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When to Sell Apple and the NASDAQ? Trading Bubbles with a Stochastic Disorder Model
Abstract
In this paper, the authors apply a continuous time stochastic process model developed by Shiryaev and Zhutlukhin for optimal stopping of random price processes that appear to be bubbles. By a bubble we mean the rising price is largely based on the expectation of higher and higher future prices. Futures traders such as George Soros attempt to trade such markets. The idea is to exit near the peak from a starting long position. The model applies equally well on the short side, that is when to enter and exit a short position. In this paper we test the model in two technology markets. These include the price of Apple computer stock AAPL from various times in 2009{2012 after the local low of March 6, 2009; plus a market where it is known that the generally very successful bubble trader George Soros lost money by shorting the NASDAQ-100 stock index too soon in 2000. The Shiryaev-Zhitlukhin model provides good exit points in both situations that would have been protable to speculators following the model. who employed the model.
We provide a historical perspective focusing on Ziemba's experiences and research on the bond-stock earnings yield differential model (BSEYD) starting from when he first used it in Japan in 1988 through to the present in 2014. The model has called many but not all crashes. Those called have high interest rates in long term bonds relative to the trailing earnings to price ratio. In general, when the model is in the danger zone, almost always there will be a crash. The model predicted the crashes in China, Iceland and the US in the 2006-9 period. Iceland had a drop of fully 95%. For the US the call was on June 14, 2007 and the stock market fell 56.8%. A longer term study for the US, Canada, Japan, Germany, and UK shows that over long periods being in the stock market when the bond-stock signal is not in the danger zone and in cash when it is in the danger zone provides a final wealth about double buy and hold for each of these five countries. The best use of the model is for predicting crashes. Finally we compare Shiller's high PE ratio crash model to the BSEYD model for the US market from 1962-2012. While both models add value, the BSEYD model predicts crashes better.
A method is proposed to solve optimal stopping problems. Several examples - classical and new ones - are discussed. Especially the values of American options (straddle and strangle) with innite horizon are calculated.
A straightforward guide focused on life cycle investing-namely aging, retirement, and pensions Life cycle investing and the implications of aging, retirement, and pensions continues to grow in importance. With people living longer, the relative and absolute number of retirees is growing while the number of workers contributing to pension funds is declining. This reliable resource develops a detailed economic analysis-at the micro (individual) and macro (economy wide) levels-which addresses issues regarding the economics of an aging population. Topics touched upon include retirement and the associated health care funding of the aged as well as social security and the asset classes that are considered asset-liability choices over time. The probability of achieving adequate return patterns from various investment strategies and asset classes is reviewed Shares rich insights on the aging, retirement, and pensions dilemma An assessment of the resources the real economy will be able to commit to non-workers is provided The three pillars of retirement are social security, company pensions, and private savings. Each of these pillars is confronted with a variety of asset-liability problems, and this book will addresses them. © 2010 Marida Bertocchi, Sandra L. Schwartz, and William T. Ziemba. All rights reserved.
Question: How can aggregate stock market valuation ratios - the dividend-price ratio and earnings-price ratio - fail to predict future stock price movements, movements in the denominator, given that these ratios themselves are mean-reverting? Answer: If these ratios predict the growth rates of dividends or earnings, movements in the numerator. Given their analysis of long aggregate historical stock market data ti-om the United States and eleven other countries, the authors conclude that these ratios do not forecast dividends or earnings, certainly not consistently in the right direction. The analysis suggests a gloomy next four or ten years for the United States and some other stock markets.
The Wiener disorder problem seeks to determine a stopping time which is as close as possible to the (unknown) time of 'disorder' when the drift of an observed Wiener process changes from one value to another. In this paper we present a solution of the Wiener disorder problem when the horizon is finite. The method of proof is based on reducing the initial problem to a parabolic free-boundary problem where the continuation region is determined by a continuous curved boundary. By means of the change-of-variable formula containing the local time of a diffusion process on curves we show that the optimal boundary can be characterized as a unique solution of the nonlinear integral equation.
The papers in this symposium represent the divergent views of economists on an important issue: the extent to which prices of assets represent “fundamental” values. While the papers in the symposium present different formal definitions of what a bubble is, the basic intuition is straightforward: if the reason that the price is high today is only because investors believe that the selling price will be high tomorrow—when “fundamental” factors do not seem to justify such a price—then a bubble exists.
In this article, we apply real options theory and modern capital budgeting to the problem of valuing an Internet company. We formulate the model in continuous time, form a discrete time approximation, estimate the model parameters, solve the model by simulation, and then perform sensitivity analysis. Depending on the parameters chosen, we find that the value of an Internet stock may be rational given high enough growth rates in revenues. Even with a very real chance that a firm may go bankrupt, if the initial growth rates are sufficiently high, and if there is enough volatility in this growth rate over time, then valuations can be what would otherwise appear to be dramatically high. In addition, we find a large sensitivity of the valuation to initial conditions and exact specification of the parameters. This is also consistent with the observation that the returns of Internet stocks have been strikingly volatile. 3 RATIONAL PRICING OF INTERNET COMPANIES 1. INTRODUCTION It is diffic...