MSBC 5060Chapter 10Risk and Return:

Lessons From Capital Market History

1

We already know :Capital budgeting requires calculating the NPV:• Discounting future Cash Flows (Numerator)• At the Require Rate of Return (Denominator)

We also know :• Which Cash Flows to use…• Use the Stand-Alone Principle• Use Incremental Cash Flows associated with:

– Operations (OCF)– Capital Spending (NCS)– Working Capital (DNWC)

• Test the CF forecasts used to calculate the NPV – Sensitivity and Scenario analysis

Now we will start looking at the Required Rate of Return

2

The General Idea:• The appropriate discount rate for a

project (or a company)• Reflects the project’s risk

– The riskier the project, the higher the required return

– Why? Investors are RISK AVERSE– So how do we measure the project’s risk?– And once we know the risk, what is the

correct rate of return for that risk?

3

Start with this Assumption: • The new project has the SAME risk as the firm’s current

projects• Then we can use the rate or return firm is currently paying• But how do we calculate that?

• Later: What if the new project’s risk is different,– We can adjust the use the rate or return firm is currently

paying to account for difference in risk

• So we will look at:1. The general historic risk and return for all companies (the

market)2. The risk and return for different types of companies3. The risk for the company we’re analyzing

4

Goals1. The Mechanics of Calculating Returns2. Return Variability (aka Risk) – Standard

Deviation3. Look at the Historical Record for various

investment types4. Understand the Normal Distribution5. Arithmetic vs. Geometric Returns

5

Chapter Outline10.1 Returns10.2 Holding-Period Returns10.3 Return Statistics (Arithmetic Average Return)10.4 Average Stock Returns and Risk-Free Returns10.5 Risk Statistics

(Variance and Standard Deviation)10.6 More on Average Returns

(Arithmetic Mean vs. Geometric Mean) 10.7 The U.S. Equity Risk Premium: Historical and

International Perspectives10.7 2008: A Year of Financial Crisis

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10.1 ReturnsDollar Returns:

Bond Example:– You bought a bond for $950 1 year ago. – You have received two coupons of $30 each. – You can sell the bond for $975 today.

• Calculate your total dollar return:– Income = $30 + $30 = $60– Capital gain = $975 – $950 = $25– Total dollar return = $60 + $25 = $85

7

Dollar Returns:

Stock Example:– 1 year ago, you bought stock for $50 per share.– You received 4 dividends of $1.25 each– Today the price of the stock is $48

• Calculate your total dollar return:– Income = 4($1.25) =$5.00– Capital gain = $48 – $50 = -$2.00– Total dollar return = $5.00 – $2.00 = $3.00

8

Percent Returns:Of course dollar returns aren’t very useful!New Stock Example:

– 1 year ago, you bought stock for $100 per share.– You received 4 dividends of $1.25 each– Today the price of the stock is $98

• Calculate your total dollar return:– Income = 4($1.25) =$5.00– Capital gain = $98 – $100 = -$2.00– Total dollar return = $5.00 – $2.00 = $3.00

• Dollar returns are the same for $50 and $100 stocks!– Make $3.00 on $100 vs. Make $3 on $50

• We can see this is 3% vs. 6%

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Percent Return Formula

A little Algebra:

10

%3%5%2Return Total

%505.0$100

5$

P

D YieldDividen

%202.0$100

100$98$

P

PP YieldGain Capital

t

1t

t

t1t

1P

DP

P

D1

P

PReturn Total

P

D YieldDividen

1P

P

P

P

P

P

P

PP YieldGain Capital

t

1t1t

t

1t

t

1t

t

1t

t

1t

t

t

t

1t

t

t1t

Percent Return FormulaTotal Return = (P1 + D1)/ P0 - 1• A stock costs $100 today.• One year ago is was $90.• It paid a $3 dividend today• Calculate the return over the last year:

Total Return = R = ($100 + $3)/$90 - 1 = 1.1444 – 1 = 0.1444 = 14.44%

Note: $90(1 + R) = $90(1.1444) = $103

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10.2 Holding Period ReturnsThe Cumulative return• Earn 10% per year for 3 years:

– HPR = (1 + .10) x (1 + .1) x (1+ .1) – 1 = 33.10%– This is equal to (1 + .1)3 – 1 = 33.10%

• Instead earn 10%, -5%, 20% • HPR = (1 + .10) x (1 + -.05) x (1+ .2) -1 = 25.40%

HPR = (1 + R1) x (1 + R2) x … x (1 + RT) - 1

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10.3 Return Statistics• Measures of Dispersion: Variance and Standard

Deviation• Variance is the sum of the squared deviations from

the mean• Standard Deviation is the square-root of the Variance

Why divided the sum by T – 1 and not T when calculating Variance?13

T

1RRR

T

R R T21

T

1t t

RRRRRR1T

1

1T

RR RVar

2

T

2

2

2

1

T

1t

2

t2

2Var(R)RSD

How to Calculate Variance (s2) and Stdev (s)

Mean Return = 0.42/4 = 0.105 = 10.5%s2 = (Sum of Squared Deviations)/(T – 1) = 0.0045/(4 – 1) = 0.0015s = Square Root of Variance = (0.0015)½ = 0.0387 = 3.87% • The Standard Deviation is in the SAME units as the variable

– In this case % return, so it can be expresses as a %• Variance is NOT, so it can not be expressed as a %

Year ReturnAverage Return

Deviation from the Mean

Squared Deviation

1 .15 .105 .045 .002025

2 .09 .105 -.015 .000225

3 .06 .105 -.045 .002025

4 .12 .105 .015 .000225

Sum .42 .00 .0045

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How to Calculate Variance (s2) and Stdev (s)We’ll use Excel:

Year Return

1 15%

2 9%

3 6%

4 12%

=average() 10.5%

=var.s() .0015

=stdev.s() 3.87%

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The Historical Record• Why do we look at the historical record?• Do we care (directly) about what happened in

the past?– Maybe…

• What we do care about is the future.• So what will happen in the future?• Maybe our best guess is what has happened in

the past.• So we do care - indirectly - about the past

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So lets look at the Historical record:What has happened to:1. Large Stocks2. Small Stocks3. Corporate Bonds4. Long-Term Government debt (T-Bonds)5. Short-Term Government debt (T-Bills)

• Securities trade in financial markets– And market prices allow us to measure past returns and risk for

different securities

• So we’ll look at:– the historic returns – the variation in historic returns – Variance and Standard Deviation 17

Financial Markets: • Match SAVERS of funds with USERS of funds• Savers of funds INVEST in financial assets

– They can defer consumption (Save!)– And earn a return to compensate for the deferred

consumption• Users have access to unused capital

– They can invest in productive assets (Invest!)– IF… They can earn enough from those assets to pay the

return required by savers• We’ll examine financial markets to provide us with

information about the returns savers require for various levels of risk– Based on the type of security

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We’ll look at 5 types of Securities:1. Large-Company Stocks

– The S&P 500

2. Small-Company Stocks– Bottom 20% of NYSE by market cap

• So really “smaller” stocks• These are still NYSE stocks, so not that small

3. Long-Term, High-Quality Corporate Bonds– 20 years to maturity

4. Long-Term US Government Bonds– 20 year T-bonds

5. US Treasury Bills– 3 month T-bills

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20

Linear Scale vs Log ScaleWhat’s the difference?• Log Scale shows percent changes with equal

vertical size• From 100 to 110 is the same as 1000 to 1100• See to FF Spreadsheet…

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22

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Figures 10.5 and 10.6 • Note the Different Scales• Note the correlation between returns

Large Stocks Returns

Small Stocks Returns

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T-Bond Returns

T-Bill Returns

Figure 10.7• Again note the Different Scales T-Bonds -10% to 50%, T-bills 0 to 16% (never negative)• Again note the correlation between returns

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Figure 10.8• Annual Inflation• Again note Scale

Average Returns of Investment Categories

RReal = (1 + RNom)/(1 + i) – 1 = (1 +0.1650)/(1.0310) - 1 = 13.00%

Risk Premium = RNom – Risk-Free = 0.1650 – 0.0336 = 13.14%(T-Bills are risk-free)

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Category NominalReturn

RealReturn

Risk Premium

Small Stocks 16.50% 13.00% 13.14%

Large Stocks 11.80% 8.44% 8.44%

Long-term Corporate Bonds 6.40% 3.20% 3.04%

Long-term Government Bonds 6.10% 2.91% 2.74%

U.S. Treasury Bills 3.36% 0.25%

Inflation 3.10%

Average Returns RReal = (1 + RNom)/(1 + Inflation) – 1

For Small Stocks: RNom = 16.5% RReal = 13.00%

Money Doubled in Small Stocks:• Rule of 72’s: 72/16.5 = 4.36 years• =nper(rate, pmt, pv, [fv],[type])• =nper(.165,0,-1,2) = 4.54

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Average Returns RReal = (1 + RNom)/(1 + Inflation) – 1

For Small Stocks: RNom = 16.5% RReal = 13.0%

Purchasing Power Doubled in Small Stocks:• Rule of 72’s: 72/13.0 = 5.54 years• =nper(rate, pmt, pv, [fv],[type])• =nper(.130,0,-1,2) = 5.67

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10.4 Average Stock Returns and Risk-Free Returns

• The Risk-Premium is the return earned above the risk-free rate

• T-bills are risk free (Why?)Risk Premium = Average Return - Average T-bill Return

• This is the compensation for incurring risk associated with this investment class

• Make sure you can distinguish Risk Premium from Real Return

Average Risk Premium:Small stocks 16.50% – 3.36% = 13.14%Large stocks 11.80% – 3.36% = 8.44%

Risk Premium is a RETURN measure, not a risk measure 29

Variability of Returns (Risk)Recall Figure 10.4:• Why would you own

anything but small stocks?– Since the return is higher

• Because the variability is also higher

• If you have a short investment horizon…

• You could lose large amount in that short period

• How much could you lose in T-Bills over a short period?

• Nothing (or not very much?)• This is the essence of the

risk-return trade-off

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Risk: A Picture of the Dispersion of ReturnsStart with a Frequency Distribution for Large Stocks (Fig 10.9):Calculate Returns since 2009:

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Date S&P 500 Ann Return12/31/2008 903.25 12/31/2009 1,115.1012/31/2010 1,257.6412/30/2011 1,257.6012/31/2012 1,426.1912/31/2013 1,848.3612/31/2014 2,058.90

Risk: A Picture of the Dispersion of ReturnsStart with a Frequency Distribution for Large Stocks (Fig 10.9):Calculate Returns since 2009:

32

2009

Date S&P 500 Ann Return12/31/2008 903.25 12/31/2009 1,115.10 23.45%12/31/2010 1,257.6412/30/2011 1,257.6012/31/2012 1,426.1912/31/2013 1,848.3612/31/2014 2,058.90

Risk: A Picture of the Dispersion of ReturnsStart with a Frequency Distribution for Large Stocks (Fig 10.9):Calculate Returns since 2009:

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2009

2010Date S&P 500 Ann Return12/31/2008 903.25 12/31/2009 1,115.10 23.45%12/31/2010 1,257.64 12.78%12/30/2011 1,257.6012/31/2012 1,426.1912/31/2013 1,848.3612/31/2014 2,058.90

Risk: A Picture of the Dispersion of ReturnsStart with a Frequency Distribution for Large Stocks (Fig 10.9):Calculate Returns since 2009:

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2009

2010

2011

Date S&P 500 Ann Return12/31/2008 903.25 12/31/2009 1,115.10 23.45%12/31/2010 1,257.64 12.78%12/30/2011 1,257.60 0.00%12/31/2012 1,426.1912/31/2013 1,848.3612/31/2014 2,058.90

Risk: A Picture of the Dispersion of ReturnsStart with a Frequency Distribution for Large Stocks (Fig 10.9):Calculate Returns since 2009:

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2009

2010

2011

2012Date S&P 500 Ann Return12/31/2008 903.25 12/31/2009 1,115.10 23.45%12/31/2010 1,257.64 12.78%12/30/2011 1,257.60 0.00%12/31/2012 1,426.19 13.41%12/31/2013 1,848.3612/31/2014 2,058.90

Risk: A Picture of the Dispersion of ReturnsStart with a Frequency Distribution for Large Stocks (Fig 10.9):Calculate Returns since 2009:

36

2009

2010

2011

2012Date S&P 500 Ann Return12/31/2008 903.25 12/31/2009 1,115.10 23.45%12/31/2010 1,257.64 12.78%12/30/2011 1,257.60 0.00%12/31/2012 1,426.19 13.41%12/31/2013 1,848.36 29.60%12/31/2014 2,058.90

2013

Risk: A Picture of the Dispersion of ReturnsStart with a Frequency Distribution for Large Stocks (Fig 10.9):Calculate Returns since 2009:

37

2009

2010

2011

2012Date S&P 500 Ann Return12/31/2008 903.25 12/31/2009 1,115.10 23.45%12/31/2010 1,257.64 12.78%12/30/2011 1,257.60 0.00%12/31/2012 1,426.19 13.41%12/31/2013 1,848.36 29.60%12/31/2014 2,058.90 11.39%

2013

2014

Distributions and s’s 1926 to 2011

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Mean and Standard Deviation of Historic Returns

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Category Mean Return

Standard Deviation

Small Stocks 16.50% 32.50%Large stocks 11.80% 20.30%Long-term Corporate Bonds 6.40% 8.40%Long-term Government Bonds 6.10% 9.80%U.S. Treasury Bills 3.60% 3.10%Inflation 3.10% 4.20%

Interpreting the Distribution Measure (s)• What does s mean?

– It depends…• If we assume that the data is from a Normal Distribution

– Then s tells us a lot

• Recall for the Normal Distribution:– Mean +/- 1s contains 68.27% of the observations– Mean +/- 2s contains 95.45% of the observations – Mean +/- 3s contains 99.73% of the observations

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Interpreting the Distribution Measure (s)For the Large Stock Portfolio:• Mean Return = 11.8%• Standard Deviation (s) = 20.3%

• 68.27% of observations between 11.8% +/- 1 x 20.3% • Between -8.5% and 32.1%

• 95.45% of observations between 11.8% +/- 2 x 20.3%• Between -28.8% to 52.4%

• 99.73% of observations between 11.8% +/- 3 x 20.2%• Between -49.1% to 72.7%

Notice you can be MORE CONFIDENT about a WIDER interval! 41

Normal Distribution

• A large enough sample drawn from a normal distribution looks like a bell-shaped curve.

Probability

Return onlarge company commonstocks

99.73%

- 3 s- 49.1%

- 2 s- 28.8%

- 1 s- 8.4%

011.8%

+ 1 s32.1%

+ 2 s52.4%

+ 3 s72.7%

The probability that an annual return will fall within -8.5% and 32.1% is 68.26% (approximately 2/3).

68.27%

95.45%

Return Distributions (Risk) for Different Invest Classes:

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SS

LS

T-Bonds

-60.00% -40.00% -20.00% 0.00% 20.00% 40.00% 60.00% 80.00% 100.00%

Range of Returns with 95% Confidence (Mean +/- 2σ)

-2σ -1σ Mean +1σ +2σSS -48.50% -16.00% 16.50% 49.00% 81.50%LS -28.80% -8.500% 11.80% 32.10% 52.40%

T-Bonds -13.50% -3.70% 6.10% 15.90% 25.70%

95%

Return Probabilities Assuming NormalityAnother thing we can do:• Large Stock Mean = 11.8% and σ = 20.3%• Calculate the probability of a negative return in large stocks• P(R < 0) = ?

How far from the mean is 0?• How many stdevs to the left of the mean to get to 0?• z = (x – mean)/σ = (0 – 0.118)/0.203 = -0.581• So a little more than ½ a stdev from the mean to 0

How much of the curve is to the left of the mean - 0.581σ?• =NORMDIST(x, mean, standard_dev, cumulative)• =NORMDIST(0,0.118,0.203,1) = 0.2805 = 28.05%

28.05% chance of a negative return next year in large stocks44

Return Probabilities Assuming NormalityAnother way to do it:• Large Stock Mean = 11.8% and σ = 20.3%• Calculate the probability of a negative return in large stocks

How far from the mean is 0?• How many stdevs to the left of the mean to get to 0?• z = (x – mean)/σ = (0 – 0.118)/0.203 = -0.581

How much of the curve is to the left of the mean - 0.581σ?• =NORMSDIST(z)• =NORMSDIST(-.581) = 0.2805 = 28.05%

NORMDIST: Enter x, mean and σNORMSDIST: Enter only z

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Return Probabilities Assuming NormalityOne more example:• Large Stock Mean = 11.8% and σ = 20.3%• Calculate the probability of a return of at least 50% (R > 50%)

How far from the mean is 50%?• How many stdevs to the right of the mean to get to 50%?• z = (x – mean)/σ = (0.50 – 0.118)/0.203 = 0.382/0.203 = 1.882

How much of the curve is to the RIGHT of the mean + 1.86σ?• =NORMSDIST(z)• =NORMSDIST(1.882) = 0.9701 = 97.01%• 97.01% to the left or right?

• So what is the probability of a return greater then 50%?• P(R > 50%) = 1 – 0.9701 = 2.99%

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Return Probabilities Assuming NormalityLast example:• Large Stock Mean = 11.8% and σ = 20.3%• Calculate the probability earning between 10% and 30%

How far from the mean is 10%?• z = (x – mean)/σ = (0.10 – 0.118)/0.203 = -0.018/0.203 = -.089• =NORMSDIST(-0.089) = 0.4647• P(R < 10%) = 0.4647 = 0.4647 = 46.47%

How far from the mean is 30%?• z = (x – mean)/σ = (0.30 – 0.118)/0.203 = 0.182/0.203 = 0.897• =NORMSDIST(0.897) = 0.8150• P(R < 30%) = 0.8150 = 81.50%

P(R > 10% and R < 30%) = 81.50% - 46.47% = 35.03%47

How Good is the Normal Distribution Assumption?

• Are security returns Normally distributed?• It’s okay, but not great.

The actual distribution tends to have:• Larger Left Tail:

– Large negative returns are more likely than predicted by the Normal Dist

– This is measure by the “negative skew”

• “Fatter Tails”– Large returns are more likely than predicted by the

Normal Dist– This is measured by the “kurtosis” 48

How Good is the Normal Distribution Assumption?• Recall for large stocks: • Mean 11.8% and Stdev 20.3%

• So If you assume Normality:• =normsinv(0.05) = -1.645• 5% of the curve is to the left of:

11.8% + (-1.645) x 20.3% = -21.59%

• So assuming Normality, we estimate that there is only a 5% chance you will lose more than 21.59% in large stocks in a year

• This is called the 5% Value at Risk • But if the distributional assumption IS NOT CORRECT…• Then the probability of a loss greater than 21.59%

is greater than 5% 49

What do we do with these Values?• Suppose we have a project we believe has the same

risk as the risk associated with “large stocks”– The historic Risk Premium for large stocks is 8.44% – (See slide 24)

• On 7/29/2015, 1 year T-Bills were paying 0.33%– So we can earn 0.33% over the next year without risk

• So on this project we might expect to earn:– The risk free rate plus a Premium for incurring risk– Risk Free = 0.33% – Premium for incurring the risk = 8.44%– Expected Return = 0.33% + 8.44% = 8.77%– This might be a reasonable Expected Return for a project

of this risk50

What do we do with these Return and Risk Values?• What if the proposed project is 25% riskier than large

stocks?– This means the volatility of the project’s return will be 25%

greater than large stock volatility– So the project needs to earn more than 0.33% + 8.44% = 8.77%– But how much more?

• Increase the Risk Premium by 25%:– Multiply the risk premium by (1 + 0.25) = 1.25– Then add the risk-free rate

• Expected Return = 0.33% + 1.25(8.44%) = 0.33% + 10.55% = 10.88%

• This is an application of something called the CAPM• We’ll talk about how to get the 25% riskier (or the 1.25) soon

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Geometric Mean vs. Arithmetic Mean Returns• Two Different Questions:1. What can I expect to earn next year?

– Was the average of the annual returns?– Calculate the return for an average year– In any year, what can I expect the return to be?– This is the Arithmetic mean

2. What was the average annual return over the holding period?– In annualized terms, what return did I earn over the holding period?– What return, that is same in each year, replicates the performance?– This is the Geometric Mean

Arithmetic Mean = (R1 + R2… + RN)/NGeometric Mean = [(1 + R1)(1 + R2)…(1 + RN)]1/N – 1

Example Calculations:R1 = -20% and R2 = 25%Arithmetic Mean = (-0.20 + 0.25)/2 = 0.025 = 2.5%Geometric Mean = [(1 +(-0.20))(1 + 0.25)]1/2 =[(0.80)(1.25)]1/2 – 1 = 0%

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Geometric vs. Arithmetic (Continued 1)• Let’s see why these answers are not that same:Recall the 2 Different Questions:• Arithmetic Mean:

– What can I expect the return to be next year?

• Geometric Mean: – In annual terms, what return did I earn over the holding period?

Example: P0 = $100, P1 = $80, P2 = $100• Calculate the two annual returns and then the averages:

R1 = $80/$100 – 1 = -0.20 = -20%

R2 = $100/$80 – 1 = 0.25 = 25%

Arithmetic Mean = (-20% + 25%)/2 = 2.5%Geometric Mean = [(1 +(-0.20))(1 + 0.25)]1/2 =[(0.80)(1.25)]1/2 – 1 = 0%

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Review Question:• Two years ago, a manager lost 40%.• Last year the manager made 25%What was the annualized return over the two years?What return do you expect the manager to earn this year?

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Review Answer:• Two years ago, a manager lost 40%.• Last year the manager made 25%

• What was the Annualized Return over the two years?Geometric Mean: (1 - 0.40)(1 + 0.25)½ - 1 = -13.40%

• What return do you Expect the manager to earn this year?Arithmetic Mean: (-0.40 + 0.25)/2 = -7.50%

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Extra Explanation:• Note that $100 after the first year would be worth:

$100(1 + R) = $100(1 - 0.40) = $100(0.60) = $60• After the second year it would be worth:

$60(1 + R) = $60(1 + 0.25) = $60(1.25) = $75

• A 40% loss followed by a 25% gain is the same as two 13.40% losses:

• $100(1 – 0.1340) = $86.60$86.60(1 – 0.1340) = $75

• So the Geometric Mean Return is the ONE annual return that is equivalent to the observed series

Lose 40%, then make 25% same as lose 13.40% twice

Geometric vs. Arithmetic

• Note that the Geometric Mean is smaller than the Arithmetic Mean– Always true (unless they are equal)

• The difference is a function of the level of volatility of the returns– If there is no volatility (which all the returns are equal) then Geometric Mean

equals Arithmetic Mean• An approximate relationship:

Geometric Mean = Arithmetic Mean – σ2/2Large Stocks: 0.1180 – (0.2030)2/2 = 0.0974 = 9.74% ≈ 9.78%Small Stocks: 0.1650 – (0.3250)2/2 = 0.1122 = 11.22% ≈ 11.88%

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Category Arithmetic Geometric σLarge stocks 11.80% 9.78% 20.30%Small Stocks 16.50% 11.88% 32.50%

Geometric vs. Arithmetic

Recall Figure 10.4• Use these values to

calculate Annualized Holding Period Returns:

Large Stocks: $1 to $3,045.03 over 86 yrs($3,045.03/$1)(1/86) – 1 = 9.78%

Small Stocks: $1 to $15,534.66 over 86 yrs($15,534.66/$1)(1/86) – 1 = 11.88%

Geometric Return also equal to:

R = (FV/PV)(1/N) – 1Same as:

R = (PN/P0)(1/N) – 1

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Geometric Mean• Returns earned each year by Large Stocks between 1925 and 2011 • From Table 10.1 Page 315

Earning all of these returns, results in $1 growing to $3,045.22 in 86 years

Earning 9.78% in each year also results in $1 growing to $3,045.22 in 86 years

So 9.78% is the geometric mean of this series of returns.

Alternative Formulas:R = (FV/PV)(1/N) – 1R = (PN/P0)(1/N) – 1

59

Geometric vs. ArithmeticThink about risk and return and how it effects holding period return:• Look at the arithmetic mean and s of the historic returns for two investments• Think about what the annualized holding period return might be in the future

Category Arith Mean s Investment 1 18% 30% Investment 2 21% 40%

Annualized Holding Period Return:1: Geometric Mean ≈ Arithmetic Mean – s2/2 = 0.18 – 0.302/2 = 13.5%

2: Geometric Mean ≈ Arithmetic Mean – s2/2 = 0.21 – 0.402/2 = 13.0%

• Investment 2 has the higher expected return in any given year• Investment 1 has the higher expected holding period return

Why?

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Longer Holding Periods:• Look at 20 year holding periods for Small Stocks and Large Stocks • I used a “Bootstrap Simulation” to estimate a large number of 20

year holding period returns for each asset class. • Next I calculate the arithmetic mean of the 20yr holding-period

returns• This is the arithmetic mean of the geometric means

What does this tell us about holding Stocks for 20 years?

61

Arithmetic Mean of 20 yr Holding Periods σ

SS 12.1% 5.1%LS 9.5% 4.1%

Return Distributions (Risk) for 1yr and 20yr

62

-2σ -1σ Mean +1σ +2σSS 1yr -48.5% -16.0% 16.5% 49.0% 81.50%

SS 20yr 1.9% 7.0% 12.1% 17.2% 22.3%

SS 1yr

SS 20yr

-50% -40% -30% -20% -10% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90%

Range of Returns with 95% Confidence (Mean +/- 2σ)

95%

Other Common Stock Categories:• Besides large and small

A common way to categorized stocks by:1. Market Value aka Market Cap

–Categories are Large, Mid and Small–Multiply the price per share by number of shares–This is what is costs to buy the company

2. The relative position of the company in the range of PE and Market-to-Book ratios –Categories are Growth, Balanced, Value–Are you buying a company’s stock because

• You expect it to grow or because it has current profits?

• These two factors (3x3) create nine categories – Called “styles”– Represented by “Style Boxes”– See Morningstar.com

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Indices and ETF tickers that Track Each Style:

• But for now we’ll stick to just two categories of stocks (Small and Large ) as well as bonds

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Value Balanced Growth

Large S&P 500 Value(IVE)

S&P 500(IVV)

S&P 500 Growth(IVW)

Mid S&P 400 Value(IJJ)

S&P 400(IJH)

S&P 400 Growth(IJK)

Small S&P 600 Value(IJS)

S&P 600(IJR)

S&P 600 Growth(IJT)

65

Where do we go from here?

MORE Risk and Return• We have an idea of how to measure TOTAL

risk• Can we break risk down into categories?• What happens if we combine stocks into a

portfolio?• What is the portfolio’s risk?• For what types of risk are you compensated?• We’ll introduce a basic model to look at this…• The CAPM