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ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

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Page 1: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

1

ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM

Mayur AgrawalVarun AgrawalDebabrata MohapatraVikas Yadav

Page 2: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

2

Outline Introduction Experimental Setup Simulation with risk measures Sanity Check on Simulations Multi Risk Portfolio Development GUI for the Project Conclusions

Page 3: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

3

Capital Asset Pricing Model (CAPM) Introduced by Jack Treynor(1961), William

Sharpe (1964), John Lintner(1965) and Jan Mossin (1966) independently

Attempts to relate the expected return of a stock with the systematic risk associated with it

The model has been very influential with William Sharpe winning the Nobel Prize for CAPM in 1990

Page 4: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

4

Issues with CAPM Does not appear to adequately explain the

variation in stock returns. Empirical results contrary to the model obtained

as early as in 1972 [1]. Many more results published subsequently

contradicting the CAPM findings.

[1] Fischer Black, Myron Scholes, & Micheal Jensen, "The Capital-Asset Pricing Model: Some empirical tests", in Jensen, editor, Studies in the Theory of Capital Markets (1972).

Page 5: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

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Objective Contribute to the study of counter intuitive

results on CAPM for various risk measures Demonstrate that ‘higher risk’ does not

necessarily translate into higher returns

Page 6: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

6

Measures of Risk Beta

Volatility

Market Capitalization

Price-to-Book Ratio

Cov( , )

Var( )s m

m

r r

r

2 Var( )s sr

MC = No. of outstanding shares Price per share

Market Price per sharePB Ratio =

Book Value per share

Page 7: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

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Experimental Setup Model the return of the market as the return

(value weighted/equal weighted) on S&P 500 index

Limit the universe of stocks to S&P 500 constituents

Page 8: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

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Experimental Setup (contd…)

Update S&P 500 member list every K months Estimate measure of risk for each stock in the list using

past N months of historical data Sort the stocks based on risk values Form P portfolios and readjust the portfolios every K

months If a security gets delisted, transfer all its investments to

the market portfolio

1st Jan 1962 31st Dec 2008Current Time

K monthsN months

Page 9: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

9

Simulations

Gross return of the market over the last 40 years(1969-2008)

0

20

40

60

80

100

120

140

160

1969

0102

1970

0903

1972

0503

1974

0107

1975

0905

1977

0505

1979

0105

1980

0904

1982

0506

1984

0104

1985

0903

1987

0505

1989

0103

1990

0831

1992

0501

1993

1230

1995

0830

1997

0430

1998

1230

2000

0830

2002

0509

2004

0109

2005

0912

2007

0516

Value weighted

Equal Weighted

Page 10: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

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Simulations: Beta

Low Beta

2 3 4 5 6 7 8 9 High Beta

-4.00%

-3.00%

-2.00%

-1.00%

0.00%

1.00%

2.00%

3.00%

4.00%

Relative market cap weighted return

1970-2005

S&P = 11.1%

Rela

tive

Retu

rn

Low Beta

2 3 4 5 6 7 8 9 High Beta

-3.00%

-2.50%

-2.00%

-1.50%

-1.00%

-0.50%

0.00%

0.50%

1.00%

1.50%

2.00%

Relative return from Exhibit 4 [2]

1969-2005

Rela

tive

Retu

rn

[2] J. Grantham,“The Nature of Risk III: The Role of Value and the Premium for Excitement or Speculation”, GMO Letters to the Investment Committee IX, October 2006

Page 11: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

11

Simulations: Beta (contd…)

-6.00%

-5.00%

-4.00%

-3.00%

-2.00%

-1.00%

0.00%

1.00%

2.00%

Low 2 3 4 5 6 7 8 9 High

Relative Return on Beta Portfolio

1969-2008

S&P = 11.5%

0

0.2

0.4

0.6

0.8

1

1.2

Low 2 3 4 5 6 7 8 9 High S&P

Annualized Sharpe Ratio for Beta

1969-2008

Rela

tive

Retu

rn

Sha

rpe

Rat

io

Page 12: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

12

Simulations: Beta (contd…)

0

50

100

150

200

250

1969

0102

1970

0216

1971

0326

1972

0504

1973

0619

1974

0730

1975

0909

1976

1018

1977

1129

1979

0110

1980

0220

1981

0401

1982

0512

1983

0621

1984

0731

1985

0910

1986

1021

1987

1201

1989

0111

1990

0221

1991

0403

1992

0512

1993

0622

1994

0802

1995

0912

1996

1021

1997

1201

1999

0113

2000

0224

2001

0405

2002

0523

2003

0707

2004

0817

2005

0927

2006

1107

2007

1220

Low

2

High

9

S&P

Gross return of beta portfolios over the last 40 years(1969-2008)

Page 13: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

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Simulations: Volatility

-3.50%

-3.00%

-2.50%

-2.00%

-1.50%

-1.00%

-0.50%

0.00%

0.50%

1.00%

1.50%

Low 2 3 4 5 6 7 8 9 High

Relative Return on Volatility Portfolio

1969-2008

S&P = 11.5%

00.10.20.30.40.50.60.70.80.9

1

Low 2 3 4 5 6 7 8 9 High S&P

Annualized Sharpe Ratio for Volatility

1969-2008

Rela

tive

Retu

rn

Sha

rpe

Rat

io

Page 14: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

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Simulations: Volatility (contd…)

0

20

40

60

80

100

120

140

160

180

1969

0102

1969

1210

1970

1112

1971

1019

1972

0921

1973

0830

1974

0806

1975

0711

1976

0615

1977

0519

1978

0426

1979

0330

1980

0305

1981

0209

1982

0114

1982

1217

1983

1121

1984

1025

1985

1002

1986

0908

1987

0812

1988

0718

1989

0621

1990

0525

1991

0501

1992

0403

1993

0310

1994

0210

1995

0118

1995

1221

1996

1125

1997

1030

1998

1007

1999

0914

2000

0817

2001

0725

2002

0708

2003

0612

2004

0518

2005

0425

2006

0330

2007

0308

2008

0212

Low

2

9

High

S&P

Gross return of volatility portfolios over the last 40 years (1969-2008)

Page 15: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

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Simulations: Market Cap

-3.00%

-2.50%

-2.00%

-1.50%

-1.00%

-0.50%

0.00%

0.50%

1.00%

1.50%

Low 2 3 4 5 6 7 8 9 High

Relative Return on market cap

1969-2008

00.10.20.30.40.50.60.70.80.9

Low 2 3 4 5 6 7 8 9 High S&P

Sharpe Ratio for market Cap

1969-2008

Rela

tive

Retu

rn

Sha

rpe

Rat

io

Page 16: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

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Simulations: Market Cap (contd…)

0

50

100

150

200

250

1969

0102

1970

0216

1971

0326

1972

0504

1973

0619

1974

0730

1975

0909

1976

1018

1977

1129

1979

0110

1980

0220

1981

0401

1982

0512

1983

0621

1984

0731

1985

0910

1986

1021

1987

1201

1989

0111

1990

0221

1991

0403

1992

0512

1993

0622

1994

0802

1995

0912

1996

1021

1997

1201

1999

0113

2000

0224

2001

0405

2002

0523

2003

0707

2004

0817

2005

0927

2006

1107

2007

1220

Low

2

9

High

S&P

Gross return of market cap portfolios over the last 40 years (1969-2008)

Page 17: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

17

Simulations: PB Ratio

-3.00%

-2.50%

-2.00%

-1.50%

-1.00%

-0.50%

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

Low 2 3 4 5 6 7 8 9 High

Relative Return on P/B ratio

1969-2008

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Low 2 3 4 5 6 7 8 9 High S&P

Sharpe Ratio for P/B ratio

1969-2008

Rela

tive

Retu

rn

Sha

rpe

Rat

io

Page 18: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

18

Simulations: PB Ratio (contd…)

0

50

100

150

200

250

300

350

400

1969

0102

1970

0227

1971

0420

1972

0608

1973

0803

1974

0925

1975

1114

1977

0107

1978

0302

1979

0424

1980

0613

1981

0806

1982

0928

1983

1116

1985

0109

1986

0304

1987

0424

1988

0615

1989

0807

1990

0927

1991

1118

1993

0111

1994

0302

1995

0425

1996

0614

1997

0806

1998

0929

1999

1119

2001

0112

2002

0314

2003

0507

2004

0630

2005

0822

2006

1013

2007

1207

Low

2

9

High

S&P

Gross return of PB ratio portfolios over the last 40 years (1969-2008)

Page 19: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

19

Sanity Check on Simulations

0

20

40

60

80

100

120

140

160

1969

0102

1970

0126

1971

0211

1972

0301

1973

0323

1974

0411

1975

0501

1976

0519

1977

0608

1978

0628

1979

0718

1980

0805

1981

0825

1982

0914

1983

0930

1984

1018

1985

1107

1986

1126

1987

1216

1989

0105

1990

0124

1991

0212

1992

0303

1993

0322

1994

0408

1995

0428

1996

0516

1997

0605

1998

0625

1999

0716

2000

0803

2001

0823

2002

0919

2003

1009

2004

1029

2005

1117

2006

1208

2008

0102

Beta

S&P 500

Plot the gross return of equal weighted S&P 500 along with gross return for equal investment across 10 portfolios

Page 20: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

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Sanity Check on Simulations (contd…)

0

20

40

60

80

100

120

140

160

1969

0102

1970

0126

1971

0211

1972

0301

1973

0323

1974

0411

1975

0501

1976

0519

1977

0608

1978

0628

1979

0718

1980

0805

1981

0825

1982

0914

1983

0930

1984

1018

1985

1107

1986

1126

1987

1216

1989

0105

1990

0124

1991

0212

1992

0303

1993

0322

1994

0408

1995

0428

1996

0516

1997

0605

1998

0625

1999

0716

2000

0803

2001

0823

2002

0919

2003

1009

2004

1029

2005

1117

2006

1208

2008

0102

Market Cap

S&P 500

0

20

40

60

80

100

120

140

160

1969

0102

1970

0126

1971

0211

1972

0301

1973

0323

1974

0411

1975

0501

1976

0519

1977

0608

1978

0628

1979

0718

1980

0805

1981

0825

1982

0914

1983

0930

1984

1018

1985

1107

1986

1126

1987

1216

1989

0105

1990

0124

1991

0212

1992

0303

1993

0322

1994

0408

1995

0428

1996

0516

1997

0605

1998

0625

1999

0716

2000

0803

2001

0823

2002

0919

2003

1009

2004

1029

2005

1117

2006

1208

2008

0102

Volatility

S&P 500

Page 21: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

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Sanity Check on Simulations (contd…)

0

20

40

60

80

100

120

140

160

1969

0102

1970

0126

1971

0211

1972

0301

1973

0323

1974

0411

1975

0501

1976

0519

1977

0608

1978

0628

1979

0718

1980

0805

1981

0825

1982

0914

1983

0930

1984

1018

1985

1107

1986

1126

1987

1216

1989

0105

1990

0124

1991

0212

1992

0303

1993

0322

1994

0408

1995

0428

1996

0516

1997

0605

1998

0625

1999

0716

2000

0803

2001

0823

2002

0919

2003

1009

2004

1029

2005

1117

2006

1208

2008

0102

PB Ratio

S&P500

Page 22: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

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Sanity Check on Simulations (contd…)

Average Beta is calculated by taking average over all stocks in the portfolio

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Low 2 3 4 5 6 7 8 9 High

Average Beta

1969-2008

Average Betas

Page 23: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

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Sanity Check on Simulations (contd…)

Average Beta is calculated by taking average over all stocks in the portfolio Portfolio Beta is estimated using portfolio return in last N (=60) months

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Low 2 3 4 5 6 7 8 9 High

Average Beta Portfolio Beta

1969-2008

Average and Portfolio Betas

Page 24: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

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Sanity Check on Simulations (contd…)

Average Beta is calculated by taking average over all stocks in the portfolio Portfolio Beta is estimated using portfolio return in last N (=60) months Future Beta is estimated using portfolio returns in next K (=12) months

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Low 2 3 4 5 6 7 8 9 HighAverage Beta Portfolio Beta Future Beta

Portfolio Betas

1969-2008

Page 25: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

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Multi Risk Portfolio Development It is known that single risk measures cannot

explain the expected stock returns [3],[4] Exploit multiple risk measures to develop better

portfolios We will limit to generation of portfolios based on

two risk measures

[3] Gabriel Hawawini, Donald B Keim, “The Cross Section of Common Stock Returns: A review of the evidence and some new findings”, 1997

[4] Eugene E. Fama, Kenneth R. French, “ Common Risk Factors in the Returns on Stock and Bonds”,1993

Page 26: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

Multi Risk Portfolio Development (contd…)

Re-sorting of each bin of stock based on beta

26

Page 27: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

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Multi Risk Portfolio Development (contd…)

-5.00%

-4.00%

-3.00%

-2.00%

-1.00%

0.00%

1.00%

2.00%

Low Vol 2 3 4 High Vol Low beta

2

3

High Beta

Rela

tive

Retu

rn

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Low Vol 2 3 4 High Vol S&P

Low Beta

2

3

High Beta

Sha

rpe

Rat

io

Page 28: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

28

Multi Risk Portfolio Development (contd…)

Page 29: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

29

Multi Risk Portfolio Development (contd…)

Page 30: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

30

AP Poll Style Portfolio Development Assign score to each stock in S&P 500 based on

its beta, volatility, market cap and PB ratio value. Example: Consider stock A with

• 10th lowest beta• 51st lowest volatility• 101st lowest market cap• 2nd lowest PB ratio value

Score = 10 + 51 + 101 + 2 = 164 Sort the stocks based on the score from the

lowest to the highest

Page 31: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

31

AP Poll Style Portfolio Development (contd…)

-7.00%

-6.00%

-5.00%

-4.00%

-3.00%

-2.00%

-1.00%

0.00%

1.00%

2.00%

1 2 3 4 5 6 7 8 9 10

Relative Return on AP Poll Portfolio

1969-2008

0

0.2

0.4

0.6

0.8

1

1.2

1 2 3 4 5 6 7 8 9 10 S&P

Sharpe Ratio of Portfolios

1969-2008

Rela

tive

Retu

rn

Sha

rpe

Rat

io

Page 32: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

32

TCL based GUI Implemented on the

Linux platform using Tcl

Two levels of sorting supported based on the risk measures

Automatic generation of plots shown previously

Page 33: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

33

Values entered are fed as command line parameters to the C++ executable running in the background

Tcl script calls MATLAB after the relevant data files have been generated by the C++ executable

MATLAB reads the data files and plots the required figures

Tcl used to integrate C++ and MATLAB code execution

Additional information on the parameters can be found under Help

Clear used to clean the message board Exit used to close the GUI session

TCL based GUI (contd…)

Page 34: ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav 1

34

Conclusions Investigated historical performance of stocks

against various risk measures Results obtained are fairly consistent with the

other contrary results present in the literature Optimal combination of risk measures to come

up with an ‘efficient portfolio’ is something worth exploring.