# Momentum trading produces outsized losses, paper

Piling in on the hot stock can be all too exciting not just because of the exuberance from outsized gains but also because of the pain of outsized losses such trading strategy can bring and which one of these possibilities happens depends on when such trading strategy is employed, says the latest paper from a triplet of professors.

It has been well documented that price momentum strategy – long position in past winners and an equal short position in past loser – produces outsized gains but based on data from July 1927 to December 2010, authors Kent Daniel, Ravi Jagannathan and Soohun Kim, find that such strategy inflicts staggering losses suggesting that the strategy has a hidden bias in it.

“Given the low unconditional volatility of the momentum strategy, if returns were normal the probability of observing a month with a loss exceeding 42% in a sample of 1002 months would be one in 29,000, and the probability of seeing five or more months with losses exceeding 42% would be almost zero. Yet the lowest five monthly returns in the sample are: -79%, -60%, -46%, -44%, and -42%, a rare black swan like occurrence from the perspective of someone who believes that the time series of monthly momentum returns are generated from an i.i.d. normal distribution,” calculate the authors.

The authors then spend some time looking for a mathematical model that would capture these two states of events, and after some discussion they settle on the “two state hidden Markov model” – a jingo for breaking up the market into two characters: turbulent or calm.

Based on the 1002 months of data, the authors calculate that the “average duration of 16 months and turbulent months have an average duration of 4 months” and it is within these 4 months that these staggering losses occur.

“All the 13 months with losses exceeding 20%/month occur during turbulent months, i.e., months when the predicted probability of the hidden state being turbulent exceeds 0.5 [50%],” write the authors.

“We find that it is possible to predict which of the two hidden states the economy is in with some degree of confidence,” say the authors but even when “such turbulent states are avoided, the monthly Sharpe Ratio of momentum strategy returns increases to 0.32 and price momentum poses still more of a challenge to standard asset pricing models.”

Authors leave this “challenge” perhaps for another paper, but as far as this one is concerned, there are some additional informative data points.

For example, not every turbulent month produced negative returns but rather a subset within that time period. Out of 1002 trading months in the sample, 206 months are classified as turbulent and within this time only 124 months or 60% of the turbulent time produced negative returns on the momentum portfolio. Otherwise, on the whole of 1002, 303 months produced negative returns.

In other words, less then 12.5% of the trading time [124/1002] is responsible for the outsized negativity but being able to predict this small sliver of negativity can be nearly impossible: if in the standard normal distribution probability of a 79% loss is 3 x 10-24 [basically zero] then this is a good approximation of the probability of being able to guess when such a loss would occur in a non-normally distributed momentum strategy.

Ergo the confirmation of traditional trading dictums: can’t predict the direction of the market all the times; avoid momentum plays during turbulent times like these.

Paper is available here.