Financial Mathematics - Stanford University： -金融数学-斯坦福大学.ppt

1991 Breeders’ Cup Race 5 Trading ideas and the results of one hedged strategy You sell the options with negative expected value and buy those with positive expected value and have various levels of hedging using SP500 futures. 20 years of actual trading with real money and extensive simulation and other research suggests which ones and when to sell/buy/hedge in the various strategies to provide good, steady gains with minimal risk. Bias strategy in various forms. Hedged currencies Positive mean Optimal betting Risk control - must protect against extreme events, bad scenarios Reference: W. T. Ziemba (December 2003) Stochastic Programming approach to Asset-Liability and Wealth Management, AIMR, text plus separate appendix. The results of one hedged strategy (simulation) The geometric mean is about 45% net for top graph which uses a short term overpriced market indicator to eliminate five deemed risky of the 70 plays; you win in 60 of 65. The bottom graph has all 70 plays, including the Oct 1987 crash and July 2002 which the measure eliminated. Tests with real money in two small futures accounts of WTZ Long euro, long canadian hedged also in this account Mean 0 in my view weak dollar Small positions to weather storms, still results very good Watch entry and exit and rollups carefully Jan 2002 to present Oct 2003 to present Inefficiencies are possible since: ? 1) more complex wager 2) prob(horse places) prob(horse wins) == favorites may be good bets To investigate place bets we need: ? 1) determine place payoffs? 2) their likelihood? 3) expected place payoffs 4) betting strategy, if expected payoffs are positive Place market in horseracing Bettors do not like place and show bets. The Idea Use data in a simple market (win) to generate probabilities of outcomes Then use those in a complex market (place and show) to find positive expectation bets Then bet on them following the capital growth theory to maximize long run wealth Breiman