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Applied Corporate Finance

Session 5:

Risk, Returns andFinancial Markets

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Learning Outcomes

1. Know how to calculate the return on an investment2. Understand the historical returns on various types of

investments

3. Understand the historical risks on various types of

investments4. Understand the implications of market efficiency

5. Know how to calculate expected returns

6. Understand the impact of diversification

7. Understand the systematic risk principle8. Understand the security market line

9. Understand the risk-return trade-off

10. Be able to use the Capital Asset Pricing Model

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1. Return on Investment Total dollar return = income from

investment + capital gain (loss) due tochange in price

Example: You bought a bond for $950 one year ago. You

have received two coupons of $30 each. Youcan sell the bond for $975 today. What is your

total dollar return? Income = 30 + 30 = 60

Capital gain = 975950 = 25

Total dollar return = 60 + 25 = $85

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Percentage Returns

It is generally more intuitive to think in termsof percentage, rather than dollar, returns

Dividend yield = income / beginning price

Capital gains yield = (ending pricebeginning price) / beginning price

Total percentage return = dividend yield +

capital gains yield

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ExampleCalculating Returns

You bought a stock for $35, and you receiveddividends of $1.25. The stock is now sellingfor $40.

What is your dollar return?

Dollar return = 1.25 + (4035) = $6.25

What is your percentage return?

Dividend yield = 1.25 / 35 = 3.57% Capital gains yield = (4035) / 35 = 14.29%

Total percentage return = 3.57 + 14.29 = 17.86%

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Arithmetic Mean vs.

Geometric Mean

An example: Year 1 -- $100 to $50R1= -50%

Year 2 -- $50 to $100R2= 100%

Whats your average return? Arithmetic average = (-50+100)/2 = 25%!!

From $100 back to $1000% returnGeometric mean

Arithmetic averagereturn earned in an average periodover multiple periods

Geometric averageaverage compound return perperiod over multiple periodsThe geometric average will be less than the arithmeticaverage unless all the returns are equal

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Arithmetic Mean vs.

Geometric Mean (cont.)

Which is better? The arithmetic average is overly optimistic for long horizons The geometric average is overly pessimistic for short horizons So, the answer depends on the planning period under

consideration

1520 years or less: use the arithmetic 2040 years or so: split the difference between them 40 + years: use the geometric

Another example Year 1 5%

Year 2 -3% Year 3 12%

Arithmetic average = (5 + (3) + 12)/3 = 4.67% Geometric average =

[(1+.05)*(1-.03)*(1+.12)]1/31 = 0.0449 = 4.49%

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2. Risk, Return and

Financial Markets

The Importance of Financial Markets Financial markets allow companies, governments and

individuals to increase their utility Savers have the ability to invest in financial assets so that they can

defer consumption and earn a return to compensate them for doing so

Borrowers have better access to the capital that is available so thatthey can invest in productive assets

Financial markets also provide us with information about thereturns that are required for various levels of risk

We can examine returns in the financial markets to help usdetermine the appropriate returns on non-financial assets

Lessons from capital market history1. There is a reward for bearing risk

2. The greater the potential reward, the greater the risk

This is called the risk-return trade-off

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Historical Record in US Financial Markets

Insert Figure 12.4 here

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See Figures

12.5 to 12.7for moredetaileddistributionsof returns.

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Average Returns

Investment Average Return

Large Stocks 12.3%

Small Stocks 17.1%

Long-term CorporateBonds

6.2%

Long-term GovernmentBonds

5.8%

U.S. Treasury Bills 3.8%

Inflation 3.1%

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Table 12.3 Average Annual Returnsand Risk Premiums

Investment Average Return Risk Premium

Large Stocks 12.3% 8.5%

Small Stocks 17.1% 13.3%

Long-term Corporate

Bonds

6.2% 2.4%

Long-termGovernment Bonds

5.8% 2.0%

U.S. Treasury Bills 3.8% 0.0%

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Risk premium = the extra return earned for taking on risk Treasury bills are considered to be risk-free The risk premium is the return over and above the risk-free rate

Do youstillrememberthe firstlessonfrom stock

markethistory?1.Thereis areward forbearing

risk

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Variability of returns


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Review: Variance and

Standard Deviation

Variance and standard deviation measure thevolatility of asset returns

The greater the volatility, the greater the

uncertainty

Historical variance, 2= (R-)2/ (N-1)

Standard deviation, = 2

See example in text and also in the next slide

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Variance and Standard Deviation

Year ActualReturn

(R)

AverageReturn

()

Deviation fromthe Mean

d = (R-)

SquaredDeviation

d2

1 0.15 0.105 0.045 0.002025

2 0.09 0.105 -0.015 0.000225

3 0.06 0.105 -0.045 0.002025

4 0.12 0.105 0.015 0.000225

Totals 0.42 0.00 0.0045

Variance2=0.0045 / (4-1) = 0.0015

Standard Deviation= 0.03873 or 3.87 %

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Historical Returns and Std. Dev.

14

Secondlesson:2. The

greater thepotentialreward, thegreater therisk

Risk-Return

Tradeoff

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The Normal Distribution

Insert figure 12.11 here

Assumes normality but recent studies have shown that distributionshave fat tails. Whats the implication?

Extreme events are not that improbable!!! See Nassim Talebs Black Swan and Anti-Fragile

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Discussion on Risk premium

Suppose you want to invest in a project withthe same risk as a small-cap company, whatshould be the expected return?

Whats the return for small caps?

17.1% !!

So your IRR must be at least 17%.

If not better to invest in small-cap portfolio! See Fig 12.12 for risk premiums across the

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3. Efficient Capital Markets

Stock prices are in equilibrium or are fairlypriced If this is true, then you should not be able to earn

abnormal or excess returns What Makes Markets Efficient? There are many investors out there doing research

As new information comes to market, this information isanalyzed and trades are made based on this information

Therefore, prices should reflect all available publicinformation

If investors stop researching stocks, then the marketwill not be efficient

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EMH and Reaction to new information

Insert figure 12.13 here

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Common Misconceptions

about EMH

Efficient markets DO NOTimply that investorscannot earn a positive return in the stockmarket

They do mean that, on average, you will earna return that is appropriate for the riskundertaken and there is not a bias in pricesthat can be exploited to earn excess returns

Market efficiency will not protect you fromwrong choices if you do not diversifyyou stilldont want to put all your eggs in one basket

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Forms of Market Efficiency

Market efficiency is about whether informationgets incorporated in the price.

Eugene Fama suggests that information can

be organized into 3 categories. Each category relates to a particular form of

market efficiency.

Strong formSemistrong form

Weak formAll Information

All publicly available information

Information frommarketprices/vol

20

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Strong Form Efficiency

Prices reflect all information, including publicand private (insider information)

If the market is strong form efficient, then

investors could not earn abnormal returnsregardless of the information they possessed

Empirical evidence indicates that markets are

NOT strong form efficient and that insiders couldearn abnormal returns

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Semistrong Form Efficiency

Prices reflect all publicly available informationincluding trading information, annual reports,press releases, etc.

If the market is semistrong form efficient, theninvestors cannot earn abnormal returns bytrading on public information

Implies that fundamental analysis will not lead toabnormal returns

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Weak Form Efficiency Prices reflect all past market information

such as price and volume

If the market is weak form efficient, then

investors cannot earn abnormal returns bytrading on market information

Implies that technical analysis will not leadto abnormal returns

Empirical evidence indicates that marketsare generally weak form efficient

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4. Expected Returns

Expected returns are based on theprobabilities of possible outcomes

In this context, expected means averageif the process is repeated many times

The expected return does not even haveto be a possible return

where pi = probability of state i occurring

Ri= return when state i occurs

n

i

iiRpRE1

)(

24

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Example: Expected Returns

Suppose you have predicted the followingreturns for stocks C and T in threepossible states of the economy. What arethe expected returns?

State Probability C T

Boom 0.3 15 25

Normal 0.5 10 20

Recession ??? 2 1

RC= 0.3(15) + 0.5(10) + 0.2(2) = 9.9%

RT= 0.3(25) + 0.5(20) + 0.2(1) = 17.7%

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Variance and Standard

Deviation

Variance and standard deviation measure thevolatility of returns

Using unequal probabilities for the entirerange of possibilities

Weighted average of squared deviations

n

i

ii RERp1

22 ))((

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Example: Variance and Std. Dev.

Consider the previous example. What are thevariance and standard deviation for each stock?

Stock C

2= 0.3(15-9.9)2+ 0.5(10-9.9)2+ 0.2(2-9.9)2= 20.29

= 4.50%

Stock T

2= 0.3(25-17.7)2+ 0.5(20-17.7)2+ 0.2(1-17.7)2

= 74.41

= 8.63%

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5. Portfolios

A portfolio is a collection of assets

An assets risk and return are important in howthey affect the risk and return of the portfolio

The risk-return trade-off for a portfolio ismeasured by the portfolio expected return andstandard deviation, just as with individual assets

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Example: Portfolio Weights

Suppose you have $15,000 to invest and youhave purchased securities in the followingamounts. What are your portfolio weights in

each security? $2000 of DCLK

$3000 of KO

$4000 of INTC

$6000 of KEI

DCLK: 2/15 = 0.133

KO: 3/15 = 0.2

INTC: 4/15 = 0.267

KEI: 6/15 = 0.4

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Portfolio Expected Returns

The expected return of a portfolio is the weightedaverage of the expected returns of the respective assetsin the portfolio

You can also find the expected return by finding the

portfolio return in each possible state and computing theexpected value as we did with individual securities

m

j

jjP REwRE1

)()(

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Example: Expected Portfolio

Returns

Consider the portfolio weights computed previously. Ifthe individual stocks have the following expected returns,what is the expected return for the portfolio?

DCLK: 19.69%

KO: 5.25%

INTC: 16.65%

KEI: 18.24%

E(RP) = 0.133(19.69) + 0.2(5.25) + 0.267(16.65) +0.4(18.24) = 15.41%

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Portfolio Variance

Compute the portfolio return for each state:RP= w1R1+ w2R2+ + wmRm

Compute the expected portfolio return using the

same formula as for an individual asset Compute the portfolio variance and standard

deviation using the same formulas as for an

individual asset

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Example: Portfolio Variance

Consider the following information Invest 50% of your money in Asset A

State Probability A B

Boom 0.4 30% -5%

Bust 0.6 -10% 25% What are the expected return and standard

deviation for each asset? A-(6% & 19.6%) B-(13% & 14.7%)

What are the expected return and standarddeviation for the portfolio? 9.5% & 2.45%

Portfolio12.5%

7.5%

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6. Expected vs. Unexpected Returns

Realized returns are generally not equal toexpected returns There is the expected component and the

unexpected component At any point in time, the unexpected return can be either

positive or negative Over time, the average of the unexpected component is

zero

Announcements and news contain both anexpected component and a surprise component

It is the surprise component that affects a stocks priceand therefore its return This is very obvious when we watch how stock prices

move when an unexpected announcement is made orearnings are different than anticipated

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Efficient Markets

Efficient markets are a result of investorstrading on the unexpected portion ofannouncements

The easier it is to trade on surprises, themore efficient markets should be

Efficient markets involve random price

changes because we cannot predictsurprises

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7. Systematic & Unsystematic Risk

Systematic risk Risk factors that affect a large number of assets

Also known as non-diversifiable risk or market risk

Includes such things as changes in GDP,inflation, interest rates, etc.

Unsystematic risk

Risk factors that affect a limited number of assets

Also known as unique risk and asset-specific risk

Includes such things as labor strikes, partshortages, etc.

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Returns

Total Return = expected return + unexpectedreturn

Unexpected return = systematic portion +

unsystematic portion Therefore, total return can be expressed as

follows:

Total Return = expected return + systematic portion +

unsystematic portion

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8. Diversification & Portfolio Risk

Portfolio diversification is the investment in severaldifferent asset classes or sectors Diversification is not just holding a lot of assets For example, if you own 50 Internet stocks, you are not

diversified However, if you own 50 stocks that span 20 different industries,

then you are diversified Diversification can substantially reduce the variability of

returns without an equivalent reduction in expectedreturns This reduction in risk arises because worse than expected

returns from one asset are offset by better than expectedreturns from another

So, can the risk of a portfolio be totally diversifiedaway?

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Diversification and Portfolio Risk (cont)

M. Statman selected at random stocks from theNYSE to include in a portfolio.

Starting with one stock he kept on adding more

stocks to a portfolio and calculated the resultingrisk of the portfolio.

As more stocks were added, the portfolio riskdeclined . However, most of the benefits from

diversification were obtained with 10 stocks.With 30 stocks, there was little remaining benefitfrom diversification.

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Table 13.7 Std Dev of Annual Portfolio Returns

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Figure 13.1: Portfolio Diversification

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Unsystematic risk isessentially eliminatedby diversification

Total Risk =Systematic risk +Unsystematic risk

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9. Systematic Risk and Beta

There is a reward for bearing risk

There is not a reward for bearing riskunnecessarily

The expected return on a risky assetdepends only on that assets systematic risksince unsystematic risk can be diversified

away How do we measure systematic risk?

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Measuring Systematic Risk

How do we measure systematic risk? We use the beta coefficient

What does beta tell us?

A beta of 1 implies the asset has the same systematicrisk as the overall market

A beta < 1 implies the asset has less systematic riskthan the overall market

A beta > 1 implies the asset has more systematic risk

than the overall market E.g. If the markets returns increases by 10%, the stocks

return will increase by more than 10%

However, if the markets return decreases by 10%, the stocksreturn will decrease by more than 10%

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Table 13.8 coefficients for selected firms

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Total vs. Systematic Risk

Consider the following information:

Standard Deviation BetaSecurity C 20% 1.25

Security K 30% 0.95 Which security has more total risk?

Which security has more systematic risk?

Which security should have the higher expectedreturn?

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Example: Portfolio Betas

Consider the previous example with thefollowing four securities

Security Weight Beta

DCLK 0.133 2.685

KO 0.2 0.195

INTC 0.267 2.161

KEI 0.4 2.434

What is the portfolio beta? 0.133(2.685) + 0.2(0.195) + 0.267(2.161) +

0.4(2.434) = 1.947

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10 S it M k t Li d

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10. Security Market Line andCapital Asset Pricing Model

Remember that the risk premium = expectedreturnrisk-free rate

The higher the beta, the greater the risk

premium should be Can we define the relationship between the risk

premium and beta so that we can estimate the

expected return? YES!

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Market Equilibrium

In equilibrium, all assets and portfolios musthave the same reward-to-risk ratio, and they allmust equal the reward-to-risk ratio for the market

This is illustrated in the graph on the next slide.

M

fM

A

fA RRERRE

)()(

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Portfolio Expected Returns and Betas

0%

5%

10%

15%

20%

25%

30%

0 0.5 1 1.5 2 2.5 3

Beta

ExpectedR

eturn

Rf

E(RA)

A

ACF 2013

See pg455/6 fordata anddiscussion

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Reward-to-Risk Ratio

The reward-to-risk ratio is the slope of the lineillustrated in the previous example

Slope = (E(RA)Rf) / (A0)

Reward-to-risk ratio for previous example =(208) / (1.60) = 7.5

What if an asset has a reward-to-risk ratio of 8(implying that the asset plots above the line)?

What if an asset has a reward-to-risk ratio of 7(implying that the asset plots below the line)?

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Security Market Line

The security market line (SML) is therepresentation of market equilibrium

The slope of the SML is the reward-to-risk ratio:

(E(RM)Rf) / M But since the beta for the market is ALWAYS

equal to one, the slope can be rewritten

Slope = E(RM)Rf= market risk premium

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The Capital Asset Pricing

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The Capital Asset Pricing

Model (CAPM)

The capital asset pricing model defines therelationship between risk and return

E(RA

) = Rf

+ A

(E(RM

)Rf

)

If we know an assets systematic risk, wecan use the CAPM to determine itsexpected return

This is true whether we are talking aboutfinancial assets or physical assets

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Fig. 13.4: The Security Market Line

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Factors Affecting Expected

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Factors Affecting Expected

Return

Pure time value of money: measured bythe risk-free rate

Reward for bearing systematic risk:

measured by the market risk premium

Amount of systematic risk: measured bybeta

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Example - CAPM

Consider the betas for each of the assets givenearlier. If the risk-free rate is 4.15% and the marketrisk premium is 8.5%, what is the expected returnfor each?

Security Beta Expected ReturnDCLK 2.685 4.15 + 2.685(8.5) = 26.97%

KO 0.195 4.15 + 0.195(8.5) = 5.81%

INTC 2.161 4.15 + 2.161(8.5) = 22.52%KEI 2.434 4.15 + 2.434(8.5) = 24.84%

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Ethics Issues

Program trading is defined as automated tradinggenerated by computer algorithms designed toreact rapidly to changes in market prices. Is itethical for investment banking houses to operatesuch systems when they may generate tradeactivity ahead of their brokerage customers, towhich they owe a fiduciary duty?

Suppose that you are an employee of a printing firmthat was hired to proofread proxies that containedunannounced tender offers (and unnamed targets).Should you trade on this information, and would itbe considered illegal?

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