Aug

6

As a hedge fund manager you have nine assistants employed solely to give you advice. Each of the assistants has a different perspective on the markets. They are all good advisers, as any one of them improves your trading immeasurably. For example, the market has a 2 percent annual return, but with your skills you can generate a 10 percent return. If you also add the advice of any one of your assistants you can bump that return up to between 12 and 18 percent.

Over the last 12 representative years there have been times when the nine were universally bullish. But despite their unanimity the market did not always rise. Conversely, even in the protracted down moves of 2008, their bearishness was not unanimous. Put another way, there was always one or two that wanted to go long at the worst times. Yet each and every one over time provided great advice.

You would like to find a way to combine their advice to get even better results than by using any one alone. But that's not easy. Sometimes, adviser A is early, and late at other times on a move. Likewise with the other assistants. One simple solution would be to have them vote, but the performance result of the vote underperforms some of the individuals, although still better than not having any adviser.

*Note here that we are only considering return and not the risk taken to achieve that return. Risk should always be considered, but for the sake of moving along, let us assume that taking the advice of your advisors never increases risk and that their respective upside contribution to profits is directly proportional to their downside exposure to risk. That is, much of their positive return contributions come from reducing risk, which is what we have observed generally.

Now, let's suppose that these advisers are not people, but algorithms. That's actually better because as algorithms they can be combined in ways that individuals cannot. They can be viewed logically (on/off) as in the voting experiment, or they can be ranked by their actual values. If they have scalar values they should be normalized (given the same order of magnitude or scale). For example, you cannot compare the slope of the Dow Industrials with that of the S&P 500, as the former is an order of magnitude larger. But if you put them on the same scale (e.g. divided by price), you can easily compare them.

Normalization is exactly what you would do to your inputs if you were using a neural net, and you might be tempted to go the NN route. But NNs have problems; among them would be your inability to discover the actual combination of what worked best. You might say "who cares" as long as it works, but that philosophy does not have a good history. However there is a very good use for a NN, and that is as a trial. That is, if you are good at NNs (and most people fail), then you should by all means try. If the NN gives you good results, then proceed on your own to find a good combination without the NN. But if using a NN does not improve results for the experienced practitioner, then it is going to be very difficult to find a better combination.

But how do you combine them to your best advantage? Well, there's an app for that. It's called linear algebra. It is somewhat vertigo-inducing for most traders, because most of them are comfortable with things they can chart. For your average trader that means two dimensions; options traders tend to be comfortable in three dimensions. But with our illustration we are likely progressing to higher dimensions, and they are not chartable, although the problem's solution is indeed a chart, albeit a virtual one.

Subsequent "chapters" (if the topic flies): Operations, Testing.

Jim Sogi writes: 

"But with our illustration we are likely progressing to higher dimensions, and they are not chartable, > although the problem's solution is indeed a chart, albeit a virtual one."

One of my first posts ever to the SL was Flatland, and the idea that multiple dimensionality is lost in two dimension charts which are typically used.

Easan Katir writes: 

Flatland, one of my all-time favorite books since I read it 40 years ago, offers insights in many arenas. Perhaps some enterprising ex-game coder would turn his attention to finance and provide charts where the point of view can be changed with a click. Will traders of the future be trading on an X-box-like device?


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