Picking Winners is For Losers: A Strategy for Optimizing Investment
Transcription
Picking Winners is For Losers: A Strategy for Optimizing Investment
Picking Winners is For Losers: A Strategy for Optimizing Investment Outcomes Clay graham DePaul University Risk Conference Las Vegas - November 11, 2011 REMEMBER Picking a winner is not at all the same as making a smart investment ! Pathway Mission Implementation Investments Control Decisions Methods Probabilities Some Questions Sought to Be Addressed • Is the amount of the investment as important as selecting a “winner”? • Market inequities identified? – Pricing of investment – Value market “Ripped From Today’s Headlines” Mission “Have Fun Make Money” Tom Peters Our Credo • Learn to cope with variance • Keep a perspective on long term and commitment to invest • Go where the numbers take you • Capture the greatest long term reward as a function of a tempered risk • What gets measured gets done • Discipline… Discipline… Discipline ! Investments Value > Price Some Value Measurements (can be compounded and complex) • Return on Investment – Yield – Capital gain • Risk – Price volatility – Probability variation of success – Money management • Duration – Short versus Long Term – Available liquidity Various Investments (Sure things just don’t exist) • • • • • • • Stocks Options (and derivatives) Bonds Currency Metals (other “hard assets”) Real Estate Gaming The Process (gaming) • “Sniff and kick” – Kind of investments available – What game – Probabilities of success – Payoff and price – Invest or not – If so How Much? • Modeling game and economics Methods …..(join) the ultimate baptism into the religion of statistics. Jeff Ma da “Vig” (as we say in Chicago) Vigorish, or simply “the vig”, is also known as “juice” or the “take”, is the amount charged by the house for its services. Bets: -110 Home, -110 Road House receives 220 in bets pays out 210 Makes 10/220 or 4.5% profit or Juice Methods of Sports Gaming Investments • Money Line – Select team to win at specific price • Over Under – Pick above or below a specific total – Grand Salami (same as above but for games that day) • Spread – Win or lose by fix number of points (runs) Probabilities (value > price) Probability Winning (event) > Implied Probability of Line + Vig Implied probabilities: -125 = (125)/(100+125) = 56% 100 = (100)/(100+100) = 50% 150 = (100)/(100+150) = 40% Probabilities Probabilities of success must be associated and tailored to each method of investment. – Money line - Probability of Team winning – Over Under - Probability over “x” or under “x” – Spread - Probability Team A wins by “y” points (runs) Modeling Baseball First and Foremost: Runs are the Currency of baseball Modeling Baseball Traditional measures ineffective in quantifying run production Key Metric must be: Comparable among and between: Batters Pitchers Teams Additive Accurate & reproducible Expected Runs / Plate Appearance (EVR/PA) Production Function Runs = k(EVR/PAB)α (1/ EVR/PAP)β Where: EVR/PAB means expected value of runs per plate appearance batter (pitcher) Hey Dude: this is linear in logs and you can solve it! Solve for α , β and anti log of k (since above equation is linear in logs!) (∂r / ∂B) = α = elasticity of run production attributable to batters (.66) (∂r / ∂P) = β = elasticity of run production attributable to pitchers (.34) Probability of Winning (game) 1. Pythagorean (traditional): P(W ) = (RH )2 / [(RH )2 + (RR )2 ] H 2. Neutral (player based): P(WH) = f(EVR/PARP,B, EVR/PAHP,B) 3. 8 Variable: P(W ) = f(EVR/PARP,B, EVR/PAH , RANKRO,D , RANKRO,D) H P,B 4. Sigma (dispersion & variance): P(WH) = f(δRO / δHO , δRO / δHO , Δ Rank) Decisions “They (all) have a way of looking at numbers in a truly creative way. They understand the right question to ask to let numbers solve these problems.” Michael Lewis Money Line • Price of investment set by the market – Nomenclature (US lines) • -180 means: pay 180 to win 100 • 125 means: pay 100 to win 125 • Select one team as having an economically viable return on investment • Keep in mind that the home team is favored: – 70% of the time yet wins only 52% Over Under (total points or runs) • Points (runs scored) either over or under a specified total • Market usually tends to be balanced; i.e., price of bets closely symmetrical. • Caveat: – Grand Salami – Over / under on all games played on given day Observation (baseball) 60% of the time the winning team scores an odd number of runs Source: Baseball Prospectus.com 2011 Season Tabulated by: CJG Negative Binomial vs. Gamma (Expected Runs / Game) Decision Processes • Quantify all possible investments – EVROI – Expected run margin – Performance ranking variation – Filter above criteria to add accuracy to forecat • Identify just where there is an “Edge” – Accuracy an imperative • Probability of winning • Price (line) Considerations (market inequities) • Home Team – Basketball favored 71% yet wins just 61% – Baseball favored 70% wins 52% • Over Under – Basketball over / under with line 50/50 – Baseball • Over / under: 52% / 48% • Odd number of runs 60% • 90% of Sport Gamblers Loose! Selection Optimizing Filtration (using Evolver for Road and Home Models) Lines EVROI P(W) Rankings DB Duratio n Maximize: Profitable Investments How Much to Invest? (% bankroll or each bet) • Bob Stoll, aka, “Dr. Bob” – Football about 2% – Basketball about 1.5% • San Francisco “betting community” – Consensus 1% to 6% • Kelly Criteria (major investors) Kelly Criterion (I) Objective: maximize bankroll (long run) f = (bp-q) – q / b Where: f = fraction of bankroll to wager b = profit (proportion of payoff) p = probability of winning q = probability of losing Kelly Criterion (II) f = (bp – q) / b = (p(b+1) -1)/p Note: 1. f = expected winnings / bet net winnings 2. Definition of the “Edge”= p*b – q (numerator) 3. Expected value ROI = edge/cost Kelly Criterion (III) More Risk = Increase Probabilities of: Both Good and Bad Outcomes Road @ 13% Home @ 9% Overbetting is worse than Underbetting Some Problems with Kelly • Proportion of bankroll too much exposure • Pragmatic gaming judgment not considered – Maximum bet – Maximum at risk on a given day • Over dependence on probability of winning • Nominal emphasis on economics Seasonal Return on Bankroll Period Bob Stoll1 “(Dr. Bob)” 1999-2000 162.6% 2000-2001 140.2% 2001-2002 165.2% 2002-2003 -49.7% 2003-2004 62.9% 2004-2005 81.6% 2005-2006 210.7% 2006-2007 -.1.1% 2007-2008 -77.4% 2008-2009 34.8% 2009-2010 2010-2011 average 73.0% Source:(1) DrBobSports.com; Spread - football @ 2% and basketball @1.5% Actual Bankroll Pattern 350,000 300,000 Fund per contract 250,000 Bankroll 200,000 150,000 100,000 Client Cut Available Bankroll 50,000 10/21 10/14 10/7 9/30 9/23 9/16 9/9 9/2 8/26 8/19 8/12 8/5 7/29 7/22 7/15 7/8 7/1 6/24 6/17 6/10 6/3 5/27 5/20 5/13 5/6 4/29 0 Money Management • Reasonable Criteria – Bet size upper and lower constraints – Economically targeted • Invest more when with higher expected value of return • Transition over finite range • Different formulations predicated upon – Type of investment – Investment configuration Goal Focused Control Equation Staking % = Ab+((At-Ab) / (1+Exp (-(EVROI-X0) / W))) Where: Ab = minimum proportion of bankroll At = maximum proportion of bankroll W = transition slope X0 = shifting factor EVROI = expected ROI of specific investment Staking Level Tied to Expected ROI What are the Results? Money Line Description Flat Kelly Slade Average Invest Rate 2.5% 2.5% 2.5% Maximum bet 10,000 10,000 10,000 Starting Bankroll 200,000 200,000 200,000 % Profit (season) 12.5% 7.2% 49.8% What are the Results? Over / Under Description Kelly Slade Average Invest Rate 2.5% 2.5% Maximum bet 10,000 10,000 Starting Bankroll 200,000 200,000 % Profit (season) 90% 210% Implementation “Do not put your faith in what statistics say until you have carefully considered what they do not say.” William Watt Implementation • Data Preparation – Model(s) – Day to day updating • Players • Lines • Exogenous factors • Placing investments – Accuracy – Timing Implementation • Why Betters Fail? – – – – – Inaccurate implementation (making wrong bet) Head for the hills syndrome (short term perspective) Reactive (reduce investment after losses) Realistic expectations Dumb ass rules ,i.e., no bets when probability of winning is less than 50% – Violate 3Ps • Preparation • Persistence • Patience Control “Winning (profitability) isn’t everything; it’s the only thing.” Vince Lombardi Control • To assure success it is an imperative to: – Maintain a History of all decisions including logic in their derivation – Review and validate functional algorithms – Maintain daily, weekly, monthly and TYD records performance • Never be content with just good results The Magnitude of Investment can play a more dominant role to long run profitability than that of the probability of winning!