Jun

19

Dear Victor,

We discovered your review of our paper [link] and just wanted to address a few of the points you raise and correct some erroneous statements.

a) We do not stitch our time series together, but simulate a standalone P&L equally allocated between the various instruments. The correlations between markets are indeed present but irrelevant to the estimate of the t-stat which is simply estimated using the daily returns of the strategy i.e. signal*next day (or next month) returns, which are for all intents and purposes uncorrelated (even if the signals themselves are obviously not). The resulting t-stat measurement we feel is made more robust by the fact that t-stats are also significant for all sub-periods and all individual asset classes. We therefore don’t understand your comments about overlapping 5 month windows or the correlations between tickers.

b) Your interpretation of our regression results seems strange. We are simply looking how much the market moves on the subsequent day (on average of course), conditional to a certain value of the signal (the normalised five month trend). We find that when the signal is 1 at one sigma (not one percent!), the next day return is three times bigger than its long term average, i.e. the return of the long only strategy. We find difficult not to see this as “economically significant”; besides, the trend following industry has certainly made very significant profits in the last thirty years.

c) Our “armchair explanations” are proposed as possible (plausible) explanations for which we do not have direct statistical evidence. Still, we refer to recent, well documented academic papers based on surveys that pretty convincingly show that most people have “extrapolative expectations”, i.e. they tend to follow trends. See Shiller, Menkhoff, Hommes, Greenwood & Schleifer, etc.

Looking forward, we believe that long term trends will persist, albeit delivering a strategy with a low Sharpe ratio. There is however only our best guess based in part on the results of our paper that shows that trend following has delivered a highly significant Sharpe over a long history.

Sincerely yours — the authors of “Two Centuries of Trend Following”


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