October 4, 2017

A Price Tag on Alpha - Part I of III

The other day, someone in a Quantopian forum, probably referring to his stock trading strategy, asked the question: What would people pay for performance of over 25% on a yearly basis?

The answer evidently should be a lot as this might put someone at the very top of the 0.1% of portfolio managers. For instance, to give this some perspective, Mr. Buffett has maintained a 20% CAGR over the years. And, look at what he achieved for his shareholders and himself. Maintaining a 25% CAGR (compounded annual growth rate) would be nothing less than most impressive.

Of course, this would be on the premise that the trading strategy could last for an extended period of time, and that it could handle large sums. The larger the better. In such a case, the alpha could indeed be quite valuable.

However, just as a caveat, it is not because one has a backtest showing a few years at a 25% CAGR that a strategy is necessarily designed to last and, at the same time, able to handle a large portfolio. There remains a need to demonstrate this beforehand, including the overall feasibility and sustainability of such a trading strategy. This is where backtesting, under the then prevailing market conditions, could help to at least show it was doable in the past. If it was not, then we already know the strategy's value.

A stock trading strategy might be unique, but it is not alone in the world of trading strategies. It has to compete, prove itself to be better than most, better than the millions of other strategies of which little is known. Even if we can compare them to each other, determining which will be best going forward will still remain to some extent a speculation and a matter of individual preferences.

Nonetheless, let's try to put a price tag on this alpha.

Nowadays, there are many definitions for "alpha". Here, I will use the one as defined by Jensen in the late 60's: Alpha is the added performance over and above the long-term market average.

A basic stock market return equation is  F(t) = F0∙(1 + rm)t, where the initial capital F0 is growing at the most expected average market return (rm) over time interval t.

It is the same formula used to determine the future value of any compounded return: F(t) = F0(1+ r)t. You have a starting point, the initial capital F0, and an endpoint at termination time F(T). Knowing the time interval and the return rate, we can estimate by how much a portfolio would have grown for any time period.

Since we know from the start how much we have and how long we intend to participate in the game, all we have left to deal with is obtaining an estimate for the return we might get for the duration.

It might sound naive, but that is all we will be trying to do: get the best portfolio return we can by whatever trading methods we have at our disposal or could find. It might not matter that much which trading methods and procedures will be taken as long as we do get the return and reach our goals.

It could turn out to be more a matter of preference for one set of tools over another. But this preference will only develop over the set of tools we have found. It totally ignores all the other unselected trading methods, especially those we are not even aware of.

We can backtest a gazillion simulations using our trading strategies, but in the end, we will have to select just a few. And once the selection has been made, the future will happen only once. There is no rerun button going forward.

Trading strategies are easy to compare, their outputs are all measured in dollars. This does not say that the strategy producing the most dollars is the best, only that the best is the one you prefer most, that shows the most potential for going forward among those you have, for whatever reason.

Could somebody else have a better trading strategy than yours? Most certainly. I would even dare say: almost surely. Acknowledging that trading strategies do participate in a survival of the fittest competition. In a compounded return equation, the compounding rate and the time interval over which the capital is compounded will make a major difference the longer the time interval is extended.

Your best trading strategy will remain so as long as you do not find a better one to replace it. It should be the only reason why you replace a trading strategy. However, the most cited reasons for replacing a trading strategy is that it has broken down, if failed, and was losing money. Which raises the question: what was the value of all those backtests? Did those people really do their homework?

The way to determine the best trading strategy should not be based on a small group of trades but on the overall strategy's behavior and final outcome. Is F1(T) > F2(T) > ... > Fn(T) ? That is the question. As long as your preferred strategy (F1) remains on top, performance wise, with other considerations included, it should be your better choice.

The Alpha Generation

If a trading strategy can do better than average market return (r_m), then, we could express it as generating some alpha: F(t) = F0(1+ rm + α)t where alpha represents this added performance.

Any alpha greater than zero (α > 0) will evidently improve overall performance. The higher this positive alpha can be, the higher the final outcome and the higher its potential value. The longer this alpha can last, again the higher its value as it is being compounded too.

Since the formula does not have other parameters, it, therefore, becomes the only elements you have to work with. Whatever you do trading could be simplified to those few parameters.

The following chart shows an idealized expected market return curve: (1+rm)t. However, the market is never that smooth, the return curve could appear more or less like the erratic path shown on the chart.

 #1  10% CAGR – 20 Years – With Random Path 
10pct CAGR 20 years

(click to enlarge)

This erratic path was randomly generated. Is shown only one such curve from a quasi-infinite set of possibilities.

From any one year, you could not guess what would be the outcome for the next one or the one after. Except that, both curves had to reach the same endpoints; that you got there randomly or not. And therefore, the smooth curve becomes a fair representation for whatever erratic path was taken to get there.

The same would apply if you extended the time interval. Again, you would not know the exact erratic path taken, but you would still reach the endpoints.

 #2  10% CAGR – 30 Years – With Random Path 
10pct CAGR 30 years

(click to enlarge)

On chart #2, the first 20 years are the same as in chart #1. Everything in the first chart now appears more subdued, showing relatively less amplitude and smaller deviations from the exponential curve. Yet, the first 20 years are exactly the same, only the perspective has changed. Those last 10 years generated more than double the first 20. A graphical representation of the power of compounding.

... to be continued...


Created... October 4,  2017   © Guy R. Fleury. All rights reserved  

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