I was discussing our model with someone close to the work, and I realize the value of this effort may be hard to see.

In short, there are many economic, philosophical, or even emotional ways to pick stocks.  Some try to value stocks so they can 'buy low and sell high.'  Some do cash flow analysis (at least they say they do...I don't know anyone who does this personally).  Some look at growth rates, debt loads, new products, placement in an industry, and social 'quality' of the firm. 

Others have a fear of missing out of the next big thing (I bid on the Google IPO at $85 / share and missed out...but probably could have bought it at $135 at the open).  I missed out.

We leave those ideas to the thousands of analysts employed in selecting and recommending stocks.

We have a different idea and place in the investment value chain.  

We look at how stocks move together.  We believe that you can pick stocks that move together in a way that cancels out some of the risk in holding those stocks. Simply put, then some stocks increase in price, the others decrease, and vice versa.  However, as a group, they move with the market.  If the market is going up, these stocks go up, but in more of a straight line than other stocks would.   

Why does this matter?  Most people don't follow the stock market every hour or even every day.  They buy stocks, or mutual funds, or bonds, or invest in variable annuities as they have extra income and hold it for either retirement, or a big expense like buying a car, a house, or paying for college.  For that individual investor, they only care about the price of the stocks when they want to sell them, for example when they need the money invested in those assets.

A lower amount of movement up or down, because of this ripple effect, means that it is more likely that their investment is doing well, or at least moving with the market, instead of really high or really low when they need it.  Since we don't know when that is...it is better to invest in a way that reduces the downside risk when you need the money.

How do we do this?  We come up with a way to score stock portfolios (we call it the Chicago Quantum Net Score, or CQNS).  We search for the best portfolio with the lowest CQNS score because the variance of that group of stocks, held together, is lower than the the profit expected from holding that group of stocks.  

If there were only 5 stocks to look at (say we live on a very small island with 5 companies), there would be 2^5 combinations of stocks we could hold, or 32 portfolios to check.  We could do that with pencil and paper or a spreadsheet.  We have found a way to look at many more companies at one time. 

As of August 31, 2020, we run 64 stocks through our checker at one time, and find portfolios with expected returns that outweigh the expected variance of the portfolios.  Looking at 64 stocks at one time is challenging, because we have to search from among 18,446,744,073,709,551,615 portfolios.  We do this in under a minute, and have taught a quantum annealing computer to do this in around one second. 

Hope this helps to clarify why we are doing this work.  We help people optimize a portfolio by finding the lowest risk, highest reward combination of stocks to invest in...so they can leverage the ripple effect and have volatility cancel out.

Jeffrey P. Cohen, President, US Advanced Computing Infrastructure, Inc.
September 2, 2020
jeffrey@quantum-usaci.com

We welcome client inquiries.

See the Medium article here:

https://medium.com/@cohen.sourcing/what-happened-when-we-tried-to-run-72-stocks-on-the-quantum-annealer-d93bfdd6c94c

Will be updating this Medium Article as we learn more.  DM me for a 'friend' link with Medium.

Jeffrey Cohen, President, US Advanced Computing Infrastructure Inc.  August 20, 2020

Good news.  We submitted our article to arXiv yesterday.  Should publish Friday.  
arXiv:submit/3330970 [cs.DM] 19 Aug 2020 

What did we learn?
1.  Today's stock pickers can use either the D-Wave quantum annealer (2048 qubits), or classical methods to optimize a 60 stock universe (with 1 year of historical data). Our custom coded Genetic Algorithm found the 'ideal' portfolio in 7 seconds...and all take under a minute of computation time. 

2.  Our Chicago Quantum Net Score is a reformulation of the traditional Sharpe ratio and is used to pick efficient equity portfolios.  It seems to work well.  It quickly picks portfolios on the Efficient Frontier (return / risk).  It runs well on the D-Wave quantum annealer and in classical solvers too.

An efficient frontier is the top of a set of portfolios (highest return for each level of risk).  The upper points are either yellow, red or blue.
The yellow dots are the efficient frontier with our Monte Carlo analysis (fat-tailed, & discrete distribution around N/2).  We ran over 200K samples, and picked from every asset size.  It picked the 'ideal' portfolio.
The red dots are picked by the quantum computer.
The blue dots are picked by our genetic algorithm (random seed).

3.  We can successfully analyze 60 stocks at a time.  What might stop us from running 100 at once?
We find two challenges:
a) We are running out of room on the quantum computer (we use 1,700 qubits out of 2,048).
b) Our variance terms get very small when we choose larger portfolios (e.g., 55 stocks out of 60).  

The good news is that D-Wave has a new quantum annealer with over 5,000 qubits (more room to grow), and we continue to research and learn new methods for larger portfolios.

We will let you know when our article is available on arXiv in a comment to this post.

Sitting here writing our 2nd research article preprint to be published to arXiv by September 1, 2020.

A few key observations to share:
1.  We are getting very good at having D-Wave find valid, attractive answers.  During one run, I think it found the 'ideal' solution.  
2.  We struggle to get D-Wave to solve the problem when we have many assets.  This is due to the structure of the problem.  More assets means smaller variance and covariance terms for each stock.  Those small values are harder for an energy based analog system to find. By way of analogy, the D-Wave is like a rock climber and the wall has portions for each asset size.  At 20 assets, the hand-holds are large and easy to grab.  At 40 assets, they are more challenging.  Only an expert can grab hold.  At 60 assets, those hand-holds are maybe fingernail sized.  We may have to reformulate the problem at 80 assets again to make large portfolios easier to solve for.
3.  We have raised the bar by custom coding both a genetic algorithm and simulated annealer that solve the classical problem (finding one ideal solution per universe) in 10 - 20 seconds.  We also use a simulated annealer solver from D-Wave that solves the 60 asset problem in 11 seconds.
4.  We created a new way of using a random number generator to execute a Monte Carlo random strategy.  This one works really well.  We send a relatively small number of random portfolios to be scored, and we send them for each number of assets.  So, for 60 assets we query (N=1,2,3,4,.....56, 57, 58, 59) assets.  This helps us to see if the answer is at the tails (very small or very large portfolios) and we can then focus on those asset sizes.  In the case of our current sample, our random, fat-tailed Monte Carlo analysis finds the optimal answer in just over 220,000 trials.
We are eager to try 80 or more assets on the D-Wave quantum annealer.  Look for updates once we complete our current 60 asset paper.

Jeffrey Cohen, President, US Advanced Computing Infrastructure, Inc.
​August 7, 2020