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.



George said...

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 traders died on the vine while thinking their trading method was sound and they were only experiencing a normal run of losing trades, when, in fact, the edge they thought they were working had vaporized and they were simply chasing a wisp of smoke?

You create an edge by coming up with a trading strategy which generates a win:loss ratio that, when coupled with a per-trade risk:reward ratio, gives you an acceptable return after factoring in commissions and fees. Say you come up with a trading strategy where 54.5 percent of your trades are winners, a win:loss ratio of 1.2:1. You decide to couple that with a per-trade risk:reward ratio of 1:1, risking one unit to make one unit. Out of every eleven trades, six are winners, a gain of six units. Five are losers, a loss of five units. A gain of one unit for the eleven trades. One unit divided by eleven trades means you will make 0.0909 units for every trade you make, win or lose. That's a 9.09 percent edge. But those numbers are only averages. You will never consistently have six winners out of every eleven trades you make. You will only average six winners out of every eleven trades.

My understanding of probability theory and the Law of Large Numbers, which, admittedly, deals with random events, is that it is impossible to calculate the minimum number it takes to give you a large enough sampling where you can count on the averages kicking in. At the casino, in, say, a game like craps, their edge is built into the dice (and the vig, and the table limits). Even with that, the casino can only count on the averages kicking in eventually, which does allow for short-term fluctuations. But all the casino has to do is wait because the averages will kick in and they will make money in the long run. It's guaranteed.

Unfortunately, in trading, there is no built-in edge, so traders do not have the same guarantee as a casino. Since trade resolutions are not random events, the minimum number of trades that gives a large enough sampling for the averages to kick in should be far less than needed in random events; however, like random events, that number is also incalculable. So traders will inevitably be faced with the following dilemma: When a win:loss ratio that was previously enough to maintain their edge has fallen off to a ratio that is now less than they need to maintain their edge, how long should they endure this unacceptable risk:reward ratio before they finally say enough is enough (how many trades, how many more losses, where is the tipping point) and assume their trading strategy has broken down, their edge has permanently vaporized, and they should stop trading until they come up with a way to reestablish their edge, even though there is still a possibility that, under current market conditions, the strategy may very well be sound, but not enough trades have been executed for the averages to kick in? That is why I refer to this as a dilemma.

To me, this is a critical component of trading and one of the toughest decisions traders have to make because, as you mentioned, if they interpret a normal run of losing trades (that results in a risk:reward ratio that is only temporarily lower) as meaning their trading strategy is no longer sound, it will have an adverse effect on their potential for success. On the other hand, if they interpret an abnormal run of losing trades (that results in a risk:reward ratio that is permanently lower) for a normal run of losing trades, it will also have an adverse effect on their potential for success. The only way to determine what is, or isn't, normal, in the way of losses, and how many trades it takes to make that determination, is with hindsight and, by then, if the wrong call was made, the damage has already been done.

It would be interesting to read a blog entry where you talk about this.

George said...

Sorry, but in the last two major paragraphs of my comment, above, one starting with Unfortunately... and the other starting with To me..., risk:reward ratio should actually read win:loss ratio.

Not that anyone is reading this stuff. ;-)