How do You Produce a 63 Day Winning Streak?

Here is how I have been trying to figure this out. Suppose we wanted to figure out what a daily winning percentage had to be in order to observe a 50 percent probability of a 63 day winning streak. It would be (.5)^(1/63), because the probability of 63 straight wins would be Pr(one win)^(63). It turns out that (.5)^(1/63)=.989, which I will round to .99.

Now lets say a firm has a proprietary trading model that is correct 51 percent of the time. This means that on the average day, it will come out ahead (suppose all trades are $1 trades). But if a trader makes one trade a day, he will close the day ahead only 51 percent of the time. If he makes 100 trades a day, however, while his winning percentage per trade remains the same, put his winning percentage per day goes up a lot. Specifically, the standard error for a daily outcome goes down by 1/10, from sqrt(.51*.49) to sqrt(.51*.49/100), or from about .25 to .025. The chance of finishing the day losing on average is based on how many standard deviations away .5 is from .51. In this case, it does from .01/.25 (or not far at all) to .01/.025, or .4 standard deviations away. In a normally distributed world, this means there is a 65 percent chance of finishing the day ahead, assuming each trade has a .51 batting average and 100 trades per day.

To get to winning 99 percent of days, we need to get the standard error for the day to be sufficiently low that .5 is more 2.4 standard deviations away from .51, so the standard error needs to be .01/2.4 or about .004. So we need to find X such that sqrt((.49*.51)/X)=.004. or X=.25/(.004^2)=15,625 trades per day.

Three big assumptions go into this calculations. First, it assumes a stable model. Over the course of one quarter, this may be reasonable. Second, it assumes a model with a 51 percent winning percentage. This is a huge assumption (I do not know what a reasonable number might be). Third, it assumes normality. This is probably not too bad; we do know that Chebyshev’s Inequality says that (1-1/k^2) share of any distribution must be within k standard deviations of the mean. This means that 99 percent of any distribution is within 10 standards deviations, but that is an extreme outcome.

About Richard K. Green 102 Articles

Affiliation: University of Southern California

Richard K. Green, Ph.D., is the Director of the USC Lusk Center for Real Estate. He holds the Lusk Chair in Real Estate and is Professor in the School of Policy, Planning, and Development and the Marshall School of Business at the University of Southern California.

Prior to joining the USC faculty, Dr. Green spent four years as the Oliver T. Carr, Jr., Chair of Real Estate Finance at The George Washington University School of Business. He was Director of the Center for Washington Area Studies and the Center for Real Estate and Urban Studies at that institution. Dr. Green also taught real estate finance and economics courses for 12 years at the University of Wisconsin-Madison, where he was Wangard Faculty Scholar and Chair of Real Estate and Urban Land Economics. He also has been principal economist and director of financial strategy and policy analysis at Freddie Mac.

His research addresses housing markets, housing policy, tax policy, transportation, mortgage finance and urban growth. He is a member of two academic journal editorial boards, and a reviewer for several others.

His work is published in a number of journals including the American Economic Review, Journal of Economic Perspectives, Journal of Real Estate Finance and Economics, Journal of Urban Economics, Land Economics, Regional Science and Urban Economics, Real Estate Economics, Housing Policy Debate, Journal of Housing Economics, and Urban Studies.

His book with Stephen Malpezzi, A Primer on U.S. Housing Markets and Housing Policy, is used at universities throughout the country. His work has been cited or he has been quoted in the New York Times, The Wall Street Journal, The Washington Post, the Christian Science Monitor, the Los Angeles Times, Newsweek and the Economist, as well as other outlets.

Dr. Green earned his Ph.D. and M.S. in economics from the University of Wisconsin-Madison. He earned his A.B. in economics from Harvard University.

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