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

Outline Introduction Experimental Setup Simulation with risk measures Sanity Check on Simulations Multi Risk Portfolio Development GUI for the Project Conclusions 2

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

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. 4 [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).

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 5

Measures of Risk Beta Volatility Market Capitalization Price-to-Book Ratio 6

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 7

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 8 1 st Jan st Dec 2008 Current Time K months N months

Simulations Gross return of the market over the last 40 years( ) 9

Simulations: Beta 10 Relative Return [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

Simulations: Beta (contd…) 11 Relative Return Sharpe Ratio

Simulations: Beta (contd…) 12 Gross return of beta portfolios over the last 40 years( )

Simulations: Volatility 13 Relative Return Sharpe Ratio

Simulations: Volatility (contd…) 14 Gross return of volatility portfolios over the last 40 years ( )

Simulations: Market Cap 15 Relative Return Sharpe Ratio

Simulations: Market Cap (contd…) 16 Gross return of market cap portfolios over the last 40 years ( )

Simulations: PB Ratio 17 Relative Return Sharpe Ratio

Simulations: PB Ratio (contd…) 18 Gross return of PB ratio portfolios over the last 40 years ( )

Sanity Check on Simulations 19 Plot the gross return of equal weighted S&P 500 along with gross return for equal investment across 10 portfolios

Sanity Check on Simulations (contd…) 20

Sanity Check on Simulations (contd…) 21

Sanity Check on Simulations (contd…) 22 Average Beta is calculated by taking average over all stocks in the portfolio

Sanity Check on Simulations (contd…) 23 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

Sanity Check on Simulations (contd…) 24 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

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 25 [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

Multi Risk Portfolio Development (contd…) 27 Relative Return Sharpe Ratio

Multi Risk Portfolio Development (contd…) 28

29 Multi Risk Portfolio Development (contd…)

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 10 th lowest beta 51 st lowest volatility 101 st lowest market cap 2 nd lowest PB ratio value Score = = 164 Sort the stocks based on the score from the lowest to the highest 30

AP Poll Style Portfolio Development (contd…) 31 Relative Return Sharpe Ratio

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 32

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 33 TCL based GUI (contd…)

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. 34