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Statistics, and the Long-Term Return on Your Investments

There is this dismal applied science that is called "statistics". It's usually packaged together with "probability". So you take a course called "Probability and Statistics 101". And one of the very first things that you learn is that a statistic is a number whose value is derived from and is characteristic of a distribution of possible outcomes. The distribution defines the probabilities.

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But, if you buy that fund, what is it most likely to be worth in 10 years? That's probably what you really want to know. Well you can't get that from the median of the annual return ratios over the past 10 years. You couldn't even get the answer to that particular question from the median of the next 10 annual return ratios if somehow you knew those in advance. Actually, unless the historical data were distributed in a particular way the historical median isn't even a statistic of interest. Others are and we'll get to them. Do read on. Today's entry is about the statistics on fund performance that are normally made available to you and how you can use them.

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Whipsaws and Stop-Loss Trading

You hear occasionally, in trader talk, the word "whipsaw". While the word can refer to any sharp oscillatory price action in the market that is being traded, it also refers to traders panicking out of losing positions and then having to get back in at prices worse than the exit prices. "Getting whipsawed" is bad!

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The basic message is that the whipsaws are an unavoidable complication— their deleterious effects on your account equity are difficult to minimize and impossible to utterly eliminate (if you trade in and out of positions in a stop-loss manner). And I'm going to explain that a famous formula actually quantifies whipsaw losses and makes them into the price of a certain contract, via an algorithm of course.

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Real Vs. Hypothetical

Before investing with some fund or using some advisory service that one way or another provides active portfolio management, we naturally want to first look at past performance. I'm going to discuss the different kinds of performance histories that can be made available, and argue that the kind that is generally considered to be the gold standard is not necessarily what it seems to be.

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So Retail Backtest's backtested program performance is labeled "hypothetical", by me, to match expectations in that regard. However, what Retail Backtest does is the same thing that you would be doing if you were to pick funds to invest in based on their past "real-money" performance. Yes, you would simply be competing with me, performing the same function.

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"Why Most Published Research Findings Are False"

Today's note is to point to an essay of that title by John P. A. Ioannidis, Professor of Medicine and of Health Research and Policy at Stanford University School of Medicine and Professor of Statistics at Stanford University School of Humanities and Sciences. By false findings he is referring to research that passed the usual test of statistical significance but was ultimately proven to be false, non-reproducible. The problem is that the number of false findings is much, much higher than would be predicted from the researchers' own assessments of statistical significance.

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I want to talk a little about how the circumstances are a bit different for findings by quantitative analysts who work for funds managing securities. Can you guess why? Come on... it's easy.

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Objectivity and the Trailing Performance Period

One of the most easily reached conclusions in all of logical thinking is that we should always do things the way that worked best in prior experience. Oh, that's not to say that we shouldn't or don't occasionally get inventive. But we surely believe that we should never do anything in a way that worked much worst in the past than something else that worked well.

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The mistake has to do with choices. I usually frame the issue by talking about "parameters". By that I mean numbers, numbers that specify your portfolio management scheme's way of learning from the past. The mistake is to simply find out what choice of parameters would have produced the very best results in the entire available history, to thus fix those parameters, and then to use them going forward.

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