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Facebook and the St. Petersburg Paradox
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Jason Zweig cites the St. Petersburg Paradox in questioning how much someone should pay for a bet on Facebook shares at the high valuation set for this inital public offering. This riddle asks how much would one pay for playing a game in which one gets $1 for winning the first toss of a coin and the game ends, or $2 if the coin comes up heads the second time, or $4 the next time, $8 next and keep doing this , the payment doubles each time. The point is that the payoff is infinite because at each toss the probability is 50% and 12.5% for the next toss, and one could get to the 30th toss or the 60th toss, with payoff in hundreds of millions. People also could be out of the game when the heads come up and not see the later supposed gains. Because of this experts say the most people should pay for playing is $20. The Facebook offering has infinite potential of this sort, but the reality is that for businesses of this type one can only see a couple of years ahead in terms of growth, with large uncertainties ahead about growth beyond that point. Charles Lee, professor of accounting at Stanford Business School, and former head of equity research at Barclays Global Investors, says its hard to see further than two or three years for this type of company. Another problem is pointed out by Prof. Ritter of the University of Florida. He says the valuation is so high today that even if Facebook followed Google's growth and had a total market value of $190 billon that Google has today in 10 years, the annual return would be around 6.8%.
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