You can’t beat all the chimps

It is a long established fact that a reasonably well behaved chimp throwing darts at a list of stocks can outperform most professional asset managers. While there would be obvious advantages with hiring chimps over hedge fund traders, such as lower salaries and better manners, there are also a few practical obstacles to such hiring practices. For those asset management firms unable to retain the services of a cooperative primate, a random number generator may serve as a reasonable approximation of their skills.

The fact of the matter is that even a random number generator can, and will, outperform practically all mutual funds. Such random strategies may seem like a joke, and perhaps they are, but if a joke can outperform industry professionals we have to stop and ask some hard questions.

When designing investment strategies, it can be very useful to have an understanding of random strategies, how they work and what kind of results they are likely to yield. Given that random strategies perform quite well over time, they can act as a valid benchmark. After all, if your own investment approach fails to outperform a random strategy, you may as well outsource your quant modeling to the Bronx Zoo.

I spoke on this topic at the Quantcon in New York last weekend. It was a really great event with plenty of interesting speakers. The event is organized by Quantopian and they did an excellent job with that. In my presentation, I promised to publish some source code and I will do so further down in this article. No, don’t scroll down just yet. I’ll give you a summary of what I spoke about first, and why the source code is of interest.

Portfolio Modelling

Frequent readers of my articles shouldn’t be surprised that we’re dealing with portfolio models here. A portfolio model is something very different from what most retail traders call a trading system. Oddly, the perception of trading system as a set of rules for timing buys and sells in a single market is still pervasive. That’s still what you tend to see if you ever pick up a trading magazine. That’s normally not how things look in reality of course. Not on the sharp end of the business.

What we’re normally dealing with is portfolio models. In a portfolio model, the position level is of subordinate importance. The only thing that matters is how the portfolio as a whole performs. We’ll always have many positions on, and it’s the interaction of these positions that matter in the end. Portfolio modelling is a more productive way to spend your time. It would certainly be more useful in the asset management world.

What may surprise some not in the industry is that often portfolio models don’t even bother to try any sort of entry and exit timing. Stop loss methodology is rare and concepts like position pyramding would simply never be a topic. What we’re dealing with here are usually simple models, with mechanisms for selecting components, allocating to the components, rebalancing the components and of course benchmarking the result.

Benchmarking isn’t what it used to be

Let’s start with that last point. Benchmarking. Every portfolio has to be measured against something. Very few professionals actually have the zero line as their benchmark. That’s what hedge funds are for. If you work in the industry, odds are that you have a specific index as your benchmark. We’ll go with one of the most common benchmarks here, at least for American equities; the S&P 500 Total Return Index.

When you’ve got a benchmark index, you’re being measured against that. It doesn’t matter if you end the year +10% or -10%. It matters if you outperformed or underperformed the bench. At times it can be very comfortable to be measured relative to the index. It removes many difficult investment decisions. You gain and lose at the same time as everyone else. On the other hand, it can be frustrating when the markets are falling and you still have to be in.

The index we’re using in this article, S&P 500 TR is different from the normal S&P index that you always see quoted. This is a total return index, meaning that all dividends are reinvested. The traditional S&P index is highly misleading over time, as the dividends appear as losses. So keep in mind that the S&P TR index will always show a better performance than the regular price index over time.

Not too impressive, is it? Well, perhaps mutual funds can help.

Mutual Funds Can’t Help

The mutual fund industry is fundamentally flawed. There’s really no reason at all to ever, for any reason buy a mutual fund. If ever the internet memes about “You had one job…” fit any industry, this would be it. The mutual funds are tasked with tracking and outperforming an index. On average, around 85% of all mutual funds fail. How do I know that? The freaking SPIVA reports.

How can the Chimps Help?

Professor Burton Malkiel once famously wrote in A Random Walk Down Wall Street that

A blindfolded monkey throwing darts at a newspaper’s financial pages could select a portfolio that would do just as well as one carefully selected by experts.

Now I think that’s highly unfair. After all, why would we want to blindfold the monkey? In what way would that contribute?

As we all know, academic research has to be confirmed by empirical observation to be of much use. Ladies and gentlemen, I give you Ola the Ape.

Back in early 90 when I was in business school in Sweden, we had a highly prestigious national investment championship. This was normally won by the famous analysts at the big investment banks. This was quite a big deal and getting a high ranking in this competition was a big career move. Then in 1993, somehow a chimp from the local Stockholm zoo got entered into the competition. Ola the Ape threw actual darts at the actual stock listings of the newspaper to pick his stocks. And he won.

Random Simulations

Unfortunately, our office chimp Mr. Bubbles has just accepted a higher offer from a competing firm, so I will have to resort to random number generators to prove this point. The first strategy we’ll test is something you’ve probably seen elsewhere. But we have to start somewhere. Here are the rules:

Not too bad, is it? Not a single monkey failed to beat the index. But what’s going on here? Surely there’s a trick here? Let’s push this concept a little further and see if it falls apart.

Our next simulation is even randomer. Yes, I’m sure that’s a word. The previous simulation had equal weighted position allocation. Perhaps that’s the trick. But would a monkey really allocate an equal amount to each stock? Or would he pick that at random too?

Here’s our next simulation:

Yes, we’re allowing any position sizes here. Perhaps a position is 0.0001% or perhaps it’s 99.99%. Let’s go wild.

Ok, this is getting ridiculous. We’re still clearly outperforming the market. Not a single monkey loses against the index. Sure, there’s a lot wider spread here and that’s to be expected. There’s quite a large difference between the best monkey and the worst one, but they’re all better than the index and certainly better than the mutual funds.

So where’s the trick? Is it the 50 stocks? Could this whole thing have to do with the magical number 50? After all, isn’t this a Fibonacci number? And why would a monkey pick this number of stocks anyhow? Fine, let’s relax this one as well. Let’s do another one.

A random number of random stocks at random allocations. Now that’s how a proper monkey trades. Will the monkeys finally lose this time?

No. The monkeys still win. Now we see some really wild swings, but in the end our primate friends persevere. But now it’s really getting silly, isn’t it. What are we doing here that’s clearly working?

Actually, it’s the other way around. The single largest positive factor is that we avoid making a mistake. That mistake being market capitalization weights. Simply by avoiding market cap weighting, we outperform. The larger issue here is benchmarking against an equal weighted index, such as the S&P 500.

We all know that there are (approximately) 500 stocks in the S&P 500. But is that really true? Did you know that the top 10 stocks in that index has an approximate weight of 18%? And that the bottom 300 stocks also have a combined weight of about 18%? We’re all pretending that the S&P 500 is a diversified index, but it’s really not. It’s tracking a handful of the largest companies in the world and the rest really don’t matter.

To be fair to the index, and the index providers, I’d have to point out that indexes were not originally meant to be investment strategies. They were meant to measure the health of a market. As such, they’re not all that bad. But that doesn’t mean that you should invest like the index.

It’s easy to check out equal weighting performs against market cap weighting. Just compare the S&P 500 Equal Weighted Total Return Index with the S&P 500 Total Return Index. Same stocks, same index provider, same methodology. Easy.

In the random simulations above, we’ve seen that both equal weights and random weights are better than market capitalization weights. Obviously only a chimp would use random weights. Equal weights are quite common, though in my own opinion it makes much more sense to use volatility parity weights. That’s no where near as complicated as it sounds.

Vola parity just means that we size our positions according to inverse volatility. A more volatile stock gets a smaller allocation. Why? Because if you put an equal amount of cash in each stock, your portfolio will be driven by the most volatile stocks. If you buy a utility stock and a biotech, the biotech stock is likely to be the profit and loss driver of the portfolio. An equal weight in the two would mean that you put on more risk in one stock that the other. Vola parity weighting means that you, in theory, put on equal amount of risk in both stocks. Yes, I deliberately used the word risk here so the comment field will be filled up with quants pointing out that I don’t understand risk. Go ahead. I’ll wait.

Let’s do one more of these funny simulations before getting to the real stuff.

This looks pretty good, doesn’t it? Now we have better performance and more importantly, a narrower span of performance. The monkeys all do really well and there’s not all that much difference between them. If only we could figure out a way to be one of those better chimps.

Let’s be the better primate!

Why should the chimps get all the fun? Clearly these guys know how to trade, but perhaps we can figure out a way to beat them. We’ll have to take out the random factor and find a better way to pick our stocks. The volatility parity seems to work though, and so does the monthly rebalancing. We’ll keep those.

There are several valid ways of picking stocks. You could use value factors, dividend yield, quality, momentum etc. I’m going to use momentum here, because clearly it’s the best one (not at all because I wrote a really neat book on that topic). Besides, it’s the easiest one to quantify and model. The data is more readily available and so are the tools needed.

Here’s our new, chimp free simulation:

Some may recognize this as a simplified version of the one presented in Stocks on the Move. It’s much simpler, but performs in a very similar manner. It has slightly deeper drawdowns and slightly higher return.

Those of you who didn’t read Stocks on the Move, may wonder what a Clenow Momentum is, and whether or not I’m joking about that name.

The Clenow Momentum™ is clearly a silly name for a pretty decent analytic. This is just an improved way of measuring momentum. First we take the exponential regression slope, instead of the linear, since it’s measured in percent and can therefore be compared across stocks. It will tell us the slope in percent per day, which will give you a number with too many decimals to keep track of. So we annualize it get a number that we can relate to. Now the number tells us how many percent per year the stock would do, should it continue the same trajectory.

But the annualized exponential regression slope doesn’t say anything about how well the data fits the line. The coefficient of determination, R2, does. That’s a number between 0 and 1, where a higher value means a better fit. If we multiply the two, we essentially punish stocks with high volatility. And there you go. Clenow Momentum™!

Now we’re seeing some interesting results! Even without the help of the chimps, we’re now clearly outperforming the bench. It’s a consistent outperformance too, during both up and down markets. The reason that we outperform in bear markets is that we don’t buy stocks with a low absolute momentum value. When there are no stocks moving up, we don’t buy any.

This all seems good and well, but I’m sure you’re all wondering about the most important point. How did we do against the chimps?

We may not be the best primate, but we’re certainly among the smarter ones! Being in the upper 5% of the chimps is pretty good. On the evolutionary scale, we have now moved beyond the mutual fund managers, beyond the index itself and we’re competing with the best of the chimps!

So what’s the point here?

There are several important learning lessons from all of this. Perhaps the best way to summarize it would be to paraphrase Gordon Gekko:

The point, ladies and gentlemen, is that chimps are good.

Chimps are right.

Chimps work.

Chimps clarify, cut through and capture the essence of the evolutionary spirit.

Well, with all due respect to Gekko the Great, perhaps there are better ways to sum this up.

Quantopian Source Code

Fine, I guess I promised you source code to trick you into reading my long article of bad monkey jokes. I’m not an expert on Quantopian or Python so I got some great help from James Christopher at Quantopian on this. This code is tested and works fine, but I’m leaving absolutely no guarantees and certainly no support. Learn from it, modify it and make it your own. If you have no quant environment of your own, Quantopian is a great place to start modelling without the need for a costly and time consuming effort of setting up a local environment.

The below code is built to run in minute level simulations.