Tuesday, April 26, 2016

News, trading, and decision-making - Type I and Type II errors



Investment decision-making is a combination of assessment of information and action. Analysis and trading. If you are right, there is profit but if you commit an error, there is a loss. A good analyst who cannot act with a specific recommendation is not worth much. A trader who is not a good analyst is just a busy investment professional without purpose. From a macro perspective, how traders act and the type of errors they are willing to make will have an impact on price behavior.

When a trader receives some new "news", he has a set of choices which will either lead to profit or an error. Yet, all errors are not the same. Traders can make type I or type II errors which will have an impact on the type of trading conducted and affect the market in aggregate. Traders have to assess the probability of the type of error to be committed no different than any statistical test. 

Walking through a trader's decision tree will help explain the problem. New information may enter the market. For example, it could be a macro announcement on the unemployment rate. The trader then has to make a determination to either act or not to act based on this new information. Action can either lead to a gain or a loss. Similarly, no action can either be the right trade or not. 

If the trader is correct, there is no error and there is a positive gain. However, if the trader is not correct, he commits a type I error which is a false positive. He thinks prices will react from this news and decides to trade. He expects an action that does not occur. He will then have to reverse the trade given this type I error.   The trader detects and effect that is not present.


On the other hand, the trader may conclude that no action should be taken from this information. If there is no price reaction, this was the correct action. If he is wrong and there is a large move, the trader committed a type II error, a false negative. In this case, the trader does not have to reverse his mistake, but it may require a catch-up trade. There is a failure to detect an effect that is present.

A trader will get more false positives from acting too rashly while there will be more Type II errors from passivity.  More type I errors will require more reversals of trades. In aggregate, if the market makes more type I errors, there will be more mean-reversion. If the market makes more type II errors, there will be more trends or momentum.  Type I errors are costly because transaction costs are taken and capital is engaged. More Type II errors from lack of action are an opportunity cost. Good traders have to think about the balance between these errors. 

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