The Structure of Trading Strategies

[Frank 10]

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

 

Edited March 15, 2008 by Frank

[Sparrow 10]

Hi Frank,

 

good post, however very short term trading isn't everyone's favorite, good execution plays a far greater role in such strategies.

Some other problems are:

- commissions and spread have more influence if you're able to break even or not

- scalability

 

You'll want to have a larger position size on short term trades than on a longer term, because you won't be able to make a lot of money otherwise, which isn't a problem because your stops will be tighter.

A pension fund can't make enough money by employing such a strategy imo, markets are simply not liquid enough within a short period of time. If the fund could employ the strategy across a lot of different markets it might work though, although I doubt it.

 

For a retail trader what you described can be a good method to make money if it fits your trading style and you've got the execution skills if trading discretionary.

[Frank 10]

Sparrow,

 

What you mention about spreads and commissions is important. That said, my post was on the 'structure' of analyzing trading strategies you come up with, not on the execution part. Yes, it is up to you to execute efficiently. My 'expected return' is assumed to be net of commission costs and spreads etc... I am discussing this at the structural level here.

 

Also, I wasn't suggesting this was appropriate for a pension fund. I was merely taking the sophisticated way institutional asset management works and relating it back to trading strategies that we think about every day.

 

For example, say you write a Tradestation strategy that has great back-tested results --- but it has only generated 50 signals over the past 6 years. Well, this strategy appears a lot better than it is. Why?

 

Because of the 'structure' of the formula that I presented above. The more signals, the better -- because you get increased 'diversification' of the variance. Expected return, assuming it is accurarte, is compounded out by squaring the number over the number of trials --- but 'variance' increases only at the rate of the square root of the number of trials (it rises but at a slower rate than the return).

 

Go back to roulette -- this is not an attractive game for the casino in the short-run from a sophisticated money manager perspective -- you could do a lot better with an index fund --- it only gets attractive over many trials. How many trials before it gets attractive relative to others? This is what that formula reveals.

 

The other big takeaway is simply to keep a healthy respect for the market in terms of how hard it is to find a strategy that will have an exceptionally high return. I quote from my text:

 

"The first necessary ingredient for success in active management is a recognition of the challenge."[1]

 

This translates as: the 'return' you expect out of a given strategy should be properly discounted relative to its back-tested results. Finding high-returning strategies is hard -- the competitiveness of the marketplace ensures that.

 

This thread is actually the 'mantra' of the large quantitative-based firms that participate in the markets with billions every day. I am sharing it here because I think as traders, we should all think about our own strategies in the same way. Trust me on this, I know of what I speak.

 

The key is to find strategies that offer high returns that can ALSO be repeated many, many times. If you develop strategies that don't have a high number of trials --- you are likely fooling yourself -- your strategy may be profitable, its just not attractive relative to what you COULD be doing.

 

This is the beauty of that Grinold/Kahn (authors) formula I posted -- you can keep your expected returns reasonable (below the back-tested results) and still seek outsized returns through implementing the strategies that have more bets to them (and therefore diversifying out the variance).

 

 

[1] "Active Portfolio Management" Grinold and Kahn, 2000

Edited March 15, 2008 by Frank

[AgeKay 10]

I also think that there is a lot more luck involved when trading longer term since there are so little decisions to be made. Someone might make one decision per year to buy or sell something, have luck 10 times in a row and then you would hear: "This guy has been profitable for 10 consecutive years! WOW! What a great trader! Where is Schwager to interview him?"

 

Take Warren Buffet for example, he might be the best investor in the world, but it's not unlikely that someone else could have achieved the same results just by chance if you take every longer term investor into account (read "Fooled by Randomness" by Nassim Nicholas Taleb on this topic...).

 

So I have a lot more respect for the short term traders that make money consistently who probably face more trading decisions in a year than Warren Buffet in his entire life.

 

Frank, how does this information ratio change when you increase the expected return to something like 100% per year or 1000% per year?

[Frank 10]

<<Frank, how does this information ratio change when you increase the expected return to something like 100% per year or 1000% per year?>>

 

remember, the key is the # of bets a strategy uses.

 

if 1 bet and 100%, the Information Ratio is 1.00 x 1 = 1.00

this strategy is significantly worse than a 10% strategy with 400 trades in a year

.10 x sqrt(400) =

0.10 x 20 = 2.0

 

The main point behind this concept is not being fooled by randomness. You must have statistical significance (which is what this simple formula solves for) or you are quite likely to just be fooling yourself.

 

Warren Buffett has a big edge and small number of bets -- this is of course very powerful too -- but unavailable to most mere mortals -- and you are right, can't be sure if luck played large part there. Not saying it did, just can't prove that it didn't statistically.

[AgeKay 10]

Ah, now I see what this information ratio is all about. It's similar to to the expected variance calculation. I know the following formula from somewhere that tells you the expected variance which goes like this: 1/Sqrt(Sample Size) = expected variance. So if you have 400 trades, it's: 1/Sqrt(400) = 0.05 = 5%. So you can expect the actual result to deviate by 5%. So if you have a return of 10% per year with 400 trades, then you can expect your actual results to lie within 9.5% and 10.5% (<= 10% +- 10% * 5%).