15.401 finance theory - mit opencourseware · slide 2 critical concepts ... npv and other valuation...
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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
15.401
Slide 2
Critical ConceptsCritical ConceptsMotivationStatistical BackgroundEmpirical Properties of Stock ReturnsAnomalies
ReadingsBrealey, Myers, and Allen Chapters 7, 24.1, 24.4
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Slide 3
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?
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Slide 4
Statistical BackgroundStatistical BackgroundTerminology
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Slide 5
Statistical BackgroundStatistical BackgroundTerminology
Mean, variance, standard deviation:
Sample estimators:
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Slide 6
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?
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Slide 7
Statistical BackgroundStatistical Background
Negatively Skewed Distribution
-5 -4 -3 -2 -1 0 1 2 3 4 5
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Slide 8
Statistical BackgroundStatistical Background
Examples of Correlation Between Two Random Variables
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-4 -3 -2 -1 0 1 2 3 4
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-4 -3 -2 -1 0 1 2 3 4
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-4 -3 -2 -1 0 1 2 3 4
ρ = 0 ρ = .5
ρ = .8 ρ = –.5
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
15.401
Slide 9
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
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Slide 10
Statistical BackgroundStatistical Background
GM Monthly Returns
0.00
0.07
0.14
0.21
-21% -15% -9% -3% 3% 9% 15% 21%
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Slide 11
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)
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Slide 12
Empirical Properties of Stock ReturnsEmpirical Properties of Stock Returns
Predictable Price Changes$
20
30
40
50
60
70
80
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Slide 13
Empirical Properties of Stock ReturnsEmpirical Properties of Stock Returns
Random Walks with Drift
$
50
55
60
65
70
75
80
0 10 20 30 40 50 60 70 80 90 100
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Slide 14
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
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Slide 15
Empirical Properties of Stock ReturnsEmpirical Properties of Stock Returns
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
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Empirical Properties of Stock ReturnsEmpirical Properties of Stock Returns
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
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Slide 17
Empirical Properties of Stock ReturnsEmpirical Properties of Stock Returns
-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
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Slide 18
Empirical Properties of Stock ReturnsEmpirical Properties of Stock Returns
-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
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Slide 19
-25%
-20%
-15%
-10%
-5%
0%
5%
10%
15%
20%
25%
Empirical Properties of Stock ReturnsEmpirical Properties of Stock Returns
Total Returns, Motorola 1946 – 2001
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Slide 20
Empirical Properties of Stock ReturnsEmpirical Properties of Stock Returns
-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
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Slide 21
Empirical Properties of Stock ReturnsEmpirical Properties of Stock Returns
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%
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Slide 22
Empirical Properties of Stock ReturnsEmpirical Properties of Stock Returns
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%
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Slide 23
Empirical Properties of Stock ReturnsEmpirical Properties of Stock Returns
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
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Slide 24
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
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Slide 25
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
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Slide 26
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
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Slide 27
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
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Slide 28
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
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
15.401
Slide 29
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
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Slide 30
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
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Slide 31
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.
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
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Slide 32
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.
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
15.401
Slide 33
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.
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
15.401
Slide 34
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.
© 2007–2008 by Andrew W. LoLecture 12: Intro to Risk and Return
15.401
Slide 35
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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