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Although 2 percent excess returns do not seem high, if the claim were known to be valid, her skills would be in great demand. on average, portfolio managers do not beat the market. her expected two percent excess return for equivalent risk represents two-thirds of the current annual t-bill rate and three times the typical management fee management fee. 2 the statistician would construct a one-sided t-test in which the mean excess return over the sample period is divided by its standard error. to determine how many years of data are required, the statistician would set the power of the test equal to 0.95. an approximate power calculation can be obtained by examining the ratio of the expected values of the numerator and denominator of the t-statistic. the expected numerator is obtained from the manager's claim that she can produce 2 percent excess returns. let k represent this claim. the expected denominator--the expected standard error of the mean excess return--is p2 + m2 - 2ppm ; t where p and m are the annual standard deviations of the portfolio and market returns, p is their correlation and t is the sample period in years. from probability theory, we will be 95% certain that the mean is positive if the t-statistic is greater than 1.64. setting the expected t-statistic greater than 1.64 implies t 1.64 ; 2 p2 + 2ppm ; k2. if p m percent, p .9 and k 2 percent, t must be greater than 30.4 years.
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University of amsterdam & stanford university december 7, 2001 abstract. we analyze extensive games as interactive process models, using modal languages plus matching notions of bisimulation as varieties of game equivalences. our technical results show how to fit existing modal notions into this new setting. keywords: extensive games, modal logic, bisimulation and keno strategy.
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