An Aside - Ad-hoc Trades and the Take Profits Algorithm

Everybody makes ad-hoc trades, even the most rigourously algorithmic traders sometimes just pick up the mouse and click themselves into a position. If we're right, or if we're lucky, this starts as a good idea and generates a gain. However, although many people feel they have good insight about when to buy (or sell) --- following an earnings suprise, for example --- it's my observation that the decision to close a position out and take profits, or limit a loss, is a lot harder to make successfully. And this applies to myself as much as others.

So what happens is that the initial information fades and the trade turns against you, but you sit on the position waiting for it to come back. Everybody does this when they "punt" stocks; it's something about how the human brain processes decisions.

I going to describe here something that is at complete variance to the statistical-analytical trading methods I use for normal businesses. But I find that it helps. I use automated electronic trading to manage my systems, and I apply the following method to get me out of ad hoc trades with a system I call the take profits algorithm. It's a simple idea that doesn't really need the computer to be operated (although that does make it emotionally easier to deal with); you could use stop orders to do some of this.

Essentially. we're going to resign ourselves to not taking all of the profits nominally available to us. We're going to leave some profits "on the table" as discretionary traders would put it. I would claim that the profits we leave on the table, the opportunity cost of our trading, are the risk premium which we are paying out in return for our aversion to losing our gains.

I implement an algorithm in which, when a trade is profitable, we take a profit. Specifically if we have a gross gain of G on a position, we cut the position to a fraction of the initial position. I chose the fraction 1/(1+G)^2, but that is essentially an arbitary amount. The important point is that we take some profits and the more profit that exists the more of it we take. This means that if a stock goes straight up we cannot ever capture all of the gains it makes, because we will book profits on the way up. The chart "Effect of Take Profit Algorithm" shows how much you are theoretically giving up.

Sometimes, of course, we don't get it right and the stock we bought sinks instead of rising; or we bought when it was 10% up on the earnings suprise but it settles to 5% up so we actually get a 5% loss. Whenever the trade is losing I apply a different algorithm. This one is based on holding time because I'm all for giving the trade a little time to turn around (especially since academic research indicates that the initial pop on an earnings suprise generally underestimates the final net response to the news). So I cut the position to a fraction exp(-d/5) of the initial positions, where d is the number of days since the trade entry. Again the exact formalism is arbitary, but the idea is that the longer it's been since the inital trade the more you should take off. Essentially what we're saying is that if it's been a long time since the initial trade idea we have to accept the fact that we're probably wrong.

The final step is that when we have adjusted our position, we "reset the clock" and treat the new position as a new trade. (I also make all my decisions on a beta adjusted basis relative to the S&P 500 benchmark, because ad hoc trades are about residual returns not systematic risk.)

I apply this algorithm automatically to all the ad-hoc trades I do. I have a completely automated environment so the algorithm just places orders for me, I don't have to work through the rules for each trade every day.

For example, at the end of July this year I decided to take a punt on Lehman Brothers Inc. (I'm a client, and have been for years, and I also know people who work there.) I thought that the housing/credit crisis had got through the worst and that things were going to look up from now on. I bought 2,500 shares of LEH for my personal account at $15.90.

Today LEH is trading at $7.98. Although the financial stocks initially turned up, it seemed that market had underestimated the extent of the problems at Lehman and the loss from entry-to-date would have been around 50%. However, the TPA got me out at a profit. I'm pretty certain I would have been caught up in the euphoria of my gains and not closed out until it was too late. My actual trading activity is illustrated in the table "Trading in Lehman Brothers."