AQR - finansanalytiker.dk AQR CAPITAL MANAGEMENT Who is Warren Buffett? Born in Omaha, Nebraska Became the primary shareholder, chairman, and …

AQR C A P I T A LM A N A G E M E N TAQR C A P I T A LM A N A G E M E N T

Who is Warren Buffett?

Born in Omaha,

Nebraska

Became the primary shareholder, chairman, and CEO of Berkshire

Hathaway

Begins the Buffett Partnership

’30 … ’50 ’52 ’54 ’56 … ’70 … ’08 ’12

M.S. in Economics, Columbia University

Graham-Newman Corp., New York, Securities

Analyst

Buffet-Falk & Co., Omaha, Investment Salesman

Became the richest man in the world

2


Buffett’s Alpha: Outline of Talk

1. Research background:

Leverage constraints and asset prices

2. Can this theory also explain Buffett?

Track record: How good is Buffett?

Buffett’s Leverage

Decomposing Buffett: CEO vs. stock picker

Exposures: What type of stocks?

Systematic Buffett strategy

3

The Economist 9/29/12


1. Research background:

Leverage constraints and asset prices: 5 papers in 7 slides‒ For more information on this research, see http://people.stern.nyu.edu/lpederse/

Buffett’s Alpha: Outline of Talk

4


Research Background: The Day that Alpha Died

1969:

Consulting for Wells Fargo, Fischer Black and others Find that low-beta stocks have too high return relative to

CAPM

Wells Fargo decide not to trade on this effect required leverage to raise average returns

“Fischer stomped out … the nearly unique instance whenFischer lost his cool”

Attendance at aWells Fargo meeting:

Research questions:– Why do low-risk securities typically provide higher risk-adjusted returns?

– Do low-risk securities provide higher alphas– also after 1969?– within stock markets outside the U.S. stocks?– within other asset classes?– across asset classes?

– Can this explain Buffett?

Source: Provided by Wayne Wagner


Theory - Why? Theory of funding frictions and leverage constraints:

Investors like high returns, but often cannot or will not use leverage

Rather than using leverage, they overweight risky securities‒ Pushing up their price

‒ Lowering their expected return

6

The above example is for illustrative purposes only and is not based on an actual portfolio.

Exp

ecte

d R

etur

n

σ


Betting Against Beta

Proposition 1. [Frazzini-Pedersen (2010)] (i) The equilibrium required return for security s is:

where the risk premium is and ψ is the average Lagrange multiplier,measuring the tightness of funding constraints.

(ii) A security’s alpha with respect to the market decreases in the security’s market beta:

1s f s

t t t t tE r r

1M f

t t t tE r r

(1 )s st t t

Expected return

β

StandardCAPM

Funding liquidityCAPM

rf

α

αSource: Frazzini and Pedersen (2011). For illustrative purposes only.

7


Betting Against Beta: Test Across Global Asset ClassesAll Asset Classes, 1964 – 2009

8

US Stocks

‐0.40

‐0.30

‐0.20

‐0.10

0.00

0.10

0.20

0.30

0.40

0.50

P1(lowbeta)

P2 P3 P4 P5 P6 P7 P8 P9 P10(highbeta)

AlphaGlobal Stocks

‐0.70

‐0.60

‐0.50

‐0.40

‐0.30

‐0.20

‐0.10

0.00

0.10

0.20

0.30

P1(lowbeta)

P2 P3 P4 P5 P6 P7 P8 P9 P10(highbeta)Al

pha

Treasury

‐0.08

‐0.06

‐0.04

‐0.02

0.00

0.02

0.04

1 to 12months

13 to24

25 to36

37 to48

49 to60

61 to120

> 120

Alph

a

Credit Indices

‐0.08

‐0.06

‐0.04

‐0.02

0.00

0.02

0.04

0.06

1‐3 years 3‐5 year 5‐10 years 7‐10 years

Alpha

Credit ‐ CDS

‐0.05

‐0.04

‐0.03

‐0.02

‐0.01

0.00

0.01

0.02

0.03

0.04

1‐3 years 3‐5 year 5‐10 years 7‐10 yearsAlph

a

Credit ‐ Corporate

‐1.20

‐1.00

‐0.80

‐0.60

‐0.40

‐0.20

0.00

0.20

0.40

Aaa Aa A

Baa Ba B

Caa

Ca‐D

Distre

ssed

Alph

a

Equity Indices

‐0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Low beta High beta

Alph

a

Commodities

‐0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Low beta High beta

Alpha

FX

0.000.020.040.060.080.100.120.140.160.180.20

Low beta High beta

Alph

a

Country Bonds

‐0.01

‐0.01

0.00

0.01

0.01

0.02

0.02

0.03

0.03

Low beta High beta

Alph

a

Please see the Appendix for important information.


Betting Against Beta

Define a betting against beta portfolio as:

Proposition. [Frazzini-Pedersen (2010)] The expected return of a betting against betaportfolio is positive:

9

1 1 11 1BAB L f H f

t t tL Ht t

r r r r r

1 0H L

BAB t tt t tL H

t t

E r

Expected return

β

Long

Short

rf

Source: Frazzini and Pedersen (2011). For illustrative purposes only.


-0.2

0

0.2

0.4

0.6

0.8

1

US

stoc

ks

AU

S

AU

T

BEL

CA

N

CH

E

DEU

DN

K

ESP

FIN

FRA

GB

R

HK

G

ITA

JPN

NLD

NO

R

NZL SG

P

SWE

Glo

bal S

tock

s (al

l)

Cre

dit I

ndic

es

Cor

pora

te B

onds

Cre

dit H

edge

d (C

DS)

Trea

surie

s

Equi

ty In

dice

s

Cou

ntry

Bon

ds

Fore

ign

Echa

nge

Com

mod

ities

Betting Against Beta: Evidence From More than 100,000 Assets

Evidence within asset classes: Betting Against Beta

Within industries: Low-Risk Investing Without Industry Risk

Evidence across asset classes: Leverage Aversion and Risk Parity

Options and leveraged ETFs: Embedded Leverage

Source: Frazzini and Pedersen (2011). For illustrative purposes only.


Quality Minus Junk So far: risk measured using stock returns

Risk and other quality characteristics can also be measured using balance sheet data

Quality Minus Junk (QMJ): a portfolio long high quality and short low quality stocks

0.00

0.20

0.40

0.60

0.80

1.00

1.20 Risk-Adjusted Sharpe Ratio (4-factor model)

Source: Asness, Frazzini and Pedersen (2013), “Quality Minus Junk”

11


Understanding Buffett’s Alpha: Outline

1. Research background: Leverage Aversion

The Low Risk Anomaly

2. Can this theory also explain Buffett?

Track record: How good is Buffett?

Buffett’s Leverage

Decomposing Buffett: CEO vs. stock picker

Exposures: What type of stocks?

Systematic Buffett strategy

12

The Economist 9/29/12


How Good is Buffett’s Record?

Sharpe ratio: SR = excess return / volatility

Berkshire Hathaway (1976-2011): 0.76

Berskhire’s public stock holdings: 0.69

Information ratio:

Berkshire Hathaway (1976-2011): 0.66

Berskhire’s public stock holdings: 0.56

How does this stack up?

13

Please see the Appendix for important information. An investment in the above security does not suggest the achievement of a profit or loss, realized or unrealized. This security was selected merely for illustrative purposes.


How Good is Buffett’s Record? Information ratios of all U.S. stocks 1926 – 2011 in the CRSP universe

with more than 30 years of history

0

10

20

30

40

50

60

70

80

-0.40 -0.30 -0.19 -0.08 0.02 0.13 0.24 0.35 0.45 0.56 0.66

Buffett

14

Source: AQR. Please see the Appendix for important information.


Panel A: SR of Equity Mutual Funds

Number of stocks/funds

Median 95th Percentile 99th Percentile Maximum Rank Percentile

All funds in CRSP data 1976 - 2011 3,479 0.242 0.49 1.09 2.99 88 97.5%All funds alive in 1976 and 2011 140 0.37 0.52 0.76 0.76 1 100.0%All funds alive in 1976 with at least 10-year history 264 0.35 0.51 0.65 0.76 1 100.0%All funds with at least 10-year history 1,994 0.30 0.47 0.65 0.90 4 99.8%All funds with at least 30-year history 196 0.37 0.51 0.72 0.76 1 100.0%

Panel B: SR of Common StocksAll stocks in CRSP data 1926 - 2011 23,390 0.195 0.61 1.45 2.68 1360 93.9%All stocks alive in 1976 and 2011 598 0.32 0.44 0.56 0.76 1 100.0%All stocks alive in 1976 with at least 10-year history 3,633 0.27 0.45 0.61 0.86 7 99.8%All stocks with at least 10-year history 9,035 0.26 0.48 0.73 1.12 62 99.3%All stocks with at least 30-year history 1,777 0.31 0.44 0.57 0.76 1 100.0%

Buffett PerformanceSample Distribution of Sharpe Ratios

How Good is Buffett’s Record? Buffett’s track record has been exceptional

Berkshire Hathaway has a higher Sharpe ratio than any stock or mutual fund with ahistory of more than 30 years

If you could travel back in time and pick 1 stock, Berkshire Hathaway would be yourpick

15



Buffett: “I've seen more people fail because of liquor and leverage”

Stylized balance sheet of Berkshire Hathaway:

Leverage: 1.6

Does Buffett’s risk reflect the use of leverage?

Volatility of Berkshire Hathaway = 25% Volatility of the portfolio of Berkshire’s public stocks:17%

Buffett’s Leverage: The Magnitude of Leverage

Assets Liabilities and Shareholders' Equity

Publicly traded equities LiabilitiesPrivately held companies EquityCash

Total Assets Total Liabilities

16



Buffett’s Leverage: The Source of Leverage

Debt (rated AAA, 1989-2009)

Deferred income taxes (e.g., based on property, plant and equipment)

Accounts payable

Insurance float (36% of liabilities)

Derivatives:

Selling options Collects premia up front with no margin requirement Provides Embedded Leverage (Frazzini and Pedersen (2012))

17

* In years when cost of funds is reported as "less than zero" and no numerical value is available we set cost of funds to zero Please see the Appendix for important information. An investment in the above security does not suggest the achievement of a profit or loss, realized or unrealized. This security was selected merely for illustrative purposes.


Buffett’s Leverage: The Cost of Leverage Insurance float very cheap leverage for Buffett (36% of liabilities) :

Debt (AAA rated 1989-2009) Low interest term financing

Deferred income taxes (e.g., property, plant and equipment) and accounts payable Effectively zero interest

Selling expensive derivatives (provides Embedded Leverage, Frazzini and Pedersen(2012)): E.g., selling options, collects premia up front with no margin requirement

Fraction of years with negative cost

Average cost of funds (Trucated)*

T-Bill Fed Funds rate

1-Month Libor

6-Month Libor

10-Year Bond

1976-1980 0.79 1.67 -4.59 -5.65 -5.761981-1985 0.20 10.95 1.10 -0.27 -1.281986-1990 0.00 3.07 -3.56 -4.61 -4.80 -4.90 -5.301991-1995 0.60 2.21 -2.00 -2.24 -2.46 -2.71 -4.641996-2000 0.60 2.36 -2.70 -3.10 -3.33 -3.48 -3.562001-2005 0.60 1.29 -0.82 -0.96 -1.05 -1.19 -3.112006-2011 1.00 -4.00 -5.84 -6.06 -6.29 -6.59 -7.67

Full sample 0.60 2.20 -3.09 -3.81 -3.69 -3.88 -4.80

Spread over benckmark rates

18

* In years when cost of funds is reported as "less than zero" and no numerical value is available, we set cost of funds to zero


Assets Liabilities and Shareholders' Equity

Publicly traded equities LiabilitiesPrivately held companies EquityCash

Total Assets Total Liabilities

Decomposing Buffett: CEO or Stockpicker?

19

Stock picker

CEO Berkshire stock

Returns of Berkshire stock: observed directly

Publicly traded equities: observed via 13F filings and stock return data

Privately held companies inferred:

Liabilities Equity Public Cash

Private

Return decomposition:

1

Leverage:

Share of private holdings:Private Public

19


Decomposing Buffett: CEO or Stockpicker? Historical performance of Buffett’s components:

Berkshire Hathaway

Public U.S. stocks (from 13F filings)

Private holdings

Overall stock market

performance

Sample 1976-2011 1980-2011 1984-2011 1976-2011Beta 0.67 0.77 0.28 1.00Average excess return 19.0% 11.8% 9.6% 6.1%Total Volatility 24.8% 17.2% 22.3% 15.8%Idiosyncratic Volatility 22.4% 12.0% 21.8% 0.0%Sharpe ratio 0.76 0.69 0.43 0.39Information ratio 0.66 0.56 0.36 0.00Leverage 1.64 1.00 1.00 1.00Sub period excess returns:

1976-1980 42.1% 31.4% 7.8%1981-1985 28.6% 20.9% 18.5% 4.3%1986-1990 17.3% 12.5% 9.7% 5.4%1991-1995 29.7% 18.8% 22.9% 12.0%1996-2000 14.9% 12.0% 8.8% 11.8%2001-2005 3.2% 2.2% 1.7% 1.6%2006-2011 3.3% 3.0% 2.3% 0.8%

Buffett Performance

20



What Kind of Companies does Buffett Own - Who Takes the Other Side?

CAPM predicts that everyone holds the same portfolio (the market): Violated empirically in a systematic way

Evidence consistent with BAB theory of leverage constraints:

Investors with leverage aversion

Investors who apply leverage

21



What Kind of Companies does Buffett Own?

Regression to determine Buffett’s exposures:

MKT HML UMD BAB

BAB = Betting Against Beta (Frazzini and Pedersen (2011))

QMJ = Quality Minus Junk (Asness, Frazzini, and Pedersen (2012))

Alpha 12.5% 11.1% 7.0% 5.5% 4.7% 0.1% 5.8% 5.0% 4.9%(3.28) (2.92) (1.79) (2.60) (2.26) (0.04) (1.39) (1.20) (1.12)

MKT 0.84 0.78 0.97 0.86 0.83 1.04 0.40 0.35 0.35(11.49) (10.49) (10.62) (21.33) (19.86) (21.04) (4.92) (4.19) (3.33)

SMB -0.30 -0.39 -0.07 -0.18 -0.23 0.11 -0.29 -0.34 -0.33-(2.91) -(3.61) -(0.52) -(3.16) -(3.97) (1.52) -(2.53) -(2.93) -(2.09)

HML 0.47 0.30 0.21 0.30 0.19 0.10 0.26 0.14 0.13(4.24) (2.39) (1.72) (4.88) (2.74) (1.48) (2.19) (1.01) (0.97)

UMD 0.06 0.02 0.01 -0.02 -0.05 -0.06 0.08 0.05 0.05(0.86) (0.29) (0.16) -(0.60) -(1.34) -(1.69) (1.13) (0.63) (0.63)

BAB 0.27 0.18 0.16 0.07 0.18 0.18(3.12) (2.11) (3.50) (1.58) (2.07) (1.97)

Quality 1.40 1.49 0.04(3.50) (7.12) (0.08)

R2 bar 0.24 0.26 0.28 0.56 0.57 0.62 0.07 0.08 0.08

Berkshire stock 1976 - 2011 13F portfolio 1980 - 2011 Private Holdings 1984 - 20011

Please see the Appendix for important information. Past performance is no guarantee of future results. An investment in the above security does not suggest the achievement of a profit or loss, realized or unrealized. This security was selected merely for illustrative purposes. The public and private holdings are derived from Berkshire’s data as described in the paper.


Systematic Buffett-Style Strategy We can attribute a lot of Buffett’s performance to leverage and his focus on safe, high-

quality, value stocks

Can this be done in a systematic way?

Buffett-style strategy: systematic portfolio that

matches Buffett’s risk‒ beta

‒ idiosyncratic volatility

‒ total volatility

‒ simulates his use of leverage

matches Buffett’s relative factor loadings‒ simulates his investment style

rebalances monthly

23


Systematic Buffett-Style Strategy Constructing a Buffett-style portfolio:

Buffet style Buffett Active

Match Buffett’s market exposure: Buffett

Match Buffett’s active stock selection tilts:a) Find the relative active tilts:

Buffett

A

b) Apply leverage to match Buffett’s idiosyncratic volatility :

Active A A

24


Systematic Buffett-Style Strategy Based on Berkshire’s Hathaway

$0.10

$1.00

$10.00

$100.00

$1,000.00

$10,000.00

$100,000.00

Cum

ulat

ive

Ret

urn

(log

sca

le)

Berkshire HathawayBuffett-Style PortfolioOverall stock market (leveraged to same vol.)

25



Systematic Buffett-Style Strategy Based on Berkshire’s public stocks holdings

$1.00

$10.00

$100.00

$1,000.00

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010

Cum

ulat

ive

Ret

urn

(log

sca

le)

Berkshire's Public Stocks (from 13F filings)Buffett-Style Portfolio for Public StocksOverall stock market (leveraged to same vol.)

26



Berkshire Hathaway


Private holdings

Overall stock market

performance

Berkshire Hathaway


Private holdings

Sample 1976-2011 1980-2011 1984-2011 1976-2011 1976-2011 1980-2011 1984-2011Beta 0.67 0.77 0.28 1.00 0.67 0.77 0.28Average excess return 19.0% 11.8% 9.6% 6.1% 26.4% 18.4% 13.8%Total Volatility 24.8% 17.2% 22.3% 15.8% 24.8% 17.2% 22.3%Idiosyncratic Volatility 22.4% 12.0% 21.8% 0.0% 22.4% 12.0% 21.8%Sharpe ratio 0.76 0.69 0.43 0.39 1.06 1.07 0.62Information ratio 0.66 0.56 0.36 0.00 0.99 1.11 0.55Leverage 1.64 1.00 1.00 1.00 3.79 2.46 3.01Sub period excess returns:

1976-1980 42.1% 31.4% 7.8% 8.0% 30.7%1981-1985 28.6% 20.9% 18.5% 4.3% 46.4% 27.8% 22.1%1986-1990 17.3% 12.5% 9.7% 5.4% 17.9% 13.1% 7.0%1991-1995 29.7% 18.8% 22.9% 12.0% 41.7% 24.0% 30.9%1996-2000 14.9% 12.0% 8.8% 11.8% 39.4% 23.2% 28.8%2001-2005 3.2% 2.2% 1.7% 1.6% 28.5% 16.8% 10.4%2006-2011 3.3% 3.0% 2.3% 0.8% 3.3% 5.7% -8.1%

Buffett Performance Buffett-Style Portfolio

Systematic Buffett-Style Strategy Performance and Buffett and systematic Buffett-style portfolios

27



Conclusions

Buffett has delivered outstanding results over a very long time period Unique access to leverage

Leverages low-risk, high-quality, value stocks

Short sells options:‒ Securities with Embedded Leverage (Frazzini and Pedersen (2012))

Performance can be explained by His characteristics (leveraging value, low-risk, and quality stocks)

Consistent with theory of Black (1972) and Frazzini and Pedersen (2010):‒ Less-constrained investors may earn higher risk-adjusted return

‒ Leverage-constrained investors concentrate in risky assets

‒ A relatively flat Security Market Line can be part of a rational market equilibrium with constrained investors

28


What Does Buffett Say and Do – After Our Paper Buys H.J. Heinz Co.

Beta about 0.4

Profitable, stable business

Annual report, March 2013:


What Does Buffett Say and Do – After Our Paper

Annual report, March 2013:

30

Alternative Term Count

Consistent 20

Risk 74

Float 42

Term Count

Beta 0

Leverage 3


Disclosures

29

The information set forth herein has been obtained or derived from sources believed by AQR Capital Management, LLC (“AQR”) to be reliable. However, AQR does notmake any representation or warranty, express or implied, as to the information’s accuracy or completeness, nor does AQR recommend that the attached information serve asthe basis of any investment decision. The information is for illustration purposes only and neither the information nor any opinion expressed herein constitutes a solicitation orrecommendation by AQR for the purchase or sale of any securities or other financial instruments. AQR is not liable for any informational errors, incompleteness, or for anyactions taken in reliance on information contained herein. AQR is not responsible for the formatting or configuration of this material or for any inaccuracy in its presentationthereof.

An investment in the above security does not suggest the achievement of a profit or loss, realized or unrealized. This security was selected merely for illustrative purposes.

There is a risk of substantial loss associated with trading commodities, futures, options, derivatives and other financial instruments. Before trading, investors should carefullyconsider their financial position and risk tolerance to determine if the proposed trading style is appropriate. Investors should realize that when trading futures, commodities,options, derivatives and other financial instruments one could lose the full balance of their account. It is also possible to lose more than the initial deposit when tradingderivatives or using leverage. All funds committed to such a trading strategy should be purely risk capital.

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AQR - finansanalytiker.dk AQR CAPITAL MANAGEMENT Who is Warren Buffett? Born in Omaha, Nebraska Became the primary shareholder, chairman, and …