Wednesday, December 23, 2009

The Psychological Importance of Paths of Returns

In my post on risk and return, I showed how shifts in volatility and the size of a trader's edge greatly affect the path of returns over time.

Above, we can see with the aid of Henry Carstens' forecaster different possible paths of annual returns for a high frequency trader who trades a portfolio of $100,000, nets an average of $100 per trade, and has a 2% standard deviation for daily returns (i.e., two-thirds of all daily returns fall between -$1900 and +$2100).

In the four scenarios above, the annual profits for the trader fall between 10.88% and 14.5%. Note, however, that paths differ greatly simply based upon the random arrangement of the winning and losing trades.

For instance, in the third scenario down, we see a drawdown of about 17% before the trader ends up with a 14.5% profit. The fourth scenario at bottom sees a drawdown of only a little more than 3%, but quickly makes and then loses a 20% return before ending the year up 10.88%. We see a similar harrowing drawdown in the first scenario, but a rather steady and gradual move to year end returns in the second scenario.

Observe that this is a profitable trader with an objective edge, trading that edge aggressively. Depending on the path of returns, however--something outside the trader's control--it may be easier or harder to stick to the winning method. The odds are good that, during a harrowing drawdown or extended, choppy period, the trader might abandon the formula and unwittingly erode his or her edge.

The point here is that the random distribution of winning and losing trades ensures that we can have runs of winning and losing periods that we will experience as hot and cold hands. Few traders recognize the importance of the path of returns on a trader's psyche.

How many successful traders never saw their success to fruition simply because they confused a normal run of losing trades for their method not working? How many successful traders have blown up because they became too aggressive after an extended run of winning trades?

Expertise can ensure a positive destination for our trading, but cannot ensure the path we take along the way.