Here is something they teach to Financial Analysts in the Chartered Financial Analyst (CFA) program - I am going to relate this to trading ‘strategies’. This is really about how the 'structure' of analyzing strategies can be approached and why directional signals on 'daily' charts are problematic.
Pretend you are the manager of a Pension Fund and you have $30 billion in the plan. You have a team of consultants working for you that basically evaluate money managers and give you recommendations about how to divide up your $30 billion to earn a return that will meet your expected pension obligation when everyone retires. The question is: How do you compare the strategies of the portfolio managers in a structured way? They all have different strategies and you have to choose.
This is the quantitative answer and I think the ‘structure’ of the answer relates directly to how you think about trading strategies:
Take the game of Roulette for simplicity. For this game, with 37 numbers (18 red, 18 black and 1 green) – the house edge is 1/37 or 2.7027%. How do you evaluate this ‘game’ in a structured way?
Well, all strategies are measured by their return in relation to their risk. The variance of a single roll in Roulette is 99.927% making the Standard Deviation 99.963% (the Square Root of the variance).
Comparing the return of 2.7 to Standard Devitation of 99.963 gives a ratio that rounds to 0.0x. As a good pension fund manager, you learned on your CFA exam that 0.50 is a good number. Thus, the variance of Roulette is too high to make the return attractive to you relative to what you can get with other managers.
But what about if we take the 1-roll restriction off? The story changes dramatically such that owning a Roulette table is FAR better than any hedge fund strategy.
Enter the 'Fundamental Law of Active Management' --- which re-works the ratio of return/risk into a more 'research-intuitive' formula:
Where the Ratio = [Expected Return * SqRt(Independent Bets available in a given year)] <---- simple
The second half of the equation factors in the number of times that strategy can be executed over 1 investment year. (note that the 0.50 benchmark you are using to compare managers is an annual-based number).
For 100 roulette rolls, the formula is:
=[2.7% * SqRt(100)]
=[2.7% * 10]
=0.27 <--- still not that great
Turns out that the number that gets you a 0.50 ratio is 342 rolls. Thus, if you are allowed to roll the ball that many times, the strategy is now attractive vs the standard rule of thumb. The more rolls, the better. Get up to 10,000+ rolls and you are talking about a strategy that blows away 99% of hedge funds.
How does this relate to trading?
Well, I think all strategies should be thought of in the same structured way. If you have a strategy that is based on a ‘weekly’ chart – this is not much good. You won’t get enough signals to make the strategy attractive relative to others. EVEN if your ‘edge’ is good. Even a daily chart… the number of signals is limited. The variance will be high relative to the amount of bets that diversify that variance.
Thus:
There are 2 ways to make your trading better. Find strategies that increase your ‘edge’ --- difficult to do as trading is a very competitive game. Or find strategies that have similar edge but you can repeat them more. The ratio increases with either --- but the ratio increases by the SqRt of ‘bets’ you make.
This is all intuitively obvious -- but extremely important. Finding a happy balance that keeps your win-rate (edge) high and also offers enough opportunities to diversify the variance over many independent 'bets'. By thinking about all your strategies in this structured way, you will understand what makes 1 strategy attractive versus another.
Comments welcome,
Frank
