Quantitative Equity Portfolio Management

1. Quantitative Equity Portfolio Management Michael J Cooper Associate Professor of Finance Krannert Graduate School of Management Purdue University West Lafayette, IN 47907-1310 mcooper@purdue.edu http://www.mgmt.purdue.edu/faculty/mcooper

2. Outline of talk • Is there any way to beat the market? • Can we make profits following the prophets? • Performance evidence, persistence tests, performance measures, transaction costs • Can we make profits using quantitative back testing methods? • Caveats, some examples of back testing (accounting ratios, momentum), examples of real-world mutual funds that follow this approach, putting it all together; how to do your own screens and form your own portfolios, the experiences of the Purdue student managed investment fund.

3. Implications of the “professionals” inability to pick future winners • Use a method of rigorous quantitative backtesting of investment strategies. • Large body of research (using this approach) that suggests numerous investment strategies which appear to have historically outperformed the market.

4. Features of a quantitative approach • Based on comprehensive historical databases. • (CRSP) All stocks back to the early 1920’s for the USA. • Prices, volume, dividends • Studies typically forecast “returns” • Return = (Pricet-Pricet-1+ dividend)/Pricet-1 • (Compustat) Annual and quarterly accounting data (B/M, E/P, D/P, C/P, etc.) back to 1955 for the USA. • (FRED) Macro economic data (GDP, interest rates, oil prices, etc.) • International data: Datastream, Bloomberg, others.

5. Features of a quantitative approach • Employ statistical techniques such as regressions and sorts to find significant patterns in the historical data. • Typical regressions: regress monthly returns of firm i on lagged firm characteristics. • Rit = a + b1*B/Mt-1 + b2*C/Pt-1 + b3*sizet-1 + … • The significant coefficients (as judged by t-statistics) from the regressions tell us which lagged characteristics are important. • Typical sorts: sort all firms each year into ten groups (deciles) based off last year’s B/M ratio of each firm. • Bottom line: It appears that we can predict future changes in stock prices!

6. Side issues to think about concerning quantitative research based investment strategies • If it’s so good, why the heck doesn't everyone do it!!?? • Over fitting the data (data mining). • Incorporating in transaction costs to profit estimates.

7. If it’s so good, why the heck doesn't everyone do it!!?? • Many of the best quant. strategies are based on “value” type portfolios of stocks. • Many investors are “afraid” to invest in “risky” value stocks. • Many investors naively assume that past trends in earnings growth of both growth and value firms will continue, ignoring mean reversion in performance.

8. Over fitting the data (data mining). • Seeing past trends in the data that are not real, and not likely to work going forward. • Finding spurious patterns is a big problem with today’s high-powered computers. • Example: generate 100 random data series. Run 100 regressions; regress market returns against the random data, and report the best models based on rsq. What will you find?

12. Over fitting the data (data mining). • Solutions: • Historical back testing methods using out-of-sample instead of in-sample approaches. • In-sample – using the entire period to identify and test strategies • Out-of-sample – using a prior period to identify strategies, and then testing them on a hold-out-sample. • Use an in-sample approach, but examine subperiod stability of profits and relations between returns and lagged predictor variables. • Simulations: what would we find by chance. Then adjust the “null” for the by-chance profits.

13. Modeling transaction costs. • If gross profits to an investment strategy average 1% per month, but transactions costs average 1.5% round trip, you will loose 0.5% per month on average. • What are the costs to trade? • Commissions • Bid/ask spreads • Price pressure effects

15. Historical quantitative back testing • We will examine a few studies which document the predictability of future returns using firm specific information. • Accounting variables: • B/M, E/P, C/P, D/P, and others • Asset growth rates • Momentum: • Prior period firm stock price performance; Winners and losers.

16. Contrarian Investment, Extrapolation, and Risk,” 1994, Journal of Finance 49, 1541-1578. Lakonishok, J., A. Shleifer, and R. W. Vishny. • Methodology • Examine returns to trading strategies using firm-specific accounting ratios. • Annual rebalancing using yearly values of accounting ratios. • Use one-way decile and two-way 3x3 sorts. • Examine spread in annual returns across the different portfolios.

24. Asset Growth and Stock Returns, 2005, Cooper, Gulen, and Schill • Methodology • Examine returns to trading strategies using firm-specific asset growth information. • Is there an optimal firm growth rate? Is it better to grow slow or fast? Does it matter how the growth is financed? • Annual rebalancing using yearly values of growth-in-total-book assets and other accounting ratios. • Use one-way decile and two-way 5x5 sorts. • Examine spread in annual returns across the different portfolios.

27. Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency, 1993, Journal of Finance 48: 65-91, Narasimhan Jegadeesh and Sheridan Titman. • Methodology • Examine returns to trading strategies using firm-specific lagged returns (3, 6, 9, and 12 month holding period returns). • Do prior period winners keep winning, and losers keep losing? • 3, 6, 9, and 12 month rebalancing periods. • Use one-way decile sorts. • Examine spread in annual returns across the different portfolios.

29. Summary of the 3 studies • These three studies are a small sampling of the published and non-published predictability studies (see ssrn.com for a lot more!) • Many firms employ their own researchers to do "double top secret" in-house research, building on these types of studies. Lets look at some examples of investment companies that use a quantitative approach.

34. Lets go visit LSVasset.com and Dfaus.com

35. Purdue Krannert Business School Student Managed Investment Fund • Founded in 1997 • Initial Funding $100,000 Alumni Venture Capitalist, has grown to over $300k • 50+ Members • Current 4-time (2002-2005) “National Champions” of student managed investment funds (University of Dayton RISE competition, sponsored by CNBC/NYSE)

36. Purdue students get to ring the closing bell on the NYSE – it was an UP day!

37. Putting it all together…lets see how to form our own quant-based portfolios! • We will use the information from the 3 studies we discussed; accounting ratios and lagged returns. • The exact screening rule comes from SAS programs which perform regressions and sorts on a large database of stock returns and predictor variables.

38. Example SAS code: 5 way sorts %MACROCALCMEAN; proc datasets nolist;delete rulesone; %DO N=1%TO 12; /* month loop*/ %DO I=0 %TO &gridvar1-1; %DO J=0 %TO &GRIDVAR2-1; %DO k=0 %TO &GRIDVAR3-1; %DO L=0 %TO &GRIDVAR4-1; %DO M=0 %TO &GRIDVAR5-1; DATA t1TEMP;SET t2TEMP; IF gridvar1 =&I and gridvar2=&J and gridvar3=&k and gridvar4=&L and gridvar5 =&m and month=&N; PROC SUMMARY DATA=t1TEMP NWAY FW=9; CLASS caldt; VAR MRETV cvar1 cvar2 cvar3 cvar4 cvar5 lcapsum dolvol; OUTPUT OUT=LONG1 N=WEEKCT MEAN=mretv cvar1 cvar2 cvar3 cvar4 cvar5 lcap dolvol %END; %END; %end; %end; %end; %end;

39. An example of optimal rules • 3 way screen: Buy all stocks in the top quintile of B/M, top quintile of C/P, and top quintile of lagged 12 month returns. • This basket of stocks has an historical average return of about 2% per month, versus the average market return of about 1.2% per month.

40. Performing a "real-time" screen • Go to www.investor.reuters.com • Sign up for a free account • Use PowerScreener • Allows one to download all firms' B/M, C/P, 12 month returns • Download data, do actual screens in Excel using nested =If( ) formula. • =IF(AND(C29<$C$15,D29<$D$15,E29>$E$15,F29>2),A29,".") • Lets go to Reuters and try this out! • Screen: {Price}>0.AND.{Pr52W%Chg}>-999.AND.{Pr2CashFlTTM}>-999.AND.{Pr2BookQ}>-999 • See Excel file "Screeningexample.xls"

41. Conclusion Thanks for listening to me talk about quantitative equity management. "Goodness is the only investment that never fails" H. D. Thoreau In contrast, quantitative stock selection models do not always beat the market…but they appear to work well over time on average. These quantitative techniques can be applied to any type of asset. A number of real firms employ these techniques, as do many hedge funds and large Wall Street firms.