Parimutuel betting markets: racetracks and lotteries revisited

This paper surveys the state of the art in research in racetrack and lottery markets. Market efficiency and the pricing of various wagers is studied along with new developments since the Thaler and Ziemba JEP review. Other sports betting markets are also discussed. The role of syndicates, betting exchange rebates, behavioral biases and fundamental information is discussed

A response to Professor Paul A. Samuelson's objections to Kelly capital growth investing

The Kelly Capital Growth Investment Strategy maximizes the expected utility of final wealth with a Bernoulli logarithmic utility function. In 1956 Kelly showed that static expected log maximization yields the maximum asymptotic long run growth. Good properties include minimizing the time to large asymptotic goals, maximizing the median, and being ahead on average after the first period. Bad properties include extremely large bets for short term favorable investment situations because the Arrow-Pratt risk aversion index is essentially zero. Paul Samuelson was a critic of this approach and I discuss his various points sent in letters he sent me and papers reprinted in MacLean, Thorp and Ziemba (2011). Samuelson's criticism is partially responsible for the current situation that most finance academics and professionals do not recommend Kelly strategies. I was asked to explain this to Fidelity Investments, a major Boston investment firm influenced by Samuelson at MIT. Should they be using Kelly and safer fractional Kelly strategies which blend cash with the full Kelly strategy? The points of Samuelson are theoretically correct and sharpen the theory. They caution users of this approach to be careful and understand the true characteristics of these investments including ways to lower the investment exposure. Samuelson's objections help us understand the theory better, but they do not detract from numerous valuable applications

Pari-mutuel betting markets: racetracks and lotteries revisited

This survey discusses the state of the art in research in racetrack and lottery investment markets. Market efficiency and the pricing of various wagers are studied along with new developments since the Thaler & Ziemba (1988) review. The weak form inefficient market pricing approach using stochastic programming optimization models changed racetrack betting from handicapping to a financial market allowing professional syndicates to operate as hedge funds. Topics discussed include arbitrage and risk arbitrage, syndicates, betting exchange rebates, behavioral biases, and fundamental and mispricing information in racetrack and lottery markets. Similar models can be used to successfully trade stock market anomalies. Supplemental Materials are included online

Does the bond-stock earning yield differential model predict equity market corrections better than high P/E models?

In this paper, we extend the literature on crash prediction models in three main respects. First, we relate explicitly crash prediction measures and asset pricing models. Second, we present a simple, effective statistical significance test for crash prediction models. Finally, we propose a definition and a measure of robustness for crash prediction models. We apply the statistical test and measure the robustness of selected model specifications of the Price-Earnings (P/E) ratio and Bond Stock Earning Yield Differential (BSEYD) measures. This analysis suggests that the BSEYD, the logarithmic BSEYD model, and to a lesser extent the P/E ratio, are statistically significant robust predictors of equity market crashes

A tale of two indexes: predicting equity market downturns in China

Predicting stock market crashes is a focus of interest for both researchers and practitioners. Several prediction models have been developed, mostly for use on mature financial markets. In this paper, we investigate whether traditional crash predictors, the price-to-earnings ratio, the Cyclically Adjusted Price-to-Earnings ratio and the Bond-Stock Earnings Yield Differential model, predicts crashes for the Shanghai Stock Exchange Composite Index and the Shenzhen Stock Exchange Composite Inde

Land and stock bubbles, crashes and exit strategies in Japan circa 1990 and in 2013

We study the land and stock markets in Japan circa 1990 and in 2013. While the Nikkei stock average in the late 1980s and its -48% crash in 1990 is generally recognized as a financial market bubble, a bigger bubble and crash was in the land market. The crash in the Nikkei which started on the first trading day of 1990 was predictable in April 1989 using the bond-stock earnings yield model which signaled a crash but not when. We show that it was possible to use the change point detection model based solely on price movements for profitable exits of long positions both circa 1990 and in 2013

Using a mean changing stochastic processes exit-entry model for stock market long-short prediction

Stochastic processes is one of the key operations research tools for analysis of complex phenomenon. This paper has a unique application to the study of mean changing models in stock markets. The idea is to enter and exit stock markets like Apple Computer and the broad S&P500 index at good times and prices (long and short). Research by Chopra and Ziemba showed that mean estimation was far more important to portfolio success than variance or co-variance estimation. The idea in the stochastic process model is to determine when the mean changes and then reverse the position direction. This is applied to Apple Computer stock in 2012 when it rallied dramatically then had a large fall and Apple Computer and the S&P500 in the 2020 Covid-19 era. The results show that the mean changing model greatly improves on a buy and hold strategy even for securities that have has large gains over time but periodic losses which the model can exploit. This type of model is also useful to exit bubble-like stock markets and a number of these in the US, Japan, China and Iceland are described. An innovation in this paper is the exit entry long short feature which is important in financial markets

Does it pay to buy the pot in the Canadian 6/49 Lotto: implications for lottery design

The Canadian 6/49 Lotto©, despite its unusual payout structure, is one of the few government sponsored lotteries that has the potential for a favourable strategy we call "buying the pot". By "buying the pot" we mean that a syndicate buys one of each ticket in the lottery, ensuring that it holds a jackpot winner. We assume that the other bettors independently buy small numbers of tickets. This paper presents (1) a formula for the syndicate's expected return, (2) conditions under which buying the pot produces a significant positive expected return, and (3) the implications of these findings for lottery design

Optimal capital growth with convex shortfall penalties

The optimal capital growth strategy or Kelly strategy, has many desirable properties such as maximizing the asympotic long run growth of capital. However, it has considerable short run risk since the utility is logarithmic, with essentially zero Arrow-Pratt risk aversion. Most investors favor a smooth wealth path with high growth. In this paper we provide a method to obtain the maximum growth while staying above a predetermined ex-ante discrete time smooth wealth path with high probability, with shortfalls below the path penalized with a convex function of the shortfall so as to force the investor to remain above the wealth path. This results in a lower investment fraction than the Kelly strategy with less risk, and lower but maximal growth rate under the assumptions. A mixture model with Markov transitions between several normally distributed market regimes is used for the dynamics of asset prices. The investment model allows the determination of the optimal constrained growth wagers at discrete points in time in an attempt to stay above the ex-ante path

Optimal capital growth with convex shortfall penalties

The optimal capital growth strategy or Kelly strategy, has many desirable properties such as maximizing the asympotic long run growth of capital. However, it has considerable short run risk since the utility is logarithmic, with essentially zero Arrow-Pratt risk aversion. It is common to control risk with a Value-at-Risk constraint defined on the end of horizon wealth. A more effective approach is to impose a VaR constraint at each time on the wealth path. In this paper we provide a method to obtain the maximum growth while staying above an ex-ante discrete time wealth path with high probability, where shortfalls below the path are penalized with a convex function of the shortfall. The effect of the path VaR condition and shortfall penalties is less growth than the Kelly strategy, but the downside risk is under control. The asset price dynamics are defined by a model with Markov transitions between several market regimes and geometric Brownian motion for prices within regime. The stochastic investment model is reformulated as a deterministic program which allows the calculation of the optimal constrained growth wagers at discrete points in time