Portfolio Strategy

# Capitalizing On The Random Walk (Part 2)

An Alpha Theory client posed the question, “how often should we trade to maximize the benefit of trading around positions?” In this article, Cameron Hight elaborates on this and provides an example.

I wrote a blog post 3 ½ years ago about the topic of trading around positions. See part #1 of Capitalizing on the Random Walk

“Our trading models tend to buy stocks that are recently out of favor and sell those recently in favor. Thus, to some extent, our actions have the effect of dampening extreme moves in either direction, and, as a result, reducing volatility in those stocks.”
- James Simons, Legendary Investor of Renaissance Technology
“I made my money by selling too soon.”
When asked how he had become so rich?  He replied, “I sold too early.”
- JP Morgan, Famous Financier

A smart client of ours asked the question, “how often should we trade to maximize the benefit of trading around positions?” In an ideal world, you would buy at the nadir and sell at the apex of any straight-line price increase.

Example of a stock that trades from \$40 up to \$50 down to \$30 then back to \$40. The net profit for not trading is 0%. The maximum profit is a trading gap that times a sell at the apex of the trading range (\$50). The fund is assumed to have a maximum position size of 10% and the starting position size at \$40 is 6.6%.

What this example illustrates is that if the price goes down (time is irrelevant because this would apply for 1 tick, 1 day, 3 days, etc.) you would want your position to be at 0% and when it rises, you would want to be at a full position. Clearly that is not realistic, but to understand the mechanics of the system it is important to understand the extremes. The counter-extreme is to not trade at all and return 0% which is the worst outcome in a mean-reversion trading pattern. So somewhere in between lies the hybrid of ideal and practical. The exact point is different for different managers, but I would say that you should set Trade Triggers (colored highlight rules if you are an Alpha Theory user) that alert you when gaps are greater than 1% or 1.5% or 2%, whatever allows for maximum profit capture per unit of acceptable inefficiency. Basically, you need to create a heuristic like “we trade when assets are 1% away from optimal and the difference is at least 50%.” Here’s an example:

1)      OPS = 0%

2)      If %FromOptimal > 1% and Max(%fromOptimal/CPS, %fromOptimal/OPS) > 50%

ASSET #1:

% from Optimal = 2%

CPS = 1%

OPS = 3%

Max(2%/1%,3%/2%)=100%. This asset would be highlighted.

ASSET #2:

% from Optimal = 3%

CPS = 7%

OPS = 10%

Max(3%/7%,3%/10%)=43%. This asset would NOT be highlighted.

It is important to remember that while this method is sub-optimal if the stock ever trades above the selling price it is vastly superior to No Trades.

Finally, for those with tax considerations there is a different constraint. Basically, I think it ends up being a different heuristic. Let’s say we come up with a 6/1 rule of thumb. If you’re 6 months away you’ll trade 1% differences, 5 months = 2%, 4 months = 3%, 3 months = 4%, 2 months = 5%, and 1 month = 6%. I’m not sure that is perfect, but there is DEFINITELY a huge value in waiting for Long Term treatment if the fund is tax sensitive.

Portfolio Strategy
Portfolio Optimization