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ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM. Mayur Agrawal Varun Agrawal Debabrata Mohapatra Vikas Yadav. Outline. Introduction Experimental Setup Simulation with risk measures Sanity Check on Simulations Multi Risk Portfolio Development GUI for the Project Conclusions. - PowerPoint PPT Presentation
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1
ANALYZING THE NATURE OF RISK: TRUTH vs. CONVENTIONAL WISDOM
Mayur AgrawalVarun AgrawalDebabrata MohapatraVikas Yadav
2
Outline Introduction Experimental Setup Simulation with risk measures Sanity Check on Simulations Multi Risk Portfolio Development GUI for the Project Conclusions
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
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).
5
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
6
Measures of Risk Beta
Volatility
Market Capitalization
Price-to-Book Ratio
Cov( , )Var( )
s m
m
r rr
2 Var( )s sr
MC = No. of outstanding shares Price per share
Market Price per sharePB Ratio = Book Value per share
7
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
8
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
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
10
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
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
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)
13
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
14
Simulations: Volatility (contd…)
020406080
100120140160180
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)
15
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
16
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)
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
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)
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
20
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
21
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
22
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
23
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
24
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
25
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
Multi Risk Portfolio Development (contd…)
Re-sorting of each bin of stock based on beta
26
27
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
28
Multi Risk Portfolio Development (contd…)
29
Multi Risk Portfolio Development (contd…)
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 valueScore = 10 + 51 + 101 + 2 = 164
Sort the stocks based on the score from the lowest to the highest
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
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
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…)
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.