15.401 finance theory - mit opencourseware · slide 2 critical concepts ... npv and other valuation...

15.401

15.401 Finance Theory15.401 Finance TheoryMIT Sloan MBA Program

Andrew W. LoAndrew W. LoHarris & Harris Group Professor, MIT Sloan SchoolHarris & Harris Group Professor, MIT Sloan School

Lecture 12: Introduction to Risk and ReturnLecture 12: Introduction to Risk and Return

© 2007–2008 by Andrew W. Lo

© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return

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Critical ConceptsCritical ConceptsMotivationStatistical BackgroundEmpirical Properties of Stock ReturnsAnomalies

ReadingsBrealey, Myers, and Allen Chapters 7, 24.1, 24.4


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MotivationMotivation

NPV and Other Valuation Techniques Need Cost of CapitalOpportunity costRequired rate of returnRisk-adjusted discount rateDetermined by “the market”How???

Introduce Risk Into The Valuation ProcessHow to measure riskHow to estimate the required rate of return for a given level of riskRelated questions:– How risky are stocks and what have their returns been historically?– Is the stock market “efficient”?– How can we gauge the performance of portfolio managers?


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Statistical BackgroundStatistical BackgroundTerminology


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Statistical BackgroundStatistical BackgroundTerminology

Mean, variance, standard deviation:

Sample estimators:


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Statistical BackgroundStatistical BackgroundOther Statistics

Median– 50th percentile (probability of 1/2 that Rt < median)

Skewness– Is the distribution symmetric?– Negative: big losses are more likely than big gains– Positive: big gains are more likely than big losses

Correlation– How closely do two variables move together?


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Statistical BackgroundStatistical Background

Negatively Skewed Distribution

-5 -4 -3 -2 -1 0 1 2 3 4 5


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Examples of Correlation Between Two Random Variables

-4

-3

-2

-1

0

1

2

3

4

-4 -3 -2 -1 0 1 2 3 4

-4

-3

-2

-1

0

1

2

3

-4 -3 -2 -1 0 1 2 3 4

-4

-3

-2

-1

0

1

2

3

4

-4 -3 -2 -1 0 1 2 3 4

-4

-3

-2

-1

0

1

2

3

-4 -3 -2 -1 0 1 2 3 4

ρ = 0 ρ = .5

ρ = .8 ρ = –.5


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Statistical BackgroundStatistical BackgroundNormal Distribution

Bell-shaped, symmetricA model of randomnessCentral Limit Theorem

Confidence IntervalsIf R is normally distributed, then …

68% of observations fall within +/–1.00 std. deviations from mean90% of observations fall within +/–1.65 std. deviations from mean95% of observations fall within +/–1.96 std. deviations from mean99% of observations fall within +/–2.58 std. deviations from mean

-5 -4 -3 -2 -1 0 1 2 3 4 5


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GM Monthly Returns

0.00

0.07

0.14

0.21

-21% -15% -9% -3% 3% 9% 15% 21%


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Empirical Properties of Stock ReturnsEmpirical Properties of Stock ReturnsWhat Characterizes U.S. Stock Returns?

How volatile are stock returns?Are returns predictable?How does volatility change over time?What types of stocks have the highest returns?

What Properties Should Stock Prices Have In “Efficient” Markets?Random, unpredictablePrices should react quickly and correctly to newsInvestors cannot earn abnormal, risk-adjusted returns (or at least it shouldn’t be easy)


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Empirical Properties of Stock ReturnsEmpirical Properties of Stock Returns

Predictable Price Changes$

20

30

40

50

60

70

80


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Random Walks with Drift

$

50

55

60

65

70

75

80

0 10 20 30 40 50 60 70 80 90 100


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Empirical Properties of Stock ReturnsEmpirical Properties of Stock ReturnsFour facts from history of U.S. financial markets:1. Real interest rate has been slightly positive on average.2. Return on more risky assets has been higher on average than return

on less risky assets.3. Returns on risky assets can be highly correlated to each other.4. Returns on risky assets are (usually) serially uncorrelated.

Basic Statistics, U.S., 1946 – 2001 (monthly,in percent) Avg Stdev Skew Min MaxInflation 0.32 0.36 0.82 -0.84 1.85Tbill (1 yr) 0.38 0.24 0.98 0.03 1.34Tnote (10 yr) 0.46 2.63 0.61 -7.73 13.31VW stock index 1.01 4.23 -0.47 -22.49 16.56EW stock index 1.18 5.30 -0.17 -27.09 29.92Motorola 1.66 10.02 0.01 -33.49 41.67 NYSE, Amex, NASDAQ: 6,700 firms, $16.4 trillion market cap


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Total Return of Stocks, Bonds, Bills and Inflation 1946 – 2001

0.1

1

10

100

1000

10000

Dec-45 Dec-53 Dec-61 Dec-69 Dec-77 Dec-85 Dec-93 Dec-01

cpi tbill 10 note vw ew


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0%

3%

6%

9%

12%

15%

18%

Jun-53 Jan-63 Jun-72 Jan-82 Jun-91 Jan-01

1-yr Tbill 10-yr Tbond

Interest Rates 1953 – 2001


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-25%

-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%

25%

Jan-46

Jan-51

Jan-56

Jan-61

Jan-66

Jan-71

Jan-76

Jan-81

Jan-86

Jan-91

Jan-96

Jan-01

Total Returns, 10-Year U.S. T-Bond, 1946 – 2001


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-25%

-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%

25%

Jan-46

Jan-51

Jan-56

Jan-61

Jan-66

Jan-71

Jan-76

Jan-81

Jan-86

Jan-91

Jan-96

Jan-01

Total Returns, U.S. Stock Market 1946 – 2001


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-25%

-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%

25%


Total Returns, Motorola 1946 – 2001


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-2.0%

-1.0%

0.0%

1.0%

2.0%

-2.5% -1.5% -0.5% 0.5% 1.5% 2.5%

Scatterplot, VWRETD Today vs. Yesterday ,1980 – 1999


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Scatterplot, S&P 500 This Month vs. Last Month, 1926 to 1997

-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%

-25% -15% -5% 5% 15% 25%


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Scatterplot GM vs. S&P 500 Monthly Returns, 1946 – 1997

-25%

-17%

-8%

0%

8%

17%

25%

-35% -25% -15% -5% 5% 15% 25% 35%


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0%

1%

2%

3%

4%

5%

6%

Jan 26 Jan 36 Jan 46 Jan 56 Jan 66 Jan 76 Jan 86 Jan 96

Monthly Estimates of U.S. Stock Market Daily Volatility 1926 – 1997


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Anomalies: The Size Effect, 1964 Anomalies: The Size Effect, 1964 –– 2004 2004

8.0

10.0

12.0

14.0

16.0

Small 2 3 4 5 6 7 8 9 BigFirms sorted by MARKET CAPITALIZATION


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Anomalies: The January Effect, 1964 Anomalies: The January Effect, 1964 –– 20042004

0%1%2%3%4%5%6%7%8%9%

Small 2 3 4 5 6 7 8 9 Big

Firms sorted by MARKET CAPITALIZATION

All Months Januarys


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Anomalies: The Value Premium, 1964 Anomalies: The Value Premium, 1964 –– 2004 2004

8%

10%

12%

14%

16%

18%

Low 2 3 4 5 6 7 8 9 High

Firms sorted by PRICE / BOOK EQUITY


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Anomalies: Momentum, 1964 Anomalies: Momentum, 1964 –– 2004 2004

3%

6%

9%

12%

15%

18%

Low 2 3 4 5 6 7 8 9 High

Firms sorted by PAST 12-MONTH RETURN


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Anomalies: The Accrual Effect, 1964 Anomalies: The Accrual Effect, 1964 –– 20042004

3.0

5.0

7.0

9.0

11.0

13.0

15.0

Low 2 3 4 5 6 7 8 9 High

Firms sorted by last year's OPERATING ACCRUALS

*Operating income minus operating cashflows


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Anomalies: IPO Returns, 1970 Anomalies: IPO Returns, 1970 –– 1990 1990 Average Annual Returns, 1 – 5 Years After IPO

6.1%

14.1%13.3%

11.3%

14.3%

1.6%

3.6%5.0%

4.0%

11.6%

0%

4%

8%

12%

16%

1st year 2nd year 3rd year 4th year 5th yearIPOs

Non-issuers


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Anomalies: SEO Returns, 1970 Anomalies: SEO Returns, 1970 –– 19901990Average Annual Returns, 1 – 5 Years After SEO

12.9% 12.3%

16.2%17.7% 17.4%

6.6%

0.3%

7.5%9.1%

11.8%

0%

5%

10%

15%

20%

1st year 2nd year 3rd year 4th year 5th yearSEOs

Non-issuers


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Anomalies: Takeover Announcements Anomalies: Takeover Announcements Stock price of TARGET

40%

30%

20%

10%

0%

-10%-126 -105 -84 -63 -42 -21 0 21 42 63 84 105 126 147 168 189 210 231 252

Event date relative to first bid

Cum

ulat

ive

aver

age

abno

rmal

retu

rns

Stock Price of TARGET

UnsuccessfulSuccessful All

Image by MIT OpenCourseWare.


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Anomalies: Performance of Mutual FundsAnomalies: Performance of Mutual Funds

Estimates of individual mutual-fund alphas 1972 to 1991. The frequency distributionof estimated alphas for all equity mutual funds with 10-year continuous records.

36

32

28

24

20

16

12

8

4

0-3 -2 -1 0 1 2

Midpoint

# Fr

eque

ncy

Image by MIT OpenCourseWare.


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Key PointsKey PointsObservations

The average annual return on U.S. stocks from 1926 – 2004 was 11.2%.The average risk premium was 7.8%.Stocks are quite risky. The standard deviation of returns for the overall market is 4.5% monthly (16.4% annually).Individual stocks are much riskier. The average monthly standard deviation of an individual stock is around 17% (or 50% annually).Stocks tend to move together over time: when one stock goes up, other stocks are likely to go up as well. The correlation is far from perfect.Stock returns are nearly unpredictable. For example, knowing how a stock does this month tells you very little about what will happen next month.Market volatility changes over time. Prices are sometimes quite volatile. The standard deviation of monthly returns varies from roughly 2% to 20%.Financial ratios like DY and P/E ratios vary widely over time. DY hit a maximum of 13.8% in 1932 and a minimum of 1.17% in 1999. The P/E ratio hit a maximum of 33.4 in 1999 and a minimum of 5.3 in 1917.


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Key PointsKey PointsAnomalies:

Size Effect: Smaller stocks typically outperform larger stocks, especially in January.January Effect: Returns in January tend to be abnormally high.Value Effect: Low P/B (value) stocks typically outperform high P/B (growth) stocks.Momentum: Stocks with high returns over the past 12 months typically continue to outperform stocks with low past returns.Accruals and Issuances: Stocks with high past accruals and/or recent stock offerings typically underperform stocks with low past accruals and no stock offerings.


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Additional ReferencesAdditional ReferencesLefevre, E., 2006, Reminiscences of a Stock Operator. New York: John Wiley & Sons.

Malkiel, B., 1996, A Random Walk Down Wall Street: Including a Life-Cycle Guide to Personal Investing. New York: W.W. Norton.

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15.401 Finance Theory I Fall 2008

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15.401 finance theory - mit opencourseware · slide 2 critical concepts ... npv and other valuation...

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