually all diversifiable risk, eliminate virtually all diversifiable risk, the only relevant risk the only relevant risk is nondiversifiable risk.is nondiversifiable risk.

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Figure 8.7 Risk Figure 8.7 Risk ReductionReduction

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Risk and Return: Risk and Return: The CAPMThe CAPM

The beta coefficient (b) is a relative measure of nondiversifiable risk. An index of the degree of movement of an asset’s return in response to a change in the market return. An asset’s historical returns are used in finding the

asset’s beta coefficient. The beta coefficient for the entire market equals

1.0. All other betas are viewed in relation to this value.

The market return is the return on the market portfolio of all traded securities.

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Figure 8.8 Beta Derivation

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Table 8.8 Selected Beta Table 8.8 Selected Beta Coefficients and Their Coefficients and Their

InterpretationsInterpretations

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Table 8.9 Beta Table 8.9 Beta Coefficients for Selected Coefficients for Selected

Stocks (June 7, 2010)Stocks (June 7, 2010)

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Risk and Return: The Risk and Return: The CAPM (cont.)CAPM (cont.)

The beta of a portfolio can be estimated by using The beta of a portfolio can be estimated by using the betas of the individual assets it includes. the betas of the individual assets it includes.

Letting Letting wwjj represent the proportion of the represent the proportion of the

portfolioportfolio’’s total dollar value represented by asset s total dollar value represented by asset j,j, and letting and letting bbjj equal the beta of asset equal the beta of asset j,j, we can use we can use

the following equation to find the portfolio beta, the following equation to find the portfolio beta, bbpp::

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Table 8.10 Mario Table 8.10 Mario Austino’s Portfolios V Austino’s Portfolios V

and Wand W

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The betas for the two portfolios, The betas for the two portfolios, bbvv and and bbww,, can be can be

calculated as follows:calculated as follows:bv = (0.10 1.65) + (0.30 1.00) + (0.20 1.30) +

(0.20 1.10) + (0.20 1.25)= 0.165 + 0.300 +0 .260 + 0.220 + 0.250 = 1.195 ≈ 1.20

bw = (0.10 .80) + (0.10 1.00) + (0.20 .65) + (0.10 .75) +(0.50 1.05)

= 0.080 + 0.100 + 0.130 +0 .075 + 0.525 = 0.91

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Using the beta coefficient to measure Using the beta coefficient to measure nondiversifiable risk, the capital asset pricing nondiversifiable risk, the capital asset pricing model (CAPM) is given in the following model (CAPM) is given in the following equation:equation:

rrjj = = RRFF + [ + [bbjj ( (rrmm –– RRFF)])]wherewhere rrtt == required return on asset required return on asset jj

RRFF == risk-free rate of return, commonly measured by the risk-free rate of return, commonly measured by the return on a U.S. Treasury billreturn on a U.S. Treasury bill

bbjj == beta coefficient or index of nondiversifiable risk for beta coefficient or index of nondiversifiable risk for asset asset jj

rrmm == market return; return on the market portfolio of assetsmarket return; return on the market portfolio of assets

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Risk and Return: The CAPM Risk and Return: The CAPM (cont.)(cont.)

The CAPM can be divided into two parts:The CAPM can be divided into two parts:1.1. The The risk-free rate of return, (risk-free rate of return, (RRFF)) which is which is

the required return on a risk-free asset, the required return on a risk-free asset, typically a 3-month U.S. Treasury bill.typically a 3-month U.S. Treasury bill.

2.2. The risk premium.The risk premium. The (The (rrmm –– RRFF) portion of the risk premium is ) portion of the risk premium is

called the called the market risk premium,market risk premium, because it because it represents the premium the investor must represents the premium the investor must receive for taking the average amount of risk receive for taking the average amount of risk associated with holding the market portfolio of associated with holding the market portfolio of assets.assets.

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Risk and Return: The CAPM Risk and Return: The CAPM (cont.)(cont.)

Historical Risk PremiumHistorical Risk Premium

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Risk and Return: Risk and Return: The CAPM (cont.)The CAPM (cont.)

Benjamin Corporation, a growing computer Benjamin Corporation, a growing computer software developer, wishes to determine the software developer, wishes to determine the required return on asset Z, which has a beta required return on asset Z, which has a beta of 1.5. The risk-free rate of return is 7%; the of 1.5. The risk-free rate of return is 7%; the return on the market portfolio of assets is 11%. return on the market portfolio of assets is 11%. Substituting Substituting bbZZ = 1.5, = 1.5, RRFF = 7%, and = 7%, and

rrmm = 11% into the CAPM yields a return of: = 11% into the CAPM yields a return of:

rrZZ = 7% + [1.5 = 7% + [1.5 (11% (11% –– 7%)] = 7% + 6% = 7%)] = 7% + 6% = 13%13%

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The security market line (SML) is the depiction of the capital asset pricing model (CAPM) as a graph that reflects the required return in the marketplace for each level of nondiversifiable risk (beta).

It reflects the required return in the marketplace for each level of nondiversifiable risk (beta).

In the graph, risk as measured by beta, b, is plotted on the x axis, and required returns, r, are plotted on the y axis.

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Figure 8.9 Security Figure 8.9 Security Market LineMarket Line

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Figure 8.10 Inflation Figure 8.10 Inflation Shifts SMLShifts SML

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Figure 8.11 Risk Aversion Figure 8.11 Risk Aversion Shifts SMLShifts SML

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The CAPM relies on historical data which means the The CAPM relies on historical data which means the betas may or may not actually reflect the future betas may or may not actually reflect the future variability of returns.variability of returns.

Therefore, the required returns specified by the model Therefore, the required returns specified by the model should be used only as rough approximations.should be used only as rough approximations.

The CAPM assumes markets are efficient.The CAPM assumes markets are efficient. Although the perfect world of efficient markets Although the perfect world of efficient markets

appears to be unrealistic, studies have provided appears to be unrealistic, studies have provided support for the existence of the expectational support for the existence of the expectational relationship described by the CAPM in active markets relationship described by the CAPM in active markets such as the NYSE. such as the NYSE.

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Review of Learning GoalsReview of Learning GoalsUnderstand the meaning and fundamentals of risk,

return, and risk preferences. Risk is a measure of the uncertainty

surrounding the return that an investment will produce. The total rate of return is the sum of cash distributions, such as interest or dividends, plus the change in the asset’s value over a given period, divided by the investment’s beginning-of-period value. Investment returns vary both over time and between different types of investments. Investors may be risk-averse, risk-neutral, or risk-seeking. Most financial decision makers are risk-averse. They generally prefer less-risky alternatives, and they require higher expected returns in exchange for greater risk.

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Review of Learning Goals Review of Learning Goals (cont.)(cont.)

Describe procedures for assessing and measuring the risk of a single asset. The risk of a single asset is measured

in much the same way as the risk of a portfolio of assets. Scenario analysis and probability distributions can be used to assess risk. The range, the standard deviation, and the coefficient of variation can be used to measure risk quantitatively.

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Discuss the measurement of return and standard deviation for a portfolio and the concept of correlation. The return of a portfolio is calculated as the

weighted average of returns on the individual assets from which it is formed. The portfolio standard deviation is found by using the formula for the standard deviation of a single asset.

Correlation—the statistical relationship between any two series of numbers—can be positive, negative, or uncorrelated. At the extremes, the series can be perfectly positively correlated or perfectly negatively correlated.

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Understand the risk and return characteristics of a portfolio in terms of correlation and diversification, and the impact of international assets on a portfolio. Diversification involves combining assets with low

correlation to reduce the risk of the portfolio. The range of risk in a two-asset portfolio depends on the correlation between the two assets. If they are perfectly positively correlated, the portfolio’s risk will be between the individual assets’ risks. If they are perfectly negatively correlated, the portfolio’s risk will be between the risk of the more risky asset and zero.

International diversification can further reduce a portfolio’s risk. Foreign assets have the risk of currency fluctuation and political risks.

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Review the two types of risk and the derivation and role of beta in measuring the relevant risk of both a security and a portfolio. The total risk of a security consists of nondiversifiable and

diversifiable risk. Diversifiable risk can be eliminated through diversification. Nondiversifiable risk is the only relevant risk. Nondiversifiable risk is measured by the beta coefficient, which is a relative measure of the relationship between an asset’s return and the market return. The beta of a portfolio is a weighted average of the betas of the individual assets that it includes.

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Explain the capital asset pricing model (CAPM), its relationship to the security market line (SML), and the major forces causing shifts in the SML. The capital asset pricing model (CAPM) uses beta to

relate an asset’s risk relative to the market to the asset’s required return. The graphical depiction of CAPM is the security market line (SML), which shifts over time in response to changing inflationary expectations and/or changes in investor risk aversion. Changes in inflationary expectations result in parallel shifts in the SML. Increasing risk aversion results in a steepening in the slope of the SML. Decreasing risk aversion reduces the slope of the SML.

Gitman, Lawrence J. and Gitman, Lawrence J. and Zutter ,Chad J.(2013) Zutter ,Chad J.(2013) Principles of Managerial Principles of Managerial Finance, Pearson,13Finance, Pearson,13thth Edition Edition

Brooks,Raymond (2013) Brooks,Raymond (2013) Financial Management: Core Financial Management: Core Concepts , Pearson, 2Concepts , Pearson, 2thth edition edition

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Questions?Questions?

Bba 2204 fin mgt week 8 risk and return

Business

return risk

fundamentals of risk

assets risk

risk defined8

relevant risk

certain risk

greater risk

types of risk