Chicago Quantum Net Score — evolution and 10 individual stock picks (updated after 9 & 17 trading days)

Update: Spoiler alert, the top 10 CQNS-scoring stocks held together (equally weighted), outperforms the S&P 500 ETF ($SPY) by an alpha return of 9.7% after 9 trading days (12.8% vs. 3.1%), and 11.6% after 17 trading days.

Six of the ten stocks outperformed the $SPY during the 9-day period, while eight of ten outperformed the $SPY during the 17 day period. We hoped a simplified output of the model (a top 10 list) would outperform the $SPY when we published it (the day we ran it), but these results are more than just significant.

In other words, if you invested $1,000 in these 10 stocks ($100 apiece) you would have earned $128 in 9 days, vs. $31 invested in the S&P 500. If you would have held that $1,000 investment for 17 days, your return would be $156 vs. $40. We are not certain why this outperformance is occurring, but have a few hypotheses.

Our methodology: Our quantitative, risk vs. return optimization model, is used each week to make investment decisions. Here is a simple screen of the top 10 stocks (not accounting for zig/zag or inter-dependencies between stocks) that we provide to a paying client. These top picks, and the best CQNS portfolios are provided to every client with every run.

This screen provides the individual stocks with the best risk-return trade-off that day, based on the prior year of trading as measured by the Chicago Quantum Net Score (described in three articles on arXiv — search Chicago Quantum & Portfolio Optimization). The way I initially describe the top 10, if you can only hold one stock, these should outperform the $SPY, or the Standard & Poors 500 stock index, or the S&P 500 exchange traded fund (ETF). I now consider this as an equally weighted portfolio of 10 stocks as a simple proxy.

Our model continues to improve. We add functionality, such as allowing clients to choose whether we pick long or short portfolios, validate for dividend payers, or validate for anomalous trading activity (either volume or price action). We report on a greater number of metrics that can be integrated into client reports and analysis (e.g., we just added stock splits).

We also add solvers and methods to our platform and software to deepen the optimizations we can find. In short, we are getting better through repetition and evolution, and out technical capabilities (and new hardware) help us too.

So, you may be asking “which stocks are being selected by the Chicago Quantum Net Score to buy and hold for ~25 trading days?”

Well, if you can only hold one stock, these 10 are a list where expected returns (based on the Capital Asset Pricing Model — CAPM) outweigh the risk (based on last year’s price variance). For those really good at math, you know that returns are a few orders of magnitude larger than variances, so we scale them down.

We tweeted out this list of stocks on May 20, 2021 and have committed to track and report on progress. This is not a portfolio. We are showing data produced in our reporting that show the 10 stocks which individually, have the best CQNS score.

The way we will measure performance is to compare each of the 10 stocks against the S&P 500 over the 25 trading days starting Wednesday, May 19, 2021. We will then indicate how many of the 10 ‘win.’ So, a tie score is a 5/10, or 50%. We will also indicate how magnitude of the difference for each stock vs. the S&P 500.


These stocks span industries, from used cars to pharma, travel, retail, energy, and finally include two bitcoin miners. This is a very diverse list.

We post our Week 20 market and firm wrap-up video which we titled “The world is flat” and talked about our picks the improvements to the model, and the state of the markets. It can be found here: Be prepared for some celebration, as our model, code and solvers are all performing better.


After almost a week of trading (May 19 open to May 25 at ~2pm ET), the initial results are in. Six stocks outperformed the SPY index, and four under-performed, for a 60% success rate. Also interesting is that the outperformance was larger in magnitude, so the average return of all 10 stocks is 5.4%, excluding trading costs and dividends vs. SPY return of 2.8%. So, your excess return, or alpha, is 2.6% in one week.

In a way, we were both lucky and unlucky during this timeframe. Both MARA and RIOT have the ability to really move since they are bitcoin miners. During this period (last weekend) bitcoin crashed, the two stocks were down, then recovered. It seems they recovered enough to make up the losses, and carry the full portfolio.

So, why is this interesting?

First, our model can provide a scoring of individual stocks to understand the risk-return tradeoff using data over the past year. This is helpful, as we see above, as it can generate alpha for investors. It can also be like a Value Line (TM) check where you see a stock and as part of due diligence you want a reading on its trading history.

Second, this is not the full power of the Chicago Quantum Net Score, so if you were to pick the best ‘portfolio’ selected by the model, you would gain the benefit of individually strong stocks, and stocks that work well together. In this way, you get a second effect where stocks zig and zag together to offset portfolio price risk. I am glad to see the market outperformance above, but would expect it to be even greater if a few stocks chosen together were held together.

This system is not infallible and investors need to do their own research into the fundamentals of each company, and do their due diligence before investing real money into stocks. For example, the model was run just against ~150 NYSE American stocks and chose one stock: $CEI, on April 30, 2021. This stock is down 22% over just under a month of trading. We did our diligence and did not invest in this stock. We had too many unanswered questions after looking at their filings, capital structure, and earnings.

We will continue to run our model and share insights as they come in. We will continue to report on this portfolio, and even share some charts and graphs over the coming weeks. We will track for about 35 trading days.

Good luck out there if you invest…and keep learning if you are in school or academia!


As you can see, these results suggest that the CQNS picks (the long picks) are not random. We see 6 of 10 stocks outperform the $SPY, and the average return of the 10 stocks is 12.8% (over 9 trading days) vs. a return of 3.1% for $SPY. It is also interesting to see that four of the stocks have returns of 21.8% or more.

This is significant outperformance and alpha. We plan to continue tracking these stocks and reporting on the results. For the record…we do not have a position in any of the individual stocks listed, but we are heavily invested in an S&P 500 index fund (so if anything, we benefit financially if $SPY wins).

Here are the results after 17 trading days (results as of ~12:10 ET delayed quotes on June 11, 2021):

We can run our model for you, so that you can consider gaining quantum advantage. Are you ready?

For more information, please visit

Jeffrey Cohen is a management consulting executive leading a quantum computing startup. He has worked across the industry in firms such as McKinsey & Company, IBM, HPe, Siemens, and KPMG Consulting.

Jeffrey Cohen, President of US Advanced Computing Infrastructure, Inc., & founder of Chicago Quantum (SM). We use quantum algorithms & our quantum platform

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